R Under development (unstable) (2024-06-02 r86665 ucrt) -- "Unsuffered Consequences" Copyright (C) 2024 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(stepp) Loading required package: car Loading required package: carData Loading required package: survival Loading required package: splines Package stepp (3.2.7) loaded. To cite, type citation("stepp"). > > # library(steppevent) > # source("/Users/Sergio/Dropbox (Personal)/stepp/packages/lazar examples/STEPPpermCI2_event algorithm.R") > > ### Example 1 ### > > data(bigKM) > rxgroup <- bigKM$trt > time <- bigKM$time > evt <- bigKM$event > cov <- bigKM$ki67 > > ## the following code performs the calculations using the steppevent package > # set.seed(101) > # noperm <- 100 > # res_old <- STEPPpermCI2(coltrt = rxgroup, coltime = time, coltype = evt, > # covar = cov, trts = c(1, 2), eventpops = 20, mineventpops = 10, > # timest = 4, noperm = noperm, minRequiredSubpops = 5, legendy = 30, > # pline = -2.5, color = c("red", "black"), ylabel = "4 year DFS", > # xlabel = "Subpopulations by Median Ki-67", ncex = 0.7, > # tlegend = c(Letrozole", "Tamoxifen"), nlas = 3, alpha = 0.05, > # pointwise = FALSE) > > # generate event-based windows > swin_e <- new("stwin", type = "sliding_events", e1 = 10, e2 = 20) > subp_e <- new("stsubpop") > subp_e <- generate(subp_e, win = swin_e, covariate = cov, coltype = evt, + coltrt = rxgroup, trts = c(1, 2), minsubpops = 5) > summary(subp_e) Window type: sliding_events Number of events per subpopulation (eventspop e2): 20 Largest number of events in common among consecutive subpopulations (mineventspop e1): 10 Number of subpopulations created: 7 Subpopulation summary information Covariate Summary Sample Type 1 Events Subpopulation Median Minimum Maximum Size Trt Group 1 Trt Group 2 1 4.00 0.0000 6.0000 815 39 22 2 7.00 6.0000 8.0000 387 20 21 3 10.00 8.0000 11.0000 469 20 26 4 12.00 10.0000 14.0000 511 30 24 5 16.00 14.0000 20.0000 541 51 26 6 22.00 20.0000 25.0000 291 21 21 7 30.00 23.0000 90.0000 430 47 27 > > # estimate and test the CI model > steppes_e <- new("steppes") > modCI_e <- new("stmodelCI", coltrt = rxgroup, trts = c(1, 2), coltime = time, + coltype = evt, timePoint = 4) > resCI_e <- estimate(steppes_e, subp_e, modCI_e) > print(resCI_e) Sample size in treatment 1: 1361 Sample size in treatment 2: 1324 Total sample size (excluding missing data): 2685 Cumulative incidence estimates for treatment group 1 at time point 4 Cumulative Subpopulation Incidence Std. Err. 1 0.0437 0.0113 2 0.1073 0.0246 3 0.0920 0.0202 4 0.0873 0.0202 5 0.0815 0.0185 6 0.1395 0.0309 7 0.1404 0.0279 Overall 0.0832 0.0085 Cumulative incidence estimates for treatment group 2 at time point 4 Cumulative Subpopulation Incidence Std. Err. 1 0.1037 0.0181 2 0.1105 0.0272 3 0.0699 0.0194 4 0.0937 0.0193 5 0.1780 0.0262 6 0.1711 0.0375 7 0.2346 0.0317 Overall 0.1348 0.0106 Cumulative incidence differences at time point 4 trt 1 vs. trt 2 Cumulative Incidence Subpopulation Difference Std. Err. 1 -0.0601 0.0214 2 -0.0031 0.0367 3 0.0221 0.0280 4 -0.0064 0.0279 5 -0.0965 0.0321 6 -0.0316 0.0486 7 -0.0942 0.0423 Overall -0.0516 0.0136 Hazard ratio estimates Subpopulation Log HR Std. Err. Hazard Ratio 1 -0.6353 0.2562 0.53 2 0.1212 0.3130 1.13 3 0.2200 0.2951 1.25 4 -0.1392 0.2725 0.87 5 -0.8157 0.2283 0.44 6 -0.2068 0.3112 0.81 7 -0.5880 0.2326 0.56 Overall -0.4495 0.1149 0.64 > set.seed(101) > noperm <- 100 > resCI_e <- test(resCI_e, noperm) Computing the p-value with 100 number of permutations comparing trt 2 with trt 1 | | | 0% | |= | 1% | |= | 2% | |== | 3% | |=== | 4% | |==== | 5% | |==== | 6% | |===== | 7% | |====== | 8% | |====== | 9% | |======= | 10% | |======== | 11% | |======== | 12% | |========= | 13% | |========== | 14% | |=========== | 15% | |=========== | 16% | |============ | 17% | |============= | 18% | |============= | 19% | |============== | 20% | |=============== | 21% | |================ | 22% | |================ | 23% | |================= | 24% | |================== | 25% | |================== | 26% | |=================== | 27% | |==================== | 28% | |===================== | 29% | |===================== | 30% | |====================== | 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| 89% | |=============================================================== | 90% | |================================================================ | 91% | |================================================================ | 92% | |================================================================= | 93% | |================================================================== | 94% | |================================================================== | 95% | |=================================================================== | 96% | |==================================================================== | 97% | |===================================================================== | 98% | |===================================================================== | 99% | |======================================================================| 100% > print(resCI_e) Sample size in treatment 1: 1361 Sample size in treatment 2: 1324 Total sample size (excluding missing data): 2685 Cumulative incidence estimates for treatment group 1 at time point 4 Cumulative Subpopulation Incidence Std. Err. 1 0.0437 0.0113 2 0.1073 0.0246 3 0.0920 0.0202 4 0.0873 0.0202 5 0.0815 0.0185 6 0.1395 0.0309 7 0.1404 0.0279 Overall 0.0832 0.0085 Cumulative incidence estimates for treatment group 2 at time point 4 Cumulative Subpopulation Incidence Std. Err. 1 0.1037 0.0181 2 0.1105 0.0272 3 0.0699 0.0194 4 0.0937 0.0193 5 0.1780 0.0262 6 0.1711 0.0375 7 0.2346 0.0317 Overall 0.1348 0.0106 Cumulative incidence differences at time point 4 trt 1 vs. trt 2 Cumulative Incidence Subpopulation Difference Std. Err. 1 -0.0601 0.0214 2 -0.0031 0.0367 3 0.0221 0.0280 4 -0.0064 0.0279 5 -0.0965 0.0321 6 -0.0316 0.0486 7 -0.0942 0.0423 Overall -0.0516 0.0136 Hazard ratio estimates Subpopulation Log HR Std. Err. Hazard Ratio 1 -0.6353 0.2562 0.53 2 0.1212 0.3130 1.13 3 0.2200 0.2951 1.25 4 -0.1392 0.2725 0.87 5 -0.8157 0.2283 0.44 6 -0.2068 0.3112 0.81 7 -0.5880 0.2326 0.56 Overall -0.4495 0.1149 0.64 The covariance matrix of the cumulative incidence differences at 4 time units for the 7 subpopulations is: trt 1 vs. trt 2 SP1-Overall SP2-Overall SP3-Overall SP4-Overall SP1-Overall 3.357100e-04 -5.444924e-05 -6.635253e-05 -7.000641e-05 SP2-Overall -5.444924e-05 1.197412e-03 1.772731e-04 -2.178028e-04 SP3-Overall -6.635253e-05 1.772731e-04 8.721190e-04 2.056059e-04 SP4-Overall -7.000641e-05 -2.178028e-04 2.056059e-04 6.904321e-04 SP5-Overall -2.478947e-04 -2.986575e-04 -2.164703e-04 -1.844338e-05 SP6-Overall -1.185586e-04 -4.794306e-04 -2.159354e-04 -1.266587e-04 SP7-Overall -1.604578e-04 -1.262798e-04 -1.661346e-04 -2.396647e-04 SP5-Overall SP6-Overall SP7-Overall SP1-Overall -2.478947e-04 -0.0001185586 -0.0001604578 SP2-Overall -2.986575e-04 -0.0004794306 -0.0001262798 SP3-Overall -2.164703e-04 -0.0002159354 -0.0001661346 SP4-Overall -1.844338e-05 -0.0001266587 -0.0002396647 SP5-Overall 8.753956e-04 0.0002932280 -0.0001637331 SP6-Overall 2.932280e-04 0.0013691046 0.0001569343 SP7-Overall -1.637331e-04 0.0001569343 0.0008975207 The covariance matrix of the log hazard ratios for the 7 subpopulations is: SP1-Overall SP2-Overall SP3-Overall SP4-Overall SP5-Overall SP1-Overall 0.025672015 -0.004861236 -0.006638200 -0.006756423 -0.013088002 SP2-Overall -0.004861236 0.075792993 0.013778563 -0.014947335 -0.020401128 SP3-Overall -0.006638200 0.013778563 0.064285145 0.008637508 -0.015132487 SP4-Overall -0.006756423 -0.014947335 0.008637508 0.042870547 -0.003862061 SP5-Overall -0.013088002 -0.020401128 -0.015132487 -0.003862061 0.052091507 SP6-Overall -0.008960390 -0.012166118 -0.010548118 -0.011502554 0.012060947 SP7-Overall -0.013918271 -0.006389835 -0.009428284 -0.007787095 -0.008326586 SP6-Overall SP7-Overall SP1-Overall -0.00896039 -0.013918271 SP2-Overall -0.01216612 -0.006389835 SP3-Overall -0.01054812 -0.009428284 SP4-Overall -0.01150255 -0.007787095 SP5-Overall 0.01206095 -0.008326586 SP6-Overall 0.09590901 0.010388105 SP7-Overall 0.01038810 0.057814150 Supremum test results trt 1 vs. trt 2 Interaction p-value based on cumulative incidence estimates: 0.12 Interaction p-value based on hazard ratio estimates: 0 Chi-square test results Interaction p-value based on cumulative incidence estimates: 0.04 > plot(resCI_e, legendy = 50, + pline = -2.5, color = c("red", "black"), ylabel = "4 year DFS", + xlabel = "Subpopulations by Median Ki-67", ncex = 0.7, + tlegend = c("Letrozole", "Tamoxifen"), nlas = 3, alpha = 0.05, + pointwise = FALSE) dev.new(): using pdf(file="Rplots1.pdf") dev.new(): using pdf(file="Rplots2.pdf") > > # # estimate and test the KM model > # steppes_e <- new("steppes") > # modKM_e <- new("stmodelKM", coltrt = rxgroup, trts = c(1, 2), survTime = time, > # censor = evt, timePoint = 4) > # resKM_e <- estimate(steppes_e, subp_e, modKM_e) > # print(resKM_e) > # set.seed(101) > # noperm <- 100 > # resKM_e <- test(resKM_e, noperm) > # print(resKM_e) > # plot(resKM_e, ylabel = "4 year DFS", > # xlabel = "Subpopulations by Median Ki-67", ncex = 0.7, > # tlegend = c("Letrozole", "Tamoxifen"), nlas = 3, alpha = 0.05) > > ### Example 2 ### > > # GENERATE THE DATA > n <- 1000 # set the sample size > mu <- 0 # set the mean and sd of the covariate > sigma <- 1 > > beta0 <- log(-log(0.5)) # set the intercept for the log hazard > beta1 <- -0.2 # set the slope on the covariate > beta2 <- 0.5 # set the slope on the treatment indicator > beta3 <- 0.7 # set the slope on the interaction > > prob2 <- 0.2 # set the proportion type 2 events > cprob <- 0.3 # set the proportion censored > > set.seed(7775432) # set the random number seed > covariate <- rnorm(n,mean=mu,sd=sigma) # generate the covariate values > Txassign <- rbinom(n,1,0.5) # generate the treatment indicator > x3 <- covariate*Txassign # compute interaction term > lambda1 <- exp(beta0+beta1*covariate+beta2*Txassign+beta3*x3) # compute the hazard for type 1 event > lambda2 <- prob2*lambda1/(1-prob2) # compute the hazard for the type 2 event > # compute the hazard for censoring time > lambda0 <- cprob*(lambda1+lambda2)/(1-cprob) > t1 <- rexp(n,rate=lambda1) # generate the survival time for type 1 event > t2 <- rexp(n,rate=lambda2) # generate the survival time for type 2 event > t0 <- rexp(n,rate=lambda0) # generate the censoring time > time <- pmin(t0,t1,t2) # compute the observed survival time > type <- rep(0,n) > type[(t1 < t0)&(t1 < t2)] <- 1 > type[(t2 < t0)&(t2 < t1)] <- 2 > > ## the following code performs the calculations using the steppevent package > # STEPPpermCI2(coltrt = Txassign, coltime = time, coltype = type, covar = covariate, trts = c(0, 1), > # eventpops = 20, mineventpops = 10, timest = 1, noperm = 250, minRequiredSubpops = 5, legendy = 30, > # pline = -2.5, color = c("red", "black"), ylabel = "PFS", > # xlabel = "Subpopulations by Median Continuous Variable", ncex = 0.7, > # tlegend = c("Trt A", "Trt B"), nlas = 3, alpha = 0.05, pointwise = FALSE) > > # generate event-based windows > swin_e <- new("stwin", type = "sliding_events", e1 = 10, e2 = 20) > subp_e <- new("stsubpop") > subp_e <- generate(subp_e, win = swin_e, covariate = covariate, coltype = type, + coltrt = Txassign, trts = c(0, 1), minsubpops = 5) > summary(subp_e) Window type: sliding_events Number of events per subpopulation (eventspop e2): 20 Largest number of events in common among consecutive subpopulations (mineventspop e1): 10 Number of subpopulations created: 21 Subpopulation summary information Covariate Summary Sample Type 1 Events Subpopulation Median Minimum Maximum Size Trt Group 1 Trt Group 2 1 -1.83 -3.2194 -1.5309 73 20 21 2 -1.50 -1.8103 -1.2829 82 22 20 3 -1.26 -1.4666 -1.0630 79 20 21 4 -1.02 -1.1902 -0.8596 81 20 22 5 -0.81 -0.9716 -0.6393 96 20 26 6 -0.63 -0.7832 -0.4943 82 20 23 7 -0.48 -0.5961 -0.3970 70 20 24 8 -0.38 -0.4742 -0.2832 68 20 20 9 -0.26 -0.3819 -0.1819 78 21 20 10 -0.18 -0.2747 -0.0902 81 21 20 11 -0.09 -0.1796 0.0273 76 20 25 12 0.04 -0.0640 0.1170 72 20 25 13 0.14 0.0568 0.2273 64 21 20 14 0.23 0.1300 0.3191 68 20 20 15 0.32 0.2358 0.4292 71 21 20 16 0.45 0.3311 0.5705 88 24 20 17 0.60 0.5004 0.7308 72 23 20 18 0.79 0.6230 0.9459 83 20 29 19 0.97 0.8064 1.1044 73 20 23 20 1.19 0.9987 1.3821 86 20 30 21 1.53 1.2371 3.3241 105 24 28 > > # estimate and test the CI model > steppes_e <- new("steppes") > modCI_e <- new("stmodelCI", coltrt = Txassign, trts = c(0, 1), coltime = time, + coltype = type, timePoint = 1) > resCI_e <- estimate(steppes_e, subp_e, modCI_e) > print(resCI_e) Sample size in treatment 0: 493 Sample size in treatment 1: 507 Total sample size (excluding missing data): 1000 Cumulative incidence estimates for treatment group 0 at time point 1 Cumulative Subpopulation Incidence Std. Err. 1 0.5084 0.0979 2 0.5631 0.1000 3 0.6187 0.0989 4 0.5509 0.0909 5 0.5263 0.0844 6 0.4669 0.0894 7 0.6279 0.0905 8 0.5138 0.0973 9 0.3937 0.0923 10 0.4462 0.0964 11 0.4116 0.0907 12 0.5554 0.0967 13 0.5453 0.1023 14 0.5691 0.1016 15 0.5307 0.0960 16 0.3482 0.0808 17 0.5169 0.0967 18 0.5880 0.0819 19 0.5676 0.0925 20 0.5349 0.0815 21 0.4063 0.0753 Overall 0.5036 0.0250 Cumulative incidence estimates for treatment group 1 at time point 1 Cumulative Subpopulation Incidence Std. Err. 1 0.2569 0.0754 2 0.3409 0.0828 3 0.3228 0.0884 4 0.4236 0.0952 5 0.3649 0.0789 6 0.3801 0.0827 7 0.5358 0.0947 8 0.5378 0.0992 9 0.5631 0.0901 10 0.4612 0.0857 11 0.5901 0.0996 12 0.7243 0.0996 13 0.6567 0.0999 14 0.6080 0.1026 15 0.7012 0.1035 16 0.6688 0.0906 17 0.6653 0.0947 18 0.7312 0.1217 19 0.7551 0.1011 20 0.6191 0.0947 21 0.5652 0.0866 Overall 0.5244 0.0258 Cumulative incidence differences at time point 1 trt 0 vs. trt 1 Cumulative Incidence Subpopulation Difference Std. Err. 1 0.2515 0.1235 2 0.2222 0.1299 3 0.2958 0.1326 4 0.1273 0.1316 5 0.1614 0.1155 6 0.0868 0.1218 7 0.0922 0.1310 8 -0.0240 0.1389 9 -0.1694 0.1290 10 -0.0150 0.1290 11 -0.1785 0.1347 12 -0.1688 0.1388 13 -0.1114 0.1430 14 -0.0389 0.1444 15 -0.1705 0.1412 16 -0.3206 0.1214 17 -0.1484 0.1353 18 -0.1432 0.1467 19 -0.1875 0.1370 20 -0.0842 0.1249 21 -0.1589 0.1148 Overall -0.0208 0.0359 Hazard ratio estimates Subpopulation Log HR Std. Err. Hazard Ratio 1 0.7132 0.3356 2.04 2 0.4455 0.3255 1.56 3 0.4662 0.3120 1.59 4 0.2059 0.3177 1.23 5 0.3883 0.2989 1.47 6 0.3263 0.3093 1.39 7 0.2468 0.3061 1.28 8 -0.0879 0.3198 0.92 9 -0.0767 0.3101 0.93 10 0.2487 0.3248 1.28 11 0.0625 0.3077 1.06 12 -0.1316 0.2991 0.88 13 -0.5043 0.3215 0.60 14 -0.4248 0.3347 0.65 15 -0.5370 0.3288 0.58 16 -0.8563 0.3275 0.42 17 -0.6664 0.3267 0.51 18 -0.1886 0.3030 0.83 19 -0.3500 0.3112 0.70 20 -0.4351 0.3176 0.65 21 -0.7769 0.3035 0.46 Overall -0.0523 0.0869 0.95 > set.seed(101) > noperm <- 250 > resCI_e <- test(resCI_e, noperm) Computing the p-value with 250 number of permutations comparing trt 1 with trt 0 | | | 0% | |= | 1% | |= | 2% | |== | 2% | |== | 3% | |=== | 4% | |=== | 5% | |==== | 5% | |==== | 6% | |===== | 7% | |===== | 8% | |====== | 8% | |====== | 9% | |======= | 10% | |======== | 11% | |======== | 12% | |========= | 12% | |========= | 13% | |========== | 14% | |========== | 15% | |=========== | 15% | |=========== | 16% | 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|======================================================================| 100% > print(resCI_e) Sample size in treatment 0: 493 Sample size in treatment 1: 507 Total sample size (excluding missing data): 1000 Cumulative incidence estimates for treatment group 0 at time point 1 Cumulative Subpopulation Incidence Std. Err. 1 0.5084 0.0979 2 0.5631 0.1000 3 0.6187 0.0989 4 0.5509 0.0909 5 0.5263 0.0844 6 0.4669 0.0894 7 0.6279 0.0905 8 0.5138 0.0973 9 0.3937 0.0923 10 0.4462 0.0964 11 0.4116 0.0907 12 0.5554 0.0967 13 0.5453 0.1023 14 0.5691 0.1016 15 0.5307 0.0960 16 0.3482 0.0808 17 0.5169 0.0967 18 0.5880 0.0819 19 0.5676 0.0925 20 0.5349 0.0815 21 0.4063 0.0753 Overall 0.5036 0.0250 Cumulative incidence estimates for treatment group 1 at time point 1 Cumulative Subpopulation Incidence Std. Err. 1 0.2569 0.0754 2 0.3409 0.0828 3 0.3228 0.0884 4 0.4236 0.0952 5 0.3649 0.0789 6 0.3801 0.0827 7 0.5358 0.0947 8 0.5378 0.0992 9 0.5631 0.0901 10 0.4612 0.0857 11 0.5901 0.0996 12 0.7243 0.0996 13 0.6567 0.0999 14 0.6080 0.1026 15 0.7012 0.1035 16 0.6688 0.0906 17 0.6653 0.0947 18 0.7312 0.1217 19 0.7551 0.1011 20 0.6191 0.0947 21 0.5652 0.0866 Overall 0.5244 0.0258 Cumulative incidence differences at time point 1 trt 0 vs. trt 1 Cumulative Incidence Subpopulation Difference Std. Err. 1 0.2515 0.1235 2 0.2222 0.1299 3 0.2958 0.1326 4 0.1273 0.1316 5 0.1614 0.1155 6 0.0868 0.1218 7 0.0922 0.1310 8 -0.0240 0.1389 9 -0.1694 0.1290 10 -0.0150 0.1290 11 -0.1785 0.1347 12 -0.1688 0.1388 13 -0.1114 0.1430 14 -0.0389 0.1444 15 -0.1705 0.1412 16 -0.3206 0.1214 17 -0.1484 0.1353 18 -0.1432 0.1467 19 -0.1875 0.1370 20 -0.0842 0.1249 21 -0.1589 0.1148 Overall -0.0208 0.0359 Hazard ratio estimates Subpopulation Log HR Std. Err. Hazard Ratio 1 0.7132 0.3356 2.04 2 0.4455 0.3255 1.56 3 0.4662 0.3120 1.59 4 0.2059 0.3177 1.23 5 0.3883 0.2989 1.47 6 0.3263 0.3093 1.39 7 0.2468 0.3061 1.28 8 -0.0879 0.3198 0.92 9 -0.0767 0.3101 0.93 10 0.2487 0.3248 1.28 11 0.0625 0.3077 1.06 12 -0.1316 0.2991 0.88 13 -0.5043 0.3215 0.60 14 -0.4248 0.3347 0.65 15 -0.5370 0.3288 0.58 16 -0.8563 0.3275 0.42 17 -0.6664 0.3267 0.51 18 -0.1886 0.3030 0.83 19 -0.3500 0.3112 0.70 20 -0.4351 0.3176 0.65 21 -0.7769 0.3035 0.46 Overall -0.0523 0.0869 0.95 The covariance matrix of the cumulative incidence differences at 1 time units for the 21 subpopulations is: trt 0 vs. trt 1 SP1-Overall SP2-Overall SP3-Overall SP4-Overall SP1-Overall 0.0162172990 0.0045006785 -0.0020460775 -0.0012604630 SP2-Overall 0.0045006785 0.0127059343 0.0048250995 -0.0008945005 SP3-Overall -0.0020460775 0.0048250995 0.0150225389 0.0057421229 SP4-Overall -0.0012604630 -0.0008945005 0.0057421229 0.0153918011 SP5-Overall -0.0011951706 -0.0015659969 -0.0014242550 0.0042608479 SP6-Overall 0.0002308006 -0.0009381014 -0.0021862552 -0.0009076221 SP7-Overall -0.0021843872 -0.0021859486 -0.0019771264 0.0008751503 SP8-Overall -0.0027653253 -0.0006180448 0.0001635269 -0.0006349789 SP9-Overall -0.0017536272 -0.0006093868 -0.0018235293 -0.0018234526 SP10-Overall -0.0020614817 -0.0006175173 -0.0028738072 -0.0015165676 SP11-Overall -0.0002733100 -0.0015785736 -0.0030394859 -0.0020265175 SP12-Overall -0.0017768632 -0.0024901657 -0.0007892756 -0.0003200624 SP13-Overall -0.0014204870 -0.0014288111 -0.0002698940 -0.0031209374 SP14-Overall -0.0003202434 0.0002588454 -0.0009928318 -0.0045891891 SP15-Overall -0.0009172231 -0.0003153278 -0.0022334923 -0.0022128295 SP16-Overall -0.0030395305 -0.0004743625 -0.0004993456 -0.0013789179 SP17-Overall 0.0005966977 0.0002114920 -0.0011215048 -0.0029576054 SP18-Overall -0.0003341305 -0.0009059007 -0.0009809684 -0.0006327988 SP19-Overall -0.0011175941 -0.0008157759 -0.0005132094 -0.0010722952 SP20-Overall -0.0012930399 -0.0009424223 -0.0015202579 -0.0017409675 SP21-Overall -0.0012313397 -0.0014657247 -0.0006903755 -0.0014778823 SP5-Overall SP6-Overall SP7-Overall SP8-Overall SP1-Overall -0.0011951706 0.0002308006 -0.0021843872 -2.765325e-03 SP2-Overall -0.0015659969 -0.0009381014 -0.0021859486 -6.180448e-04 SP3-Overall -0.0014242550 -0.0021862552 -0.0019771264 1.635269e-04 SP4-Overall 0.0042608479 -0.0009076221 0.0008751503 -6.349789e-04 SP5-Overall 0.0117307908 0.0062534205 0.0003124696 -9.963394e-04 SP6-Overall 0.0062534205 0.0158880457 0.0056576667 -1.290707e-03 SP7-Overall 0.0003124696 0.0056576667 0.0156054335 6.855635e-03 SP8-Overall -0.0009963394 -0.0012907074 0.0068556354 1.899436e-02 SP9-Overall -0.0013294775 -0.0017041860 0.0004695788 9.235147e-03 SP10-Overall -0.0011074451 -0.0029310669 -0.0008758493 -3.708236e-04 SP11-Overall -0.0018095715 -0.0016916199 -0.0017110250 -2.042269e-03 SP12-Overall -0.0004688182 -0.0009785195 -0.0016768687 -2.280213e-03 SP13-Overall -0.0018882226 -0.0012806407 -0.0021218327 -2.186868e-03 SP14-Overall -0.0022054867 -0.0013658457 -0.0025822567 8.204747e-06 SP15-Overall -0.0013659342 -0.0019032837 -0.0018448929 1.060426e-03 SP16-Overall -0.0013745332 -0.0024348949 -0.0022757241 -4.069638e-04 SP17-Overall -0.0034614554 -0.0031526917 -0.0020895477 -3.047224e-03 SP18-Overall -0.0023009365 -0.0011690323 0.0010452010 -2.810975e-03 SP19-Overall -0.0003928177 -0.0011675635 -0.0005677674 -2.185680e-03 SP20-Overall -0.0011074285 -0.0011134432 -0.0013477874 -3.250892e-03 SP21-Overall -0.0011685094 -0.0013343021 -0.0020907504 -2.244061e-03 SP9-Overall SP10-Overall SP11-Overall SP12-Overall SP1-Overall -0.0017536272 -0.0020614817 -2.733100e-04 -0.0017768632 SP2-Overall -0.0006093868 -0.0006175173 -1.578574e-03 -0.0024901657 SP3-Overall -0.0018235293 -0.0028738072 -3.039486e-03 -0.0007892756 SP4-Overall -0.0018234526 -0.0015165676 -2.026517e-03 -0.0003200624 SP5-Overall -0.0013294775 -0.0011074451 -1.809572e-03 -0.0004688182 SP6-Overall -0.0017041860 -0.0029310669 -1.691620e-03 -0.0009785195 SP7-Overall 0.0004695788 -0.0008758493 -1.711025e-03 -0.0016768687 SP8-Overall 0.0092351469 -0.0003708236 -2.042269e-03 -0.0022802131 SP9-Overall 0.0150900141 0.0054346208 -1.350378e-03 -0.0004656132 SP10-Overall 0.0054346208 0.0128669541 6.385244e-03 -0.0006196025 SP11-Overall -0.0013503780 0.0063852442 1.519064e-02 0.0063172404 SP12-Overall -0.0004656132 -0.0006196025 6.317240e-03 0.0168317693 SP13-Overall -0.0009051990 -0.0008739192 -6.080125e-04 0.0057869146 SP14-Overall 0.0007741906 -0.0001474631 -4.766526e-04 -0.0017422811 SP15-Overall 0.0009697757 -0.0003991858 -1.688622e-03 -0.0008939353 SP16-Overall -0.0005132413 -0.0003240167 -1.038569e-03 -0.0007479665 SP17-Overall -0.0019766843 0.0004241183 1.245196e-03 -0.0011497879 SP18-Overall -0.0022876569 -0.0001095212 2.482586e-05 -0.0017905320 SP19-Overall -0.0018690749 -0.0023382350 -1.653448e-03 -0.0010390374 SP20-Overall -0.0016467942 -0.0014110795 -2.486701e-03 -0.0023223323 SP21-Overall -0.0026729852 -0.0014076677 -1.344400e-03 -0.0019604302 SP13-Overall SP14-Overall SP15-Overall SP16-Overall SP1-Overall -0.0014204870 -3.202434e-04 -0.0009172231 -0.0030395305 SP2-Overall -0.0014288111 2.588454e-04 -0.0003153278 -0.0004743625 SP3-Overall -0.0002698940 -9.928318e-04 -0.0022334923 -0.0004993456 SP4-Overall -0.0031209374 -4.589189e-03 -0.0022128295 -0.0013789179 SP5-Overall -0.0018882226 -2.205487e-03 -0.0013659342 -0.0013745332 SP6-Overall -0.0012806407 -1.365846e-03 -0.0019032837 -0.0024348949 SP7-Overall -0.0021218327 -2.582257e-03 -0.0018448929 -0.0022757241 SP8-Overall -0.0021868684 8.204747e-06 0.0010604263 -0.0004069638 SP9-Overall -0.0009051990 7.741906e-04 0.0009697757 -0.0005132413 SP10-Overall -0.0008739192 -1.474631e-04 -0.0003991858 -0.0003240167 SP11-Overall -0.0006080125 -4.766526e-04 -0.0016886216 -0.0010385691 SP12-Overall 0.0057869146 -1.742281e-03 -0.0008939353 -0.0007479665 SP13-Overall 0.0187672377 8.492328e-03 -0.0016957448 -0.0017256356 SP14-Overall 0.0084923282 1.856349e-02 0.0073598580 -0.0027075061 SP15-Overall -0.0016957448 7.359858e-03 0.0166297599 0.0060046353 SP16-Overall -0.0017256356 -2.707506e-03 0.0060046353 0.0145690376 SP17-Overall -0.0003836467 -1.525730e-03 -0.0014512490 0.0041792497 SP18-Overall -0.0009455025 -6.716344e-04 -0.0019223725 -0.0015448642 SP19-Overall -0.0004708936 -1.543073e-03 -0.0024164085 -0.0007671589 SP20-Overall -0.0006614009 -6.487126e-04 -0.0006333214 -0.0003984732 SP21-Overall -0.0006509445 -1.378472e-04 -0.0012888097 -0.0014917018 SP17-Overall SP18-Overall SP19-Overall SP20-Overall SP1-Overall 0.0005966977 -3.341305e-04 -1.117594e-03 -0.0012930399 SP2-Overall 0.0002114920 -9.059007e-04 -8.157759e-04 -0.0009424223 SP3-Overall -0.0011215048 -9.809684e-04 -5.132094e-04 -0.0015202579 SP4-Overall -0.0029576054 -6.327988e-04 -1.072295e-03 -0.0017409675 SP5-Overall -0.0034614554 -2.300937e-03 -3.928177e-04 -0.0011074285 SP6-Overall -0.0031526917 -1.169032e-03 -1.167563e-03 -0.0011134432 SP7-Overall -0.0020895477 1.045201e-03 -5.677674e-04 -0.0013477874 SP8-Overall -0.0030472236 -2.810975e-03 -2.185680e-03 -0.0032508919 SP9-Overall -0.0019766843 -2.287657e-03 -1.869075e-03 -0.0016467942 SP10-Overall 0.0004241183 -1.095212e-04 -2.338235e-03 -0.0014110795 SP11-Overall 0.0012451960 2.482586e-05 -1.653448e-03 -0.0024867011 SP12-Overall -0.0011497879 -1.790532e-03 -1.039037e-03 -0.0023223323 SP13-Overall -0.0003836467 -9.455025e-04 -4.708936e-04 -0.0006614009 SP14-Overall -0.0015257301 -6.716344e-04 -1.543073e-03 -0.0006487126 SP15-Overall -0.0014512490 -1.922372e-03 -2.416409e-03 -0.0006333214 SP16-Overall 0.0041792497 -1.544864e-03 -7.671589e-04 -0.0003984732 SP17-Overall 0.0168879023 5.240583e-03 -4.589387e-04 -0.0005144886 SP18-Overall 0.0052405835 1.477951e-02 4.973242e-03 -0.0020113903 SP19-Overall -0.0004589387 4.973242e-03 1.485117e-02 0.0041393712 SP20-Overall -0.0005144886 -2.011390e-03 4.139371e-03 0.0144470902 SP21-Overall -0.0016211775 -1.665244e-03 -9.267194e-05 0.0037751891 SP21-Overall SP1-Overall -1.231340e-03 SP2-Overall -1.465725e-03 SP3-Overall -6.903755e-04 SP4-Overall -1.477882e-03 SP5-Overall -1.168509e-03 SP6-Overall -1.334302e-03 SP7-Overall -2.090750e-03 SP8-Overall -2.244061e-03 SP9-Overall -2.672985e-03 SP10-Overall -1.407668e-03 SP11-Overall -1.344400e-03 SP12-Overall -1.960430e-03 SP13-Overall -6.509445e-04 SP14-Overall -1.378472e-04 SP15-Overall -1.288810e-03 SP16-Overall -1.491702e-03 SP17-Overall -1.621178e-03 SP18-Overall -1.665244e-03 SP19-Overall -9.267194e-05 SP20-Overall 3.775189e-03 SP21-Overall 1.124126e-02 The covariance matrix of the log hazard ratios for the 21 subpopulations is: SP1-Overall SP2-Overall SP3-Overall SP4-Overall SP5-Overall SP1-Overall 0.099275939 0.0399266549 0.003552648 0.001180904 -0.006049690 SP2-Overall 0.039926655 0.0903260494 0.038472616 -0.001830032 -0.007883719 SP3-Overall 0.003552648 0.0384726156 0.091576040 0.034722091 -0.010525850 SP4-Overall 0.001180904 -0.0018300322 0.034722091 0.097294957 0.023277549 SP5-Overall -0.006049690 -0.0078837187 -0.010525850 0.023277549 0.072515711 SP6-Overall -0.005646355 -0.0141866899 -0.017085886 -0.004004705 0.034317701 SP7-Overall -0.017822496 -0.0270054824 -0.020600387 0.006096826 -0.004229566 SP8-Overall -0.016605317 -0.0082156776 -0.001665986 -0.001312106 -0.002230802 SP9-Overall -0.013667462 -0.0082873964 -0.010325598 -0.013504318 -0.002585386 SP10-Overall -0.010861058 -0.0080550804 -0.021650516 -0.017043090 -0.003820879 SP11-Overall -0.002074921 -0.0073580804 -0.019290465 -0.014241665 -0.008648344 SP12-Overall -0.012990823 -0.0116301931 -0.001171640 -0.005894382 -0.004649288 SP13-Overall -0.015727195 -0.0078343109 0.004365810 -0.012876408 -0.002493616 SP14-Overall -0.013063131 0.0022205688 -0.002429450 -0.017537353 -0.005353814 SP15-Overall -0.013621393 0.0024985236 -0.006924793 -0.013477433 -0.003889889 SP16-Overall -0.015185917 0.0007659096 -0.002604587 -0.007172916 -0.005667642 SP17-Overall -0.002560636 -0.0050068736 -0.011146778 -0.019514796 -0.017275419 SP18-Overall -0.005482887 -0.0122725563 -0.012594320 -0.014458056 -0.016453223 SP19-Overall -0.005977330 -0.0081917706 -0.002166533 -0.006318572 -0.014097955 SP20-Overall -0.005613078 -0.0105099105 -0.010918947 -0.005180915 -0.009211300 SP21-Overall -0.010787526 -0.0128953861 -0.005623041 -0.008169684 -0.007015228 SP6-Overall SP7-Overall SP8-Overall SP9-Overall SP10-Overall SP1-Overall -0.005646355 -0.017822496 -0.0166053167 -0.0136674623 -0.010861058 SP2-Overall -0.014186690 -0.027005482 -0.0082156776 -0.0082873964 -0.008055080 SP3-Overall -0.017085886 -0.020600387 -0.0016659858 -0.0103255976 -0.021650516 SP4-Overall -0.004004705 0.006096826 -0.0013121058 -0.0135043179 -0.017043090 SP5-Overall 0.034317701 -0.004229566 -0.0022308019 -0.0025853861 -0.003820879 SP6-Overall 0.086940926 0.031299840 0.0024757626 0.0020081500 -0.007523169 SP7-Overall 0.031299840 0.108922447 0.0471238075 0.0046389251 -0.010492642 SP8-Overall 0.002475763 0.047123807 0.1164410185 0.0556932263 -0.008910009 SP9-Overall 0.002008150 0.004638925 0.0556932263 0.0979041443 0.035836196 SP10-Overall -0.007523169 -0.010492642 -0.0089100093 0.0358361957 0.079987153 SP11-Overall -0.004012716 -0.010339334 -0.0215107068 -0.0136051846 0.036787226 SP12-Overall -0.008138788 -0.010659691 -0.0198624950 -0.0136783901 -0.001692598 SP13-Overall -0.007578803 -0.014964375 -0.0186087712 -0.0146388383 -0.008766893 SP14-Overall -0.002810394 -0.011613456 0.0012420452 -0.0014690358 -0.007647668 SP15-Overall -0.009733676 -0.009819217 0.0024796889 -0.0010701722 -0.005164852 SP16-Overall -0.010669677 -0.006926174 -0.0008949807 0.0002153662 -0.002217252 SP17-Overall -0.012968161 -0.007307789 -0.0123283882 -0.0050357180 0.002627696 SP18-Overall -0.001286928 0.003548302 -0.0133811580 -0.0049926855 -0.002436785 SP19-Overall -0.009451746 -0.009551685 -0.0097426671 -0.0080630444 -0.011837125 SP20-Overall -0.010369875 -0.007576260 -0.0207376837 -0.0156378931 -0.005290779 SP21-Overall -0.006759770 -0.005561603 -0.0135781764 -0.0179870358 -0.009120612 SP11-Overall SP12-Overall SP13-Overall SP14-Overall SP15-Overall SP1-Overall -0.0020749208 -0.012990823 -0.015727195 -0.0130631310 -0.013621393 SP2-Overall -0.0073580804 -0.011630193 -0.007834311 0.0022205688 0.002498524 SP3-Overall -0.0192904652 -0.001171640 0.004365810 -0.0024294495 -0.006924793 SP4-Overall -0.0142416648 -0.005894382 -0.012876408 -0.0175373527 -0.013477433 SP5-Overall -0.0086483444 -0.004649288 -0.002493616 -0.0053538143 -0.003889889 SP6-Overall -0.0040127162 -0.008138788 -0.007578803 -0.0028103940 -0.009733676 SP7-Overall -0.0103393337 -0.010659691 -0.014964375 -0.0116134565 -0.009819217 SP8-Overall -0.0215107068 -0.019862495 -0.018608771 0.0012420452 0.002479689 SP9-Overall -0.0136051846 -0.013678390 -0.014638838 -0.0014690358 -0.001070172 SP10-Overall 0.0367872260 -0.001692598 -0.008766893 -0.0076476677 -0.005164852 SP11-Overall 0.0861548332 0.037541645 -0.003059886 0.0009645925 -0.007521767 SP12-Overall 0.0375416452 0.094294057 0.035061775 -0.0025188490 -0.002867184 SP13-Overall -0.0030598856 0.035061775 0.120248330 0.0526416571 0.001255358 SP14-Overall 0.0009645925 -0.002518849 0.052641657 0.1094098446 0.043846094 SP15-Overall -0.0075217672 -0.002867184 0.001255358 0.0438460944 0.103135628 SP16-Overall -0.0110776594 -0.010259082 -0.007710523 -0.0158444954 0.042029970 SP17-Overall -0.0004971873 -0.006550427 -0.008932375 -0.0103266521 -0.006333510 SP18-Overall -0.0073203394 -0.010150561 -0.005524320 -0.0100020917 -0.014043488 SP19-Overall -0.0081792300 -0.008404399 -0.001386869 -0.0097943621 -0.011965930 SP20-Overall -0.0048222427 -0.004443059 -0.003323880 -0.0030600136 -0.006064870 SP21-Overall 0.0001565834 -0.002456174 -0.006269706 -0.0023174552 -0.014178518 SP16-Overall SP17-Overall SP18-Overall SP19-Overall SP20-Overall SP1-Overall -0.0151859174 -0.0025606356 -0.005482887 -0.005977330 -0.005613078 SP2-Overall 0.0007659096 -0.0050068736 -0.012272556 -0.008191771 -0.010509911 SP3-Overall -0.0026045865 -0.0111467778 -0.012594320 -0.002166533 -0.010918947 SP4-Overall -0.0071729157 -0.0195147963 -0.014458056 -0.006318572 -0.005180915 SP5-Overall -0.0056676418 -0.0172754186 -0.016453223 -0.014097955 -0.009211300 SP6-Overall -0.0106696769 -0.0129681614 -0.001286928 -0.009451746 -0.010369875 SP7-Overall -0.0069261736 -0.0073077890 0.003548302 -0.009551685 -0.007576260 SP8-Overall -0.0008949807 -0.0123283882 -0.013381158 -0.009742667 -0.020737684 SP9-Overall 0.0002153662 -0.0050357180 -0.004992685 -0.008063044 -0.015637893 SP10-Overall -0.0022172516 0.0026276958 -0.002436785 -0.011837125 -0.005290779 SP11-Overall -0.0110776594 -0.0004971873 -0.007320339 -0.008179230 -0.004822243 SP12-Overall -0.0102590817 -0.0065504273 -0.010150561 -0.008404399 -0.004443059 SP13-Overall -0.0077105234 -0.0089323750 -0.005524320 -0.001386869 -0.003323880 SP14-Overall -0.0158444954 -0.0103266521 -0.010002092 -0.009794362 -0.003060014 SP15-Overall 0.0420299700 -0.0063335103 -0.014043488 -0.011965930 -0.006064870 SP16-Overall 0.0906215780 0.0148140626 -0.010884086 0.001201333 -0.009144312 SP17-Overall 0.0148140626 0.1086911737 0.037499460 -0.001848179 -0.013400599 SP18-Overall -0.0108840863 0.0374994599 0.096917383 0.035931934 -0.009919567 SP19-Overall 0.0012013330 -0.0018481788 0.035931934 0.094957928 0.018501605 SP20-Overall -0.0091443120 -0.0134005988 -0.009919567 0.018501605 0.083823977 SP21-Overall -0.0173390383 -0.0066920731 -0.004218793 -0.002088354 0.024875451 SP21-Overall SP1-Overall -0.0107875260 SP2-Overall -0.0128953861 SP3-Overall -0.0056230405 SP4-Overall -0.0081696838 SP5-Overall -0.0070152278 SP6-Overall -0.0067597703 SP7-Overall -0.0055616035 SP8-Overall -0.0135781764 SP9-Overall -0.0179870358 SP10-Overall -0.0091206117 SP11-Overall 0.0001565834 SP12-Overall -0.0024561737 SP13-Overall -0.0062697063 SP14-Overall -0.0023174552 SP15-Overall -0.0141785176 SP16-Overall -0.0173390383 SP17-Overall -0.0066920731 SP18-Overall -0.0042187934 SP19-Overall -0.0020883538 SP20-Overall 0.0248754508 SP21-Overall 0.0675609790 Supremum test results trt 0 vs. trt 1 Interaction p-value based on cumulative incidence estimates: 0.184 Interaction p-value based on hazard ratio estimates: 0.048 Chi-square test results Interaction p-value based on cumulative incidence estimates: 0.024 > plot(resCI_e, legendy = 30, + pline = -2.5, color = c("red", "black"), ylabel = "PFS", + xlabel = "Subpopulations by Median Continuous Variable", ncex = 0.7, + tlegend = c("Trt A", "Trt B"), nlas = 3, alpha = 0.05, + pointwise = FALSE) dev.new(): using pdf(file="Rplots3.pdf") dev.new(): using pdf(file="Rplots4.pdf") > > ### Example 3 ### > > data(bigKM) > > ranger2 <- c(100, 450) > ranger1 <- c(50, 300) > maxnsubpops <- 30 > > res_bal <- balance_patients(ranger1, ranger2, maxnsubpops, bigKM$ki67, + plot = TRUE, verbose = TRUE, contour = TRUE, + nlevels = 6) Searching for best values of r1 and r2 in each subpopulation... | | | 0% | | | 1% | |= 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|=================================================================== | 95% | |=================================================================== | 96% | |==================================================================== | 96% | |==================================================================== | 97% | |==================================================================== | 98% | |===================================================================== | 98% | |===================================================================== | 99% | |======================================================================| 99% | |======================================================================| 100% Balanced subpopulations determination (number of patients) Range for number of patients in common in consecutive subpopulations (r1): 50 <--> 300 Range for number of patients per subpopulation (r2): 100 <--> 450 Best result for 6 subpopulations * Optimal r1 value: 62 * Optimal r2 value: 443 * Minimum variance of subpopulation sizes achieved: 407.2 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 3.00 0.0000 4.0000 489 2 6.00 5.0000 7.0000 475 3 10.00 8.0000 11.0000 469 4 13.00 11.0000 15.0000 467 5 19.00 16.0000 24.0000 478 6 30.00 23.0000 90.0000 430 Best result for 7 subpopulations * Optimal r1 value: 130 * Optimal r2 value: 427 * Minimum variance of subpopulation sizes achieved: 529.619 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 3.00 0.0000 4.0000 489 2 5.00 4.0000 6.0000 432 3 7.00 6.0000 9.0000 476 4 10.00 9.0000 12.0000 478 5 15.00 13.0000 18.0000 469 6 20.00 17.0000 25.0000 457 7 30.00 23.0000 90.0000 430 Best result for 8 subpopulations * Optimal r1 value: 62 * Optimal r2 value: 328 * Minimum variance of subpopulation sizes achieved: 714.5 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 2.00 0.0000 3.0000 383 2 5.00 4.0000 5.0000 330 3 7.00 6.0000 8.0000 387 4 10.00 9.0000 11.0000 333 5 12.00 11.0000 14.0000 329 6 16.00 15.0000 18.0000 347 7 21.00 19.0000 26.0000 342 8 35.00 26.0000 90.0000 311 Best result for 9 subpopulations * Optimal r1 value: 107 * Optimal r2 value: 307 * Minimum variance of subpopulation sizes achieved: 892 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 2.00 0.0000 3.0000 383 2 5.00 4.0000 5.0000 330 3 7.00 6.0000 8.0000 387 4 10.00 9.0000 11.0000 333 5 12.00 11.0000 14.0000 329 6 15.00 14.0000 17.0000 315 7 20.00 17.0000 22.0000 338 8 25.00 21.0000 31.0000 322 9 35.00 27.0000 90.0000 296 Best result for 10 subpopulations * Optimal r1 value: 251 * Optimal r2 value: 445 * Minimum variance of subpopulation sizes achieved: 1369.289 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 3.00 0.0000 4.0000 489 2 4.00 3.0000 5.0000 471 3 6.00 5.0000 7.0000 475 4 7.00 6.0000 9.0000 476 5 10.00 8.0000 11.0000 469 6 12.00 10.0000 14.0000 511 7 15.00 13.0000 18.0000 469 8 19.00 16.0000 24.0000 478 9 25.00 20.0000 35.0000 471 10 32.00 25.0000 90.0000 369 Best result for 11 subpopulations * Optimal r1 value: 269 * Optimal r2 value: 443 * Minimum variance of subpopulation sizes achieved: 295.9636 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 3.00 0.0000 4.0000 489 2 4.00 3.0000 5.0000 471 3 6.00 5.0000 7.0000 475 4 7.00 6.0000 9.0000 476 5 10.00 8.0000 11.0000 469 6 11.00 10.0000 13.0000 444 7 13.00 11.0000 15.0000 467 8 15.00 13.0000 18.0000 469 9 19.00 16.0000 24.0000 478 10 23.00 19.0000 31.0000 449 11 30.00 23.0000 90.0000 430 Best result for 12 subpopulations * Optimal r1 value: 60 * Optimal r2 value: 201 * Minimum variance of subpopulation sizes achieved: 745.0909 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 3.0000 4.0000 247 3 5.00 5.0000 5.0000 224 4 7.00 6.0000 7.0000 251 5 8.00 8.0000 9.0000 225 6 10.00 10.0000 11.0000 244 7 12.00 12.0000 14.0000 267 8 15.00 15.0000 16.0000 217 9 18.00 17.0000 20.0000 257 10 24.00 21.0000 26.0000 215 11 30.00 26.0000 38.0000 203 12 40.00 34.0000 90.0000 168 Best result for 13 subpopulations * Optimal r1 value: 65 * Optimal r2 value: 186 * Minimum variance of subpopulation sizes achieved: 560.2308 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 3.0000 4.0000 247 3 5.00 5.0000 5.0000 224 4 7.00 6.0000 7.0000 251 5 8.00 8.0000 9.0000 225 6 10.00 10.0000 11.0000 244 7 12.00 11.0000 12.0000 207 8 15.00 13.0000 15.0000 260 9 17.00 16.0000 18.0000 209 10 20.00 19.0000 22.0000 208 11 25.00 22.0000 28.0000 215 12 30.00 26.0000 36.0000 187 13 40.00 32.0000 90.0000 189 Best result for 14 subpopulations * Optimal r1 value: 103 * Optimal r2 value: 208 * Minimum variance of subpopulation sizes achieved: 906.2253 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 4.0000 313 3 5.00 5.0000 5.0000 224 4 7.00 6.0000 7.0000 251 5 8.00 8.0000 9.0000 225 6 10.00 9.0000 10.0000 271 7 12.00 11.0000 13.0000 262 8 15.00 13.0000 15.0000 260 9 17.00 16.0000 18.0000 209 10 19.00 18.0000 20.0000 226 11 21.00 20.0000 24.0000 233 12 25.00 22.0000 28.0000 215 13 30.00 26.0000 39.0000 209 14 39.00 31.0000 90.0000 205 Best result for 15 subpopulations * Optimal r1 value: 226 * Optimal r2 value: 308 * Minimum variance of subpopulation sizes achieved: 936.9714 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 2.00 0.0000 3.0000 383 2 3.00 2.0000 4.0000 313 3 5.00 4.0000 5.0000 330 4 5.00 5.0000 6.0000 326 5 7.00 6.0000 8.0000 387 6 9.00 8.0000 10.0000 407 7 11.00 10.0000 12.0000 389 8 12.00 11.0000 14.0000 329 9 15.00 13.0000 16.0000 339 10 16.00 15.0000 18.0000 347 11 18.00 16.0000 20.0000 336 12 20.00 18.0000 23.0000 332 13 22.00 20.0000 27.0000 319 14 26.00 22.0000 35.0000 333 15 35.00 26.0000 90.0000 311 Best result for 16 subpopulations * Optimal r1 value: 233 * Optimal r2 value: 308 * Minimum variance of subpopulation sizes achieved: 910.4667 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 2.00 0.0000 3.0000 383 2 3.00 2.0000 4.0000 313 3 5.00 4.0000 5.0000 330 4 5.00 5.0000 6.0000 326 5 7.00 6.0000 8.0000 387 6 9.00 8.0000 10.0000 407 7 11.00 10.0000 12.0000 389 8 12.00 11.0000 14.0000 329 9 15.00 13.0000 16.0000 339 10 16.00 15.0000 18.0000 347 11 18.00 16.0000 20.0000 336 12 20.00 18.0000 23.0000 332 13 21.00 19.0000 25.0000 327 14 25.00 21.0000 31.0000 322 15 29.00 24.0000 40.0000 322 16 35.00 26.0000 90.0000 311 Best result for 17 subpopulations * Optimal r1 value: 149 * Optimal r2 value: 218 * Minimum variance of subpopulation sizes achieved: 1089.882 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 4.0000 313 3 5.00 4.0000 5.0000 330 4 7.00 6.0000 7.0000 251 5 7.00 7.0000 8.0000 285 6 8.00 8.0000 9.0000 225 7 10.00 9.0000 10.0000 271 8 12.00 11.0000 13.0000 262 9 15.00 13.0000 15.0000 260 10 15.00 15.0000 17.0000 248 11 18.00 16.0000 19.0000 245 12 19.00 18.0000 20.0000 226 13 20.00 19.0000 23.0000 233 14 24.00 21.0000 27.0000 228 15 25.00 23.0000 30.0000 225 16 31.00 26.0000 40.0000 228 17 39.00 31.0000 90.0000 205 Best result for 18 subpopulations * Optimal r1 value: 166 * Optimal r2 value: 220 * Minimum variance of subpopulation sizes achieved: 1004.85 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 4.0000 313 3 5.00 4.0000 5.0000 330 4 7.00 6.0000 7.0000 251 5 7.00 7.0000 8.0000 285 6 8.00 8.0000 9.0000 225 7 10.00 9.0000 10.0000 271 8 12.00 11.0000 13.0000 262 9 15.00 13.0000 15.0000 260 10 15.00 15.0000 17.0000 248 11 18.00 16.0000 19.0000 245 12 18.00 17.0000 20.0000 257 13 20.00 19.0000 23.0000 233 14 24.00 21.0000 27.0000 228 15 25.00 23.0000 30.0000 225 16 28.00 25.0000 35.0000 238 17 32.00 27.0000 42.0000 226 18 39.00 31.0000 90.0000 205 Best result for 19 subpopulations * Optimal r1 value: 180 * Optimal r2 value: 223 * Minimum variance of subpopulation sizes achieved: 986.2749 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 4.0000 313 3 5.00 4.0000 5.0000 330 4 7.00 6.0000 7.0000 251 5 7.00 7.0000 8.0000 285 6 8.00 8.0000 9.0000 225 7 10.00 9.0000 10.0000 271 8 12.00 11.0000 13.0000 262 9 15.00 13.0000 15.0000 260 10 15.00 15.0000 17.0000 248 11 18.00 16.0000 19.0000 245 12 18.00 17.0000 20.0000 257 13 20.00 19.0000 23.0000 233 14 24.00 21.0000 27.0000 228 15 25.00 23.0000 30.0000 225 16 28.00 25.0000 35.0000 238 17 31.00 26.0000 40.0000 228 18 35.00 29.0000 53.0000 224 19 39.00 31.0000 90.0000 205 Best result for 20 subpopulations * Optimal r1 value: 182 * Optimal r2 value: 225 * Minimum variance of subpopulation sizes achieved: 947.3974 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 4.0000 313 3 5.00 4.0000 5.0000 330 4 7.00 6.0000 7.0000 251 5 7.00 7.0000 8.0000 285 6 8.00 8.0000 9.0000 225 7 10.00 9.0000 10.0000 271 8 10.00 10.0000 11.0000 244 9 12.00 11.0000 13.0000 262 10 15.00 13.0000 15.0000 260 11 15.00 15.0000 17.0000 248 12 18.00 16.0000 19.0000 245 13 18.00 17.0000 20.0000 257 14 20.00 19.0000 23.0000 233 15 24.00 21.0000 27.0000 228 16 25.00 22.0000 29.0000 227 17 27.00 24.0000 32.0000 228 18 31.00 26.0000 40.0000 228 19 35.00 29.0000 54.0000 225 20 39.00 31.0000 90.0000 205 Best result for 21 subpopulations * Optimal r1 value: 192 * Optimal r2 value: 225 * Minimum variance of subpopulation sizes achieved: 907.2905 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 4.0000 313 3 5.00 4.0000 5.0000 330 4 7.00 6.0000 7.0000 251 5 7.00 7.0000 8.0000 285 6 8.00 8.0000 9.0000 225 7 10.00 9.0000 10.0000 271 8 10.00 10.0000 11.0000 244 9 12.00 11.0000 13.0000 262 10 15.00 13.0000 15.0000 260 11 15.00 15.0000 17.0000 248 12 18.00 16.0000 19.0000 245 13 18.00 17.0000 20.0000 257 14 20.00 19.0000 23.0000 233 15 24.00 21.0000 27.0000 228 16 25.00 22.0000 29.0000 227 17 27.00 24.0000 32.0000 228 18 28.00 25.0000 35.0000 238 19 31.00 26.0000 40.0000 228 20 35.00 29.0000 54.0000 225 21 39.00 31.0000 90.0000 205 Best result for 22 subpopulations * Optimal r1 value: 197 * Optimal r2 value: 225 * Minimum variance of subpopulation sizes achieved: 883.2662 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 4.0000 313 3 5.00 4.0000 5.0000 330 4 7.00 6.0000 7.0000 251 5 7.00 7.0000 8.0000 285 6 8.00 8.0000 9.0000 225 7 10.00 9.0000 10.0000 271 8 10.00 10.0000 11.0000 244 9 12.00 11.0000 13.0000 262 10 15.00 13.0000 15.0000 260 11 15.00 15.0000 17.0000 248 12 18.00 16.0000 19.0000 245 13 18.00 17.0000 20.0000 257 14 20.00 19.0000 23.0000 233 15 21.00 20.0000 24.0000 233 16 24.00 21.0000 27.0000 228 17 25.00 22.0000 29.0000 227 18 25.00 23.0000 30.0000 225 19 28.00 25.0000 35.0000 238 20 31.00 26.0000 40.0000 228 21 35.00 29.0000 54.0000 225 22 39.00 31.0000 90.0000 205 Best result for 23 subpopulations * Optimal r1 value: 180 * Optimal r2 value: 206 * Minimum variance of subpopulation sizes achieved: 1040.443 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 3.0000 207 3 3.00 3.0000 4.0000 247 4 5.00 4.0000 5.0000 330 5 7.00 6.0000 7.0000 251 6 7.00 7.0000 8.0000 285 7 8.00 8.0000 9.0000 225 8 10.00 9.0000 10.0000 271 9 12.00 11.0000 12.0000 207 10 12.00 12.0000 14.0000 267 11 15.00 13.0000 15.0000 260 12 15.00 15.0000 16.0000 217 13 17.00 16.0000 18.0000 209 14 18.00 17.0000 20.0000 257 15 20.00 19.0000 22.0000 208 16 21.00 20.0000 24.0000 233 17 24.00 21.0000 26.0000 215 18 25.00 22.0000 28.0000 215 19 26.00 24.0000 31.0000 216 20 28.00 25.0000 34.0000 210 21 30.00 26.0000 39.0000 209 22 35.00 29.0000 47.0000 208 23 39.00 31.0000 90.0000 205 Best result for 24 subpopulations * Optimal r1 value: 181 * Optimal r2 value: 207 * Minimum variance of subpopulation sizes achieved: 1004.087 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 3.0000 207 3 3.00 3.0000 4.0000 247 4 5.00 4.0000 5.0000 330 5 7.00 6.0000 7.0000 251 6 7.00 7.0000 8.0000 285 7 8.00 8.0000 9.0000 225 8 10.00 9.0000 10.0000 271 9 12.00 11.0000 12.0000 207 10 12.00 12.0000 14.0000 267 11 15.00 13.0000 15.0000 260 12 15.00 15.0000 16.0000 217 13 17.00 16.0000 18.0000 209 14 18.00 17.0000 20.0000 257 15 20.00 19.0000 22.0000 208 16 21.00 20.0000 24.0000 233 17 24.00 21.0000 26.0000 215 18 25.00 22.0000 28.0000 215 19 25.00 23.0000 30.0000 225 20 28.00 25.0000 34.0000 210 21 30.00 26.0000 39.0000 209 22 33.00 28.0000 42.0000 213 23 35.00 29.0000 47.0000 208 24 39.00 31.0000 90.0000 205 Best result for 25 subpopulations * Optimal r1 value: 200 * Optimal r2 value: 222 * Minimum variance of subpopulation sizes achieved: 808.31 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 4.0000 313 3 5.00 4.0000 5.0000 330 4 7.00 6.0000 7.0000 251 5 7.00 7.0000 8.0000 285 6 8.00 8.0000 9.0000 225 7 10.00 9.0000 10.0000 271 8 10.00 10.0000 11.0000 244 9 12.00 11.0000 13.0000 262 10 12.00 12.0000 14.0000 267 11 15.00 13.0000 15.0000 260 12 15.00 15.0000 17.0000 248 13 18.00 16.0000 19.0000 245 14 18.00 17.0000 20.0000 257 15 20.00 19.0000 23.0000 233 16 21.00 20.0000 24.0000 233 17 24.00 21.0000 27.0000 228 18 25.00 22.0000 29.0000 227 19 25.00 23.0000 30.0000 225 20 27.00 24.0000 32.0000 228 21 28.00 25.0000 35.0000 238 22 31.00 26.0000 40.0000 228 23 34.00 28.0000 45.0000 237 24 36.50 30.0000 60.0000 226 25 39.00 31.0000 90.0000 205 Best result for 26 subpopulations * Optimal r1 value: 212 * Optimal r2 value: 223 * Minimum variance of subpopulation sizes achieved: 850.3446 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 4.0000 313 3 5.00 4.0000 5.0000 330 4 7.00 6.0000 7.0000 251 5 7.00 7.0000 8.0000 285 6 8.00 8.0000 9.0000 225 7 10.00 9.0000 10.0000 271 8 10.00 10.0000 11.0000 244 9 12.00 11.0000 13.0000 262 10 12.00 12.0000 14.0000 267 11 15.00 13.0000 15.0000 260 12 15.00 14.0000 16.0000 284 13 18.00 16.0000 19.0000 245 14 18.00 17.0000 20.0000 257 15 20.00 19.0000 23.0000 233 16 21.00 20.0000 24.0000 233 17 24.00 21.0000 27.0000 228 18 25.00 22.0000 29.0000 227 19 25.00 23.0000 30.0000 225 20 27.00 24.0000 32.0000 228 21 28.00 25.0000 35.0000 238 22 31.00 26.0000 40.0000 228 23 34.00 28.0000 45.0000 237 24 35.00 29.0000 53.0000 224 25 36.50 30.0000 60.0000 226 26 39.00 31.0000 90.0000 205 Best result for 27 subpopulations * Optimal r1 value: 213 * Optimal r2 value: 225 * Minimum variance of subpopulation sizes achieved: 835.037 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 4.0000 313 3 5.00 4.0000 5.0000 330 4 7.00 6.0000 7.0000 251 5 7.00 7.0000 8.0000 285 6 8.00 8.0000 9.0000 225 7 10.00 9.0000 10.0000 271 8 10.00 10.0000 11.0000 244 9 12.00 11.0000 13.0000 262 10 12.00 12.0000 14.0000 267 11 15.00 13.0000 15.0000 260 12 15.00 14.0000 16.0000 284 13 18.00 16.0000 19.0000 245 14 18.00 17.0000 20.0000 257 15 20.00 19.0000 23.0000 233 16 21.00 20.0000 24.0000 233 17 24.00 21.0000 27.0000 228 18 25.00 22.0000 29.0000 227 19 25.00 23.0000 30.0000 225 20 27.00 24.0000 32.0000 228 21 28.00 25.0000 35.0000 238 22 31.00 26.0000 40.0000 228 23 32.00 27.0000 42.0000 226 24 34.00 28.0000 45.0000 237 25 35.00 29.0000 54.0000 225 26 36.50 30.0000 60.0000 226 27 39.00 31.0000 90.0000 205 Best result for 28 subpopulations * Optimal r1 value: 200 * Optimal r2 value: 207 * Minimum variance of subpopulation sizes achieved: 906.6614 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 3.0000 207 3 3.00 3.0000 4.0000 247 4 5.00 4.0000 5.0000 330 5 7.00 6.0000 7.0000 251 6 7.00 7.0000 8.0000 285 7 8.00 8.0000 9.0000 225 8 10.00 9.0000 10.0000 271 9 10.00 10.0000 11.0000 244 10 12.00 11.0000 12.0000 207 11 12.00 12.0000 14.0000 267 12 15.00 13.0000 15.0000 260 13 15.00 15.0000 16.0000 217 14 17.00 16.0000 18.0000 209 15 18.00 17.0000 20.0000 257 16 20.00 19.0000 22.0000 208 17 21.00 20.0000 24.0000 233 18 24.00 21.0000 26.0000 215 19 25.00 22.0000 28.0000 215 20 25.00 23.0000 30.0000 225 21 26.00 24.0000 31.0000 216 22 28.00 25.0000 34.0000 210 23 30.00 26.0000 39.0000 209 24 31.00 27.0000 40.0000 213 25 33.00 28.0000 42.0000 213 26 35.00 29.0000 47.0000 208 27 35.00 30.0000 50.0000 209 28 39.00 31.0000 90.0000 205 Best result for 29 subpopulations * Optimal r1 value: 200 * Optimal r2 value: 201 * Minimum variance of subpopulation sizes achieved: 991.1158 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 3.0000 207 3 3.00 3.0000 4.0000 247 4 5.00 4.0000 5.0000 330 5 7.00 6.0000 7.0000 251 6 7.00 7.0000 8.0000 285 7 8.00 8.0000 9.0000 225 8 10.00 9.0000 10.0000 271 9 10.00 10.0000 11.0000 244 10 12.00 11.0000 12.0000 207 11 12.00 12.0000 14.0000 267 12 15.00 13.0000 15.0000 260 13 15.00 15.0000 16.0000 217 14 17.00 16.0000 18.0000 209 15 18.00 17.0000 20.0000 257 16 20.00 19.0000 22.0000 208 17 21.00 20.0000 24.0000 233 18 24.00 21.0000 26.0000 215 19 25.00 22.0000 28.0000 215 20 25.00 23.0000 30.0000 225 21 26.00 24.0000 31.0000 216 22 28.00 25.0000 33.0000 201 23 30.00 26.0000 38.0000 203 24 31.00 27.0000 40.0000 213 25 32.00 28.0000 41.0000 206 26 35.00 29.0000 45.0000 203 27 35.00 30.0000 50.0000 209 28 39.00 31.0000 80.0000 201 29 40.00 32.0000 90.0000 189 Best result for 30 subpopulations * Optimal r1 value: 182 * Optimal r2 value: 184 * Minimum variance of subpopulation sizes achieved: 1283.771 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 3.0000 207 3 3.00 3.0000 4.0000 247 4 5.00 4.0000 5.0000 330 5 7.00 6.0000 7.0000 251 6 7.00 7.0000 8.0000 285 7 8.00 8.0000 9.0000 225 8 10.00 9.0000 10.0000 271 9 10.00 10.0000 11.0000 244 10 12.00 11.0000 12.0000 207 11 12.00 12.0000 13.0000 200 12 15.00 13.0000 15.0000 260 13 15.00 15.0000 16.0000 217 14 17.00 16.0000 18.0000 209 15 18.00 17.0000 20.0000 257 16 20.00 19.0000 22.0000 208 17 21.00 20.0000 23.0000 197 18 23.00 21.0000 25.0000 200 19 25.00 22.0000 28.0000 215 20 25.00 23.0000 29.0000 193 21 26.00 24.0000 30.0000 200 22 28.00 25.0000 32.0000 192 23 30.00 26.0000 36.0000 187 24 31.00 27.0000 38.0000 188 25 32.00 28.0000 40.0000 200 26 35.00 29.0000 44.0000 187 27 35.00 30.0000 45.0000 191 28 38.00 31.0000 55.0000 185 29 40.00 32.0000 80.0000 185 30 40.00 33.0000 90.0000 177 Overall best result * Number of subpopulations: 11 * Best r1 value: 269 * Best r2 value: 443 * Minimum variance of subpopulation sizes achieved: 295.9636 > > # ### Examples for 'tail-oriented' windows ### > # > # library(stepp) > # > # set.seed(101) > # Y <- rnorm(100) > # summary(Y) > # > # nsubpop <- 10 > # tt <- gen.tailwin(Y, nsub = nsubpop, dir = "LE") > # ss <- stepp.win(type = "tail-oriented", r1 = tt$v, r2 = rep(min(Y), nsubpop)) > # > # # create and generate the stepp subpopulation > # sp <- new("stsubpop") > # sp <- generate(sp, win = ss, cov = Y) > # summary(sp) > # > # # --- > # > # nsubpop <- 10 > # tt <- gen.tailwin(Y, nsub = nsubpop, dir = "GE") > # ss <- stepp.win(type = "tail-oriented", r1 = rep(max(Y), nsubpop), r2 = tt$v) > # > # # create and generate the stepp subpopulation > # sp <- new("stsubpop") > # sp <- generate(sp, win = ss, cov = Y) > # summary(sp) > # > # # --- > # > # win1 <- stepp.win(type="sliding", r1=5,r2=99) > # > # # create and generate the stepp subpopulation > # sp <- new("stsubpop") > # sp <- generate(sp, win = win1, cov = Y) > # summary(sp) > # > # ### > # > # # debugonce(generate, signature = "stsubpop") > # # debugonce(generate.all) > # # debug(gen.tailwin) > > ### > > library(stepp) > > data(bigKM) > > # bigKM$ki67[1:80] <- NA > # cov_na <- which(is.na(bigKM$ki67)) > # bigKM <- bigKM[-cov_na, ] > > rxgroup <- bigKM$trt > time <- bigKM$time > evt <- bigKM$event > cov <- bigKM$ki67 > > # analyze using Cumulative Incidence method with > # sliding window size of 150 patients and a maximum of 50 patients in common > # > nsubpop_tmp <- 10 > win_tmp <- gen.tailwin(cov, nsub = nsubpop_tmp, dir = "GE") > nsubpop <- length(win_tmp$v) > swin <- new("stwin", type = "tail-oriented", r1 = rep(max(cov), nsubpop), r2 = win_tmp$v) # create a tail-oriented window > subp <- new("stsubpop") # create subpopulation object > subp <- generate(subp, win = swin, covariate = cov) # generate the subpopulations > summary(subp) # summary of the subpopulations Window type: tail-oriented Subpopulation for patients less than or equal to: 90 Subpopulation for patients greater than or equal to: 3 4 5 6 7 8 10 12 14 16 19 24 Number of subpopulations created: 13 Subpopulation summary information (including all treatments) Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 10.00 0.0000 90.0000 2685 (entire cohort) 2 12.00 3.0000 90.0000 2443 3 12.00 4.0000 90.0000 2302 4 13.00 5.0000 90.0000 2196 5 14.00 6.0000 90.0000 1972 6 15.00 7.0000 90.0000 1870 7 15.00 8.0000 90.0000 1721 8 17.00 10.0000 90.0000 1496 9 19.00 12.0000 90.0000 1252 10 20.00 14.0000 90.0000 1052 11 23.00 16.0000 90.0000 847 12 25.00 19.0000 90.0000 638 13 31.00 24.0000 90.0000 405 > > # create a stepp model using Kaplan Meier Method to analyze the data > # > smodel <- new("stmodelKM", coltrt=rxgroup, trts=c(1,2), survTime=time, censor=evt, timePoint=4) > > statKM <- new("steppes") # create a test object based on subpopulation and window > statKM <- estimate(statKM, subp, smodel) # estimate the subpopulation results > # Warning: IT IS RECOMMEND TO USE AT LEAST 2500 PERMUTATIONS TO PROVIDE STABLE RESULTS. > statKM <- test(statKM, nperm = 10) # permutation test with 10 iterations Computing the p-value with 10 number of permutations comparing trt 2 with trt 1 | | | 0% | |======== | 11% | |================ | 22% | |======================= | 33% | |=============================== | 44% | |======================================= | 56% | |=============================================== | 67% | |====================================================== | 78% | |============================================================== | 89% | |======================================================================| 100% > > print(statKM) # print the estimates and test statistics Sample size in treatment 1: 1361 Sample size in treatment 2: 1324 Total sample size (excluding missing data): 2685 Survival estimates for treatment group 1 at time point 4 Survival Subpopulation Probability Std. Err. 1 0.9168 0.0085 (entire cohort) 2 0.9137 0.0091 3 0.9115 0.0094 4 0.9098 0.0097 5 0.9013 0.0107 6 0.8994 0.0111 7 0.9000 0.0115 8 0.9043 0.0123 9 0.8964 0.0140 10 0.8934 0.0153 11 0.8893 0.0171 12 0.8750 0.0208 13 0.8690 0.0278 Survival estimates for treatment group 2 at time point 4 Survival Subpopulation Probability Std. Err. 1 0.8652 0.0106 (entire cohort) 2 0.8588 0.0113 3 0.8533 0.0119 4 0.8517 0.0122 5 0.8488 0.0129 6 0.8520 0.0130 7 0.8459 0.0138 8 0.8344 0.0151 9 0.8153 0.0173 10 0.8005 0.0197 11 0.7919 0.0222 12 0.7907 0.0255 13 0.7641 0.0325 Survival differences at time point and hazard ratio estimates trt 1 vs. trt 2 Survival differences at time point 4 Comparing trt 1 vs. trt 2 Survival Subpopulation Difference Std. Err. 1 0.0516 0.0136 (entire cohort) 2 0.0549 0.0145 3 0.0582 0.0152 4 0.0581 0.0156 5 0.0525 0.0168 6 0.0474 0.0171 7 0.0541 0.0180 8 0.0698 0.0195 9 0.0811 0.0222 10 0.0929 0.0249 11 0.0975 0.0280 12 0.0842 0.0329 13 0.1049 0.0428 Hazard ratio estimates Subpopulation Log HR Std. Err. Hazard Ratio 1 -0.449802 0.114976 0.64 (entire cohort) 2 -0.464386 0.118130 0.63 3 -0.494066 0.120475 0.61 4 -0.488962 0.122283 0.61 5 -0.412010 0.125803 0.66 6 -0.398947 0.128645 0.67 7 -0.448178 0.132867 0.64 8 -0.576706 0.141593 0.56 9 -0.616921 0.148824 0.54 10 -0.679715 0.159064 0.51 11 -0.706408 0.174732 0.49 12 -0.546361 0.197675 0.58 13 -0.651409 0.240905 0.52 The covariance matrix of the Kaplan-Meier differences at 4 time units for the 12 subpopulations is: trt 1 vs. trt 2 SP1-Overall SP3-Overall SP4-Overall SP5-Overall SP1-Overall 0 0.000000e+00 0.000000e+00 0.000000e+00 SP3-Overall 0 3.039907e-05 3.297654e-05 3.702724e-05 SP4-Overall 0 3.297654e-05 4.708006e-05 5.069980e-05 SP5-Overall 0 3.702724e-05 5.069980e-05 7.575835e-05 SP6-Overall 0 4.711366e-05 6.394013e-05 9.126392e-05 SP7-Overall 0 4.755666e-05 6.316805e-05 9.956187e-05 SP8-Overall 0 3.681990e-05 5.899549e-05 1.002788e-04 SP9-Overall 0 8.420519e-06 3.224306e-05 6.235488e-05 SP10-Overall 0 8.514649e-06 3.627291e-06 3.325858e-05 SP11-Overall 0 -1.680875e-05 -5.602913e-05 -2.589146e-05 SP12-Overall 0 -1.996055e-05 -6.197756e-05 -1.291108e-05 SP13-Overall 0 -4.201613e-05 -8.154532e-05 -8.183142e-07 SP6-Overall SP7-Overall SP8-Overall SP9-Overall SP10-Overall SP1-Overall 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 SP3-Overall 4.711366e-05 4.755666e-05 3.681990e-05 8.420519e-06 8.514649e-06 SP4-Overall 6.394013e-05 6.316805e-05 5.899549e-05 3.224306e-05 3.627291e-06 SP5-Overall 9.126392e-05 9.956187e-05 1.002788e-04 6.235488e-05 3.325858e-05 SP6-Overall 1.279519e-04 1.215283e-04 1.219759e-04 6.558957e-05 3.872224e-05 SP7-Overall 1.215283e-04 1.430422e-04 1.553777e-04 9.509161e-05 7.423001e-05 SP8-Overall 1.219759e-04 1.553777e-04 2.088415e-04 1.371618e-04 9.174116e-05 SP9-Overall 6.558957e-05 9.509161e-05 1.371618e-04 1.322444e-04 6.490181e-05 SP10-Overall 3.872224e-05 7.423001e-05 9.174116e-05 6.490181e-05 1.174429e-04 SP11-Overall -2.033695e-05 1.396385e-05 3.038968e-05 -1.137482e-05 1.337482e-04 SP12-Overall 9.681893e-06 5.178515e-05 1.058522e-04 2.249855e-05 1.838945e-04 SP13-Overall 5.523843e-05 8.578617e-05 1.699971e-04 9.628643e-05 2.689859e-04 SP11-Overall SP12-Overall SP13-Overall SP1-Overall 0.000000e+00 0.000000e+00 0.000000e+00 SP3-Overall -1.680875e-05 -1.996055e-05 -4.201613e-05 SP4-Overall -5.602913e-05 -6.197756e-05 -8.154532e-05 SP5-Overall -2.589146e-05 -1.291108e-05 -8.183142e-07 SP6-Overall -2.033695e-05 9.681893e-06 5.523843e-05 SP7-Overall 1.396385e-05 5.178515e-05 8.578617e-05 SP8-Overall 3.038968e-05 1.058522e-04 1.699971e-04 SP9-Overall -1.137482e-05 2.249855e-05 9.628643e-05 SP10-Overall 1.337482e-04 1.838945e-04 2.689859e-04 SP11-Overall 3.114281e-04 4.085902e-04 5.261046e-04 SP12-Overall 4.085902e-04 5.780762e-04 7.707207e-04 SP13-Overall 5.261046e-04 7.707207e-04 1.214412e-03 The covariance matrix of the log hazard ratios for the 12 subpopulations is: SP1-Overall SP3-Overall SP4-Overall SP5-Overall SP6-Overall SP1-Overall 0 0.0000000000 0.0000000000 0.0000000000 0.0000000000 SP3-Overall 0 0.0042445358 0.0041237501 0.0039253769 0.0041672523 SP4-Overall 0 0.0041237501 0.0044491555 0.0046966264 0.0049321965 SP5-Overall 0 0.0039253769 0.0046966264 0.0076834635 0.0081979207 SP6-Overall 0 0.0041672523 0.0049321965 0.0081979207 0.0096941710 SP7-Overall 0 0.0036057782 0.0046326057 0.0082620790 0.0088817573 SP8-Overall 0 0.0031561755 0.0044617663 0.0083874212 0.0090072085 SP9-Overall 0 -0.0017057433 -0.0001975438 0.0035512525 0.0042199367 SP10-Overall 0 0.0015329276 0.0020589425 0.0061386553 0.0070522910 SP11-Overall 0 0.0011027609 -0.0001611569 0.0005492328 0.0010762677 SP12-Overall 0 0.0000104008 -0.0018209033 0.0004519342 0.0009423134 SP13-Overall 0 -0.0017277146 -0.0042402281 -0.0006890373 0.0003652414 SP7-Overall SP8-Overall SP9-Overall SP10-Overall SP11-Overall SP1-Overall 0.0000000000 0.000000000 0.0000000000 0.000000000 0.0000000000 SP3-Overall 0.0036057782 0.003156176 -0.0017057433 0.001532928 0.0011027609 SP4-Overall 0.0046326057 0.004461766 -0.0001975438 0.002058943 -0.0001611569 SP5-Overall 0.0082620790 0.008387421 0.0035512525 0.006138655 0.0005492328 SP6-Overall 0.0088817573 0.009007208 0.0042199367 0.007052291 0.0010762677 SP7-Overall 0.0095204968 0.010884979 0.0059564570 0.008277320 0.0008667649 SP8-Overall 0.0108849790 0.017055863 0.0103617135 0.011897694 0.0017697219 SP9-Overall 0.0059564570 0.010361714 0.0118136740 0.008218874 -0.0008043154 SP10-Overall 0.0082773196 0.011897694 0.0082188742 0.014428337 0.0080349062 SP11-Overall 0.0008667649 0.001769722 -0.0008043154 0.008034906 0.0131522161 SP12-Overall 0.0010494944 0.004344286 -0.0003302752 0.008022517 0.0137072004 SP13-Overall -0.0005980078 0.002625570 -0.0027392735 0.006202976 0.0122729040 SP12-Overall SP13-Overall SP1-Overall 0.0000000000 0.0000000000 SP3-Overall 0.0000104008 -0.0017277146 SP4-Overall -0.0018209033 -0.0042402281 SP5-Overall 0.0004519342 -0.0006890373 SP6-Overall 0.0009423134 0.0003652414 SP7-Overall 0.0010494944 -0.0005980078 SP8-Overall 0.0043442860 0.0026255702 SP9-Overall -0.0003302752 -0.0027392735 SP10-Overall 0.0080225175 0.0062029765 SP11-Overall 0.0137072004 0.0122729040 SP12-Overall 0.0234143366 0.0299895630 SP13-Overall 0.0299895630 0.0485629433 Supremum test results trt 1 vs. trt 2 Interaction p-value based on Kaplan-Meier estimates: NA Interaction p-value based on hazard ratio estimates: NA Chi-square test results Interaction p-value based on Kaplan-Meier estimates: NA > plot(statKM, ncex=0.65, legendy=30, pline=-15.5, color=c("blue","gold"), + pointwise=FALSE, + xlabel="Median Ki-67 LI in Subpopulation (% immunoreactivity)", + ylabel="4-year Disease Free Survival", + tlegend=c("Letrozole", "Tamoxifen"), nlas=3) dev.new(): using pdf(file="Rplots5.pdf") dev.new(): using pdf(file="Rplots6.pdf") > > ### Example for single group analysis ### > library(stepp) > > data(bigKM) > > # bigKM$ki67[1:80] <- NA > # cov_na <- which(is.na(bigKM$ki67)) > # bigKM <- bigKM[-cov_na, ] > > rxgroup <- bigKM$trt > time <- bigKM$time > evt <- bigKM$event > cov <- bigKM$ki67 > > # analyze using Cumulative Incidence method with > # sliding window size of 150 patients and a maximum of 50 patients in common > # > nsubpop_tmp <- 10 > win_tmp <- gen.tailwin(cov, nsub = nsubpop_tmp, dir = "GE") > nsubpop <- length(win_tmp$v) > swin <- new("stwin", type = "tail-oriented", r1 = rep(max(cov), nsubpop), r2 = win_tmp$v) # create a tail-oriented window > subp <- new("stsubpop") # create subpopulation object > subp <- generate(subp, win = swin, covariate = cov) # generate the subpopulations > summary(subp) # summary of the subpopulations Window type: tail-oriented Subpopulation for patients less than or equal to: 90 Subpopulation for patients greater than or equal to: 3 4 5 6 7 8 10 12 14 16 19 24 Number of subpopulations created: 13 Subpopulation summary information (including all treatments) Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 10.00 0.0000 90.0000 2685 (entire cohort) 2 12.00 3.0000 90.0000 2443 3 12.00 4.0000 90.0000 2302 4 13.00 5.0000 90.0000 2196 5 14.00 6.0000 90.0000 1972 6 15.00 7.0000 90.0000 1870 7 15.00 8.0000 90.0000 1721 8 17.00 10.0000 90.0000 1496 9 19.00 12.0000 90.0000 1252 10 20.00 14.0000 90.0000 1052 11 23.00 16.0000 90.0000 847 12 25.00 19.0000 90.0000 638 13 31.00 24.0000 90.0000 405 > > # create a stepp model using Kaplan Meier Method to analyze the data > # > smodel <- new("stmodelKM", survTime=time, censor=evt, timePoint=4) > > statKM <- new("steppes") # create a test object based on subpopulation and window > statKM <- estimate(statKM, subp, smodel) # estimate the subpopulation results > statKM <- test(statKM, nperm = 10) # permutation test with 10 iterations > > print(statKM) # print the estimates and test statistics Total sample size (excluding missing data): 2685 Survival estimates at time point 4 Survival Subpopulation Probability Std. Err. 1 0.8913 0.0068 (entire cohort) 2 0.8864 0.0073 3 0.8827 0.0076 4 0.8811 0.0078 5 0.8751 0.0084 6 0.8759 0.0085 7 0.8733 0.0090 8 0.8696 0.0098 9 0.8561 0.0112 10 0.8484 0.0125 11 0.8425 0.0140 12 0.8344 0.0164 13 0.8158 0.0216 > plot(statKM, ncex=0.65, pline=-15.5, + xlabel="Median Ki-67 LI in Subpopulation (% immunoreactivity)", + ylabel="Survival Estimates", + nlas=3, subplot = TRUE) > > ### > > data(bigCI) > > rxgroup <- bigCI$trt > time <- bigCI$time > evt <- bigCI$event > cov <- bigCI$ki67 > > # analyze using Cumulative Incidence method with > # sliding window size of 150 patients and a maximum of 50 patients in common > # > swin <- new("stwin", type="sliding", r1=50, r2=150) # create a sliding window > subp <- new("stsubpop") # create subpopulation object > subp <- generate(subp, win=swin, covariate=cov) # generate the subpopulations > summary(subp) # summary of the subpopulations Window type: sliding Number of patients per subpopulation (patspop r2): 150 Largest number of patients in common among consecutive subpopulations (minpatspop r1): 50 Number of subpopulations created: 14 Subpopulation summary information (including all treatments) Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 5.00 4.0000 5.0000 330 4 7.00 6.0000 7.0000 251 5 8.00 8.0000 9.0000 225 6 10.00 10.0000 10.0000 182 7 12.00 11.0000 12.0000 207 8 15.00 13.0000 15.0000 260 9 17.00 16.0000 18.0000 209 10 20.00 19.0000 21.0000 174 11 23.00 21.0000 25.0000 200 12 30.00 26.0000 34.0000 152 13 36.00 31.0000 45.0000 159 14 47.00 41.0000 90.0000 83 > > # create a stepp model using Cumulative Incidences to analyze the data > # > smodel <- new("stmodelCI", coltime=time, coltype=evt, timePoint=4) > > statCI <- new("steppes") # create a test object based on subpopulation and window > statCI <- estimate(statCI, subp, smodel) # estimate the subpo10ulation results > # Warning: In this example, the permutations have been set to 0 to allow the function > # to finish in a short amount of time. IT IS RECOMMEND TO USE AT LEAST 2500 PERMUTATIONS TO > # PROVIDE STABLE RESULTS. > statCI <- test(statCI, nperm=10) # permutation test with 0 iterations > > print(statCI) # print the estimates and test statistics Total sample size (excluding missing data): 2685 Cumulative incidence estimates at time point 4 Cumulative Subpopulation Incidence Std. Err. 1 0.0421 0.0173 2 0.0159 0.0092 3 0.0324 0.0110 4 0.0807 0.0207 5 0.0367 0.0143 6 0.0266 0.0134 7 0.0674 0.0198 8 0.0756 0.0182 9 0.0804 0.0195 10 0.0989 0.0249 11 0.1145 0.0271 12 0.0897 0.0273 13 0.1784 0.0344 14 0.2592 0.0531 Overall 0.0713 0.0056 > plot(statCI, ncex=0.65, pline=-15.5, + xlabel="Median Ki-67 LI in Subpopulation (% immunoreactivity)", + ylabel="4-year Cumulative Incidence", + nlas=3, subplot = TRUE) > > ### > > data(aspirin) > > # remove cases with missing data > aspirinc <- aspirin[complete.cases(aspirin), ] > > # make a subset of patients with placebo and 81 mg > attach(aspirinc) > subset1 <- DOSE == 0 | DOSE == 81 > aspirin1 <- aspirinc[subset1,] > detach(aspirinc) > > # set up treatment assignment > trtA <- rep(0, dim(aspirin1)[1]) > trtA[aspirin1[,"DOSE"] == 81] <- 1 > > # STEPP analysis A: placebo vs 81 mg aspirin > inc_win <- stepp.win(type="sliding", r1=30, r2=100) > inc_sp <- stepp.subpop(swin=inc_win, cov=aspirin1$AGE) > > ADorLE <- as.numeric(aspirin1$AD==1 | aspirin1$AL==1) > modelA <- stepp.GLM(colY = ADorLE, glm = "binomial", link = "logit") > # Warning: In this example, the permutations have been set to 50 to allow the function > # to finish in a short amount of time. IT IS RECOMMEND TO USE AT LEAST 2500 PERMUTATIONS TO > # PROVIDE STABLE RESULTS. > statGLM <- new("steppes") # create a test object based on subpopulation and window > statGLM <- estimate(statGLM, inc_sp, modelA) # estimate the subpopulation results > # Warning: In this example, the permutations have been set to 0 to allow the function > # to finish in a short amount of time. IT IS RECOMMEND TO USE AT LEAST 2500 PERMUTATIONS TO > # PROVIDE STABLE RESULTS. > statGLM <- test(statGLM, nperm=10) # permutation test with 0 iterations > > print(statGLM) # print the estimates and test statistics Total sample size (excluding missing data): 729 Risk estimates Subpopulation Risk Std. Err. 1 0.3458 0.0460 2 0.3516 0.0422 3 0.4407 0.0457 4 0.4409 0.0441 5 0.4435 0.0463 6 0.4757 0.0492 7 0.4752 0.0497 8 0.5618 0.0526 Overall 0.4266 0.0183 > plot(statGLM, ncex=0.70, legendy=30, pline=-4.5, + xlabel="Subpopulations by Median Age", ylabel="Risk", + nlas=3, noyscale=TRUE, subplot=TRUE) > > ### Example for balanced subpopulations ### > library(stepp) > > data(bigKM) > > rxgroup <- bigKM$trt > time <- bigKM$time > evt <- bigKM$event > cov <- bigKM$ki67 > > res <- balance_patients(range.r1 = c(30, 100), range.r2 = c(50, 300), + maxnsubpops = 100, covar = cov, verbose = TRUE, + plot = TRUE, contour = FALSE) Searching for best values of r1 and r2 in each subpopulation... | | | 0% | | | 1% | |= | 1% | |= | 2% | |== | 2% | |== | 3% | |== | 4% | |=== | 4% | |=== | 5% | |==== | 5% | |==== | 6% | |===== | 6% | |===== | 7% | |===== | 8% | |====== | 8% | |====== | 9% | |======= | 9% | |======= | 10% | |======= | 11% | |======== | 11% | |======== | 12% | |========= | 12% | |========= 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|==================================================================== | 96% | |==================================================================== | 97% | |==================================================================== | 98% | |===================================================================== | 98% | |===================================================================== | 99% | |======================================================================| 99% | |======================================================================| 100% Balanced subpopulations determination (number of patients) Range for number of patients in common in consecutive subpopulations (r1): 30 <--> 100 Range for number of patients per subpopulation (r2): 50 <--> 300 Best result for 8 subpopulations * Optimal r1 value: 44 * Optimal r2 value: 275 * Minimum variance of subpopulation sizes achieved: 2553.554 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 2.00 0.0000 3.0000 383 2 5.00 4.0000 5.0000 330 3 7.00 6.0000 8.0000 387 4 10.00 9.0000 11.0000 333 5 14.00 12.0000 15.0000 405 6 18.00 16.0000 20.0000 336 7 25.00 21.0000 30.0000 306 8 36.00 29.0000 90.0000 249 Best result for 9 subpopulations * Optimal r1 value: 91 * Optimal r2 value: 293 * Minimum variance of subpopulation sizes achieved: 1085.278 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 2.00 0.0000 3.0000 383 2 5.00 4.0000 5.0000 330 3 7.00 6.0000 8.0000 387 4 10.00 9.0000 11.0000 333 5 12.00 11.0000 14.0000 329 6 15.00 14.0000 17.0000 315 7 19.00 17.0000 21.0000 304 8 25.00 21.0000 30.0000 306 9 35.00 27.0000 90.0000 296 Best result for 10 subpopulations * Optimal r1 value: 94 * Optimal r2 value: 282 * Minimum variance of subpopulation sizes achieved: 2841.956 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 2.00 0.0000 3.0000 383 2 5.00 4.0000 5.0000 330 3 7.00 6.0000 8.0000 387 4 10.00 9.0000 11.0000 333 5 12.00 11.0000 14.0000 329 6 15.00 14.0000 16.0000 284 7 18.00 16.0000 20.0000 336 8 22.00 20.0000 25.0000 291 9 28.00 24.0000 37.0000 284 10 39.00 31.0000 90.0000 205 Best result for 11 subpopulations * Optimal r1 value: 61 * Optimal r2 value: 242 * Minimum variance of subpopulation sizes achieved: 635.8545 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 3.0000 4.0000 247 3 5.00 5.0000 6.0000 326 4 7.00 7.0000 8.0000 285 5 10.00 9.0000 10.0000 271 6 12.00 11.0000 13.0000 262 7 15.00 13.0000 15.0000 260 8 18.00 16.0000 19.0000 245 9 21.00 19.0000 24.0000 269 10 26.00 23.0000 32.0000 253 11 38.00 30.0000 90.0000 237 Best result for 12 subpopulations * Optimal r1 value: 60 * Optimal r2 value: 201 * Minimum variance of subpopulation sizes achieved: 745.0909 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 3.0000 4.0000 247 3 5.00 5.0000 5.0000 224 4 7.00 6.0000 7.0000 251 5 8.00 8.0000 9.0000 225 6 10.00 10.0000 11.0000 244 7 12.00 12.0000 14.0000 267 8 15.00 15.0000 16.0000 217 9 18.00 17.0000 20.0000 257 10 24.00 21.0000 26.0000 215 11 30.00 26.0000 38.0000 203 12 40.00 34.0000 90.0000 168 Best result for 13 subpopulations * Optimal r1 value: 65 * Optimal r2 value: 186 * Minimum variance of subpopulation sizes achieved: 560.2308 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 3.0000 4.0000 247 3 5.00 5.0000 5.0000 224 4 7.00 6.0000 7.0000 251 5 8.00 8.0000 9.0000 225 6 10.00 10.0000 11.0000 244 7 12.00 11.0000 12.0000 207 8 15.00 13.0000 15.0000 260 9 17.00 16.0000 18.0000 209 10 20.00 19.0000 22.0000 208 11 25.00 22.0000 28.0000 215 12 30.00 26.0000 36.0000 187 13 40.00 32.0000 90.0000 189 Best result for 14 subpopulations * Optimal r1 value: 99 * Optimal r2 value: 208 * Minimum variance of subpopulation sizes achieved: 1008.027 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 4.0000 313 3 5.00 5.0000 5.0000 224 4 7.00 6.0000 7.0000 251 5 8.00 8.0000 9.0000 225 6 10.00 9.0000 10.0000 271 7 12.00 11.0000 13.0000 262 8 15.00 13.0000 15.0000 260 9 17.00 16.0000 18.0000 209 10 19.00 18.0000 20.0000 226 11 21.00 20.0000 24.0000 233 12 25.00 22.0000 28.0000 215 13 30.00 26.0000 39.0000 209 14 40.00 32.0000 90.0000 189 Best result for 15 subpopulations * Optimal r1 value: 99 * Optimal r2 value: 181 * Minimum variance of subpopulation sizes achieved: 1868.829 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 2.0000 242 2 3.00 2.0000 3.0000 207 3 5.00 4.0000 5.0000 330 4 7.00 6.0000 7.0000 251 5 8.00 8.0000 9.0000 225 6 10.00 9.0000 10.0000 271 7 12.00 11.0000 12.0000 207 8 15.00 13.0000 15.0000 260 9 17.00 16.0000 18.0000 209 10 19.00 18.0000 20.0000 226 11 21.00 20.0000 23.0000 197 12 24.00 22.0000 27.0000 181 13 28.00 25.0000 32.0000 192 14 35.00 29.0000 43.0000 182 15 41.00 35.0000 90.0000 159 Best result for 16 subpopulations * Optimal r1 value: 99 * Optimal r2 value: 169 * Minimum variance of subpopulation sizes achieved: 2359.529 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 5.00 4.0000 5.0000 330 4 7.00 6.0000 7.0000 251 5 8.00 8.0000 9.0000 225 6 10.00 9.0000 10.0000 271 7 12.00 11.0000 12.0000 207 8 15.00 13.0000 15.0000 260 9 17.00 16.0000 18.0000 209 10 19.00 18.0000 20.0000 226 11 20.00 20.0000 22.0000 172 12 23.00 21.0000 25.0000 200 13 26.00 24.0000 30.0000 200 14 30.00 27.0000 36.0000 172 15 38.00 31.0000 50.0000 177 16 44.50 37.0000 90.0000 124 Best result for 17 subpopulations * Optimal r1 value: 99 * Optimal r2 value: 151 * Minimum variance of subpopulation sizes achieved: 2752.684 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 5.00 4.0000 5.0000 330 4 7.00 6.0000 7.0000 251 5 8.00 8.0000 9.0000 225 6 10.00 9.0000 10.0000 271 7 12.00 11.0000 12.0000 207 8 15.00 13.0000 15.0000 260 9 17.00 16.0000 18.0000 209 10 19.00 18.0000 20.0000 226 11 20.00 20.0000 22.0000 172 12 23.00 21.0000 25.0000 200 13 25.00 24.0000 28.0000 156 14 30.00 26.0000 34.0000 152 15 34.00 29.0000 40.0000 166 16 40.00 33.0000 53.0000 152 17 44.50 37.0000 90.0000 124 Best result for 18 subpopulations * Optimal r1 value: 31 * Optimal r2 value: 105 * Minimum variance of subpopulation sizes achieved: 2954.118 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 7.00 6.0000 7.0000 251 6 8.00 8.0000 8.0000 136 7 10.00 9.0000 10.0000 271 8 12.00 11.0000 12.0000 207 9 14.00 13.0000 14.0000 122 10 15.00 15.0000 15.0000 138 11 16.00 16.0000 17.0000 110 12 18.00 17.0000 18.0000 130 13 20.00 19.0000 20.0000 127 14 22.00 21.0000 23.0000 106 15 24.00 23.0000 25.0000 119 16 28.00 26.0000 30.0000 106 17 35.00 31.0000 40.0000 122 18 45.00 39.0000 90.0000 108 Best result for 19 subpopulations * Optimal r1 value: 30 * Optimal r2 value: 100 * Minimum variance of subpopulation sizes achieved: 2837.287 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 6.00 6.0000 6.0000 102 6 7.00 7.0000 7.0000 149 7 8.00 8.0000 8.0000 136 8 10.00 9.0000 10.0000 271 9 12.00 11.0000 12.0000 207 10 14.00 13.0000 14.0000 122 11 15.00 15.0000 15.0000 138 12 16.00 16.0000 17.0000 110 13 18.00 18.0000 19.0000 135 14 20.00 20.0000 21.0000 138 15 24.00 22.0000 25.0000 153 16 28.00 26.0000 30.0000 106 17 35.00 31.0000 39.0000 103 18 41.00 36.0000 50.0000 103 19 55.00 46.0000 90.0000 46 Best result for 20 subpopulations * Optimal r1 value: 44 * Optimal r2 value: 102 * Minimum variance of subpopulation sizes achieved: 2333.147 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 6.00 6.0000 6.0000 102 6 7.00 7.0000 7.0000 149 7 8.00 8.0000 8.0000 136 8 10.00 9.0000 10.0000 271 9 12.00 11.0000 12.0000 207 10 14.00 13.0000 14.0000 122 11 15.00 15.0000 15.0000 138 12 16.00 16.0000 17.0000 110 13 18.00 17.0000 18.0000 130 14 20.00 19.0000 20.0000 127 15 22.00 21.0000 23.0000 106 16 24.00 23.0000 25.0000 119 17 28.00 26.0000 30.0000 106 18 31.00 29.0000 35.0000 118 19 38.00 34.0000 44.0000 106 20 45.00 40.0000 90.0000 102 Best result for 21 subpopulations * Optimal r1 value: 31 * Optimal r2 value: 85 * Minimum variance of subpopulation sizes achieved: 1824.19 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 6.00 6.0000 6.0000 102 6 7.00 7.0000 7.0000 149 7 8.00 8.0000 8.0000 136 8 9.00 9.0000 9.0000 89 9 10.00 10.0000 10.0000 182 10 12.00 11.0000 12.0000 207 11 14.00 13.0000 14.0000 122 12 15.00 15.0000 15.0000 138 13 16.00 16.0000 17.0000 110 14 18.00 17.0000 18.0000 130 15 20.00 19.0000 20.0000 127 16 22.00 21.0000 23.0000 106 17 24.00 23.0000 25.0000 119 18 28.00 26.0000 30.0000 106 19 35.00 31.0000 38.0000 97 20 40.00 36.0000 45.0000 85 21 50.00 42.0000 90.0000 77 Best result for 22 subpopulations * Optimal r1 value: 46 * Optimal r2 value: 88 * Minimum variance of subpopulation sizes achieved: 1771.481 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 6.00 6.0000 6.0000 102 6 7.00 7.0000 7.0000 149 7 8.00 8.0000 8.0000 136 8 9.00 9.0000 9.0000 89 9 10.00 10.0000 10.0000 182 10 12.00 11.0000 12.0000 207 11 14.00 13.0000 14.0000 122 12 15.00 15.0000 15.0000 138 13 16.00 16.0000 17.0000 110 14 18.00 17.0000 18.0000 130 15 20.00 19.0000 20.0000 127 16 22.00 21.0000 23.0000 106 17 24.00 23.0000 25.0000 119 18 28.00 26.0000 30.0000 106 19 31.00 29.0000 34.0000 90 20 35.00 31.0000 38.0000 97 21 40.00 36.0000 47.0000 90 22 47.00 41.0000 90.0000 83 Best result for 23 subpopulations * Optimal r1 value: 55 * Optimal r2 value: 86 * Minimum variance of subpopulation sizes achieved: 1749.862 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 6.00 6.0000 6.0000 102 6 7.00 7.0000 7.0000 149 7 8.00 8.0000 8.0000 136 8 9.00 9.0000 9.0000 89 9 10.00 10.0000 10.0000 182 10 12.00 11.0000 12.0000 207 11 14.00 13.0000 14.0000 122 12 15.00 15.0000 15.0000 138 13 16.00 16.0000 17.0000 110 14 18.00 17.0000 18.0000 130 15 20.00 19.0000 20.0000 127 16 22.00 21.0000 23.0000 106 17 24.00 23.0000 25.0000 119 18 28.00 26.0000 30.0000 106 19 31.00 29.0000 34.0000 90 20 35.00 31.0000 38.0000 97 21 38.00 35.0000 42.0000 89 22 42.00 37.0000 50.0000 96 23 47.00 41.0000 90.0000 83 Best result for 24 subpopulations * Optimal r1 value: 58 * Optimal r2 value: 87 * Minimum variance of subpopulation sizes achieved: 1718.174 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 6.00 6.0000 6.0000 102 6 7.00 7.0000 7.0000 149 7 8.00 8.0000 8.0000 136 8 9.00 9.0000 9.0000 89 9 10.00 10.0000 10.0000 182 10 12.00 11.0000 12.0000 207 11 14.00 13.0000 14.0000 122 12 15.00 15.0000 15.0000 138 13 16.00 16.0000 17.0000 110 14 18.00 17.0000 18.0000 130 15 20.00 19.0000 20.0000 127 16 22.00 21.0000 23.0000 106 17 24.00 23.0000 25.0000 119 18 26.00 25.0000 28.0000 120 19 28.00 27.0000 30.0000 91 20 31.00 29.0000 34.0000 90 21 35.00 31.0000 38.0000 97 22 38.00 35.0000 42.0000 89 23 42.00 37.0000 50.0000 96 24 47.00 41.0000 90.0000 83 Best result for 25 subpopulations * Optimal r1 value: 59 * Optimal r2 value: 87 * Minimum variance of subpopulation sizes achieved: 1735.823 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 6.00 6.0000 6.0000 102 6 7.00 7.0000 7.0000 149 7 8.00 8.0000 8.0000 136 8 9.00 9.0000 9.0000 89 9 10.00 10.0000 10.0000 182 10 12.00 11.0000 12.0000 207 11 14.00 13.0000 14.0000 122 12 15.00 15.0000 15.0000 138 13 16.00 16.0000 17.0000 110 14 18.00 17.0000 18.0000 130 15 20.00 19.0000 20.0000 127 16 22.00 21.0000 23.0000 106 17 23.00 22.0000 24.0000 95 18 25.00 24.0000 25.0000 94 19 26.00 25.0000 28.0000 120 20 28.00 27.0000 30.0000 91 21 31.00 29.0000 34.0000 90 22 35.00 31.0000 38.0000 97 23 38.00 35.0000 42.0000 89 24 42.00 37.0000 50.0000 96 25 47.00 41.0000 90.0000 83 Best result for 26 subpopulations * Optimal r1 value: 64 * Optimal r2 value: 87 * Minimum variance of subpopulation sizes achieved: 1671.454 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 6.00 6.0000 6.0000 102 6 7.00 7.0000 7.0000 149 7 8.00 8.0000 8.0000 136 8 9.00 9.0000 9.0000 89 9 10.00 10.0000 10.0000 182 10 12.00 11.0000 12.0000 207 11 14.00 13.0000 14.0000 122 12 15.00 15.0000 15.0000 138 13 16.00 16.0000 17.0000 110 14 18.00 17.0000 18.0000 130 15 20.00 19.0000 20.0000 127 16 22.00 21.0000 23.0000 106 17 23.00 22.0000 24.0000 95 18 24.00 23.0000 25.0000 119 19 26.00 25.0000 28.0000 120 20 28.00 26.0000 30.0000 106 21 31.00 29.0000 34.0000 90 22 35.00 31.0000 38.0000 97 23 37.00 34.0000 41.0000 91 24 40.00 36.0000 46.0000 87 25 44.00 39.0000 55.0000 88 26 47.00 41.0000 90.0000 83 Best result for 27 subpopulations * Optimal r1 value: 76 * Optimal r2 value: 89 * Minimum variance of subpopulation sizes achieved: 1871.949 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 6.00 6.0000 6.0000 102 6 7.00 7.0000 7.0000 149 7 8.00 8.0000 8.0000 136 8 9.00 9.0000 9.0000 89 9 10.00 10.0000 10.0000 182 10 12.00 11.0000 12.0000 207 11 14.00 13.0000 14.0000 122 12 15.00 14.0000 15.0000 205 13 16.00 16.0000 17.0000 110 14 18.00 17.0000 18.0000 130 15 20.00 19.0000 20.0000 127 16 22.00 21.0000 23.0000 106 17 23.00 22.0000 24.0000 95 18 24.00 23.0000 25.0000 119 19 26.00 25.0000 28.0000 120 20 28.00 26.0000 30.0000 106 21 31.00 29.0000 34.0000 90 22 35.00 31.0000 38.0000 97 23 36.00 33.0000 40.0000 94 24 38.00 35.0000 42.0000 89 25 40.00 36.0000 47.0000 90 26 44.00 39.0000 58.0000 89 27 47.00 41.0000 90.0000 83 Best result for 28 subpopulations * Optimal r1 value: 77 * Optimal r2 value: 87 * Minimum variance of subpopulation sizes achieved: 1848.852 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 6.00 6.0000 6.0000 102 6 7.00 7.0000 7.0000 149 7 8.00 8.0000 8.0000 136 8 9.00 9.0000 9.0000 89 9 10.00 10.0000 10.0000 182 10 12.00 11.0000 12.0000 207 11 14.00 13.0000 14.0000 122 12 15.00 14.0000 15.0000 205 13 16.00 16.0000 17.0000 110 14 18.00 17.0000 18.0000 130 15 20.00 19.0000 20.0000 127 16 22.00 21.0000 23.0000 106 17 23.00 22.0000 24.0000 95 18 24.00 23.0000 25.0000 119 19 26.00 25.0000 28.0000 120 20 28.00 26.0000 30.0000 106 21 31.00 29.0000 34.0000 90 22 35.00 31.0000 38.0000 97 23 36.00 33.0000 40.0000 94 24 38.00 35.0000 42.0000 89 25 40.00 36.0000 46.0000 87 26 42.00 38.0000 50.0000 93 27 45.00 40.0000 60.0000 91 28 47.00 41.0000 90.0000 83 Best result for 29 subpopulations * Optimal r1 value: 78 * Optimal r2 value: 89 * Minimum variance of subpopulation sizes achieved: 1792.123 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 6.00 6.0000 6.0000 102 6 7.00 7.0000 7.0000 149 7 8.00 8.0000 8.0000 136 8 9.00 9.0000 9.0000 89 9 10.00 10.0000 10.0000 182 10 12.00 11.0000 12.0000 207 11 14.00 13.0000 14.0000 122 12 15.00 14.0000 15.0000 205 13 16.00 16.0000 17.0000 110 14 18.00 17.0000 18.0000 130 15 20.00 19.0000 20.0000 127 16 22.00 21.0000 23.0000 106 17 23.00 22.0000 24.0000 95 18 24.00 23.0000 25.0000 119 19 26.00 25.0000 28.0000 120 20 28.00 26.0000 30.0000 106 21 30.00 28.0000 31.0000 94 22 31.00 29.0000 34.0000 90 23 32.00 30.0000 35.0000 106 24 35.00 31.0000 38.0000 97 25 36.00 33.0000 40.0000 94 26 38.00 35.0000 42.0000 89 27 40.00 36.0000 47.0000 90 28 44.00 39.0000 58.0000 89 29 47.00 41.0000 90.0000 83 Best result for 30 subpopulations * Optimal r1 value: 81 * Optimal r2 value: 89 * Minimum variance of subpopulation sizes achieved: 1745.661 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 6.00 6.0000 6.0000 102 6 7.00 7.0000 7.0000 149 7 8.00 8.0000 8.0000 136 8 9.00 9.0000 9.0000 89 9 10.00 10.0000 10.0000 182 10 12.00 11.0000 12.0000 207 11 14.00 13.0000 14.0000 122 12 15.00 14.0000 15.0000 205 13 16.00 16.0000 17.0000 110 14 18.00 17.0000 18.0000 130 15 20.00 19.0000 20.0000 127 16 22.00 21.0000 23.0000 106 17 23.00 22.0000 24.0000 95 18 24.00 23.0000 25.0000 119 19 26.00 25.0000 28.0000 120 20 28.00 26.0000 30.0000 106 21 30.00 28.0000 31.0000 94 22 31.00 29.0000 34.0000 90 23 32.00 30.0000 35.0000 106 24 35.00 31.0000 38.0000 97 25 35.00 32.0000 40.0000 106 26 38.00 35.0000 42.0000 89 27 40.00 36.0000 47.0000 90 28 42.00 38.0000 50.0000 93 29 44.00 39.0000 58.0000 89 30 47.00 41.0000 90.0000 83 Best result for 31 subpopulations * Optimal r1 value: 83 * Optimal r2 value: 89 * Minimum variance of subpopulation sizes achieved: 1719.206 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 6.00 6.0000 6.0000 102 6 7.00 7.0000 7.0000 149 7 8.00 8.0000 8.0000 136 8 9.00 9.0000 9.0000 89 9 10.00 10.0000 10.0000 182 10 12.00 11.0000 12.0000 207 11 14.00 13.0000 14.0000 122 12 15.00 14.0000 15.0000 205 13 16.00 16.0000 17.0000 110 14 18.00 17.0000 18.0000 130 15 20.00 19.0000 20.0000 127 16 22.00 21.0000 23.0000 106 17 23.00 22.0000 24.0000 95 18 24.00 23.0000 25.0000 119 19 26.00 25.0000 28.0000 120 20 28.00 26.0000 30.0000 106 21 30.00 28.0000 31.0000 94 22 31.00 29.0000 34.0000 90 23 32.00 30.0000 35.0000 106 24 35.00 31.0000 38.0000 97 25 35.00 32.0000 40.0000 106 26 38.00 35.0000 42.0000 89 27 40.00 36.0000 47.0000 90 28 42.00 37.0000 50.0000 96 29 44.00 39.0000 58.0000 89 30 45.00 40.0000 60.0000 91 31 47.00 41.0000 90.0000 83 Best result for 32 subpopulations * Optimal r1 value: 85 * Optimal r2 value: 89 * Minimum variance of subpopulation sizes achieved: 1698.113 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 6.00 6.0000 6.0000 102 6 7.00 7.0000 7.0000 149 7 8.00 8.0000 8.0000 136 8 9.00 9.0000 9.0000 89 9 10.00 10.0000 10.0000 182 10 12.00 11.0000 12.0000 207 11 14.00 13.0000 14.0000 122 12 15.00 14.0000 15.0000 205 13 16.00 16.0000 17.0000 110 14 18.00 17.0000 18.0000 130 15 20.00 19.0000 20.0000 127 16 22.00 21.0000 23.0000 106 17 23.00 22.0000 24.0000 95 18 24.00 23.0000 25.0000 119 19 26.00 25.0000 28.0000 120 20 28.00 26.0000 30.0000 106 21 30.00 28.0000 31.0000 94 22 31.00 29.0000 34.0000 90 23 32.00 30.0000 35.0000 106 24 35.00 31.0000 38.0000 97 25 35.00 32.0000 40.0000 106 26 37.00 34.0000 41.0000 91 27 38.00 35.0000 42.0000 89 28 40.00 36.0000 47.0000 90 29 42.00 37.0000 50.0000 96 30 44.00 39.0000 58.0000 89 31 45.00 40.0000 60.0000 91 32 47.00 41.0000 90.0000 83 Best result for 33 subpopulations * Optimal r1 value: 85 * Optimal r2 value: 87 * Minimum variance of subpopulation sizes achieved: 1709.256 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 3.00 2.0000 3.0000 207 3 4.00 4.0000 4.0000 106 4 5.00 5.0000 5.0000 224 5 6.00 6.0000 6.0000 102 6 7.00 7.0000 7.0000 149 7 8.00 8.0000 8.0000 136 8 9.00 9.0000 9.0000 89 9 10.00 10.0000 10.0000 182 10 12.00 11.0000 12.0000 207 11 14.00 13.0000 14.0000 122 12 15.00 14.0000 15.0000 205 13 16.00 16.0000 17.0000 110 14 18.00 17.0000 18.0000 130 15 20.00 19.0000 20.0000 127 16 22.00 21.0000 23.0000 106 17 23.00 22.0000 24.0000 95 18 24.00 23.0000 25.0000 119 19 26.00 25.0000 28.0000 120 20 28.00 26.0000 30.0000 106 21 30.00 28.0000 31.0000 94 22 31.00 29.0000 34.0000 90 23 32.00 30.0000 35.0000 106 24 35.00 31.0000 38.0000 97 25 35.00 32.0000 39.0000 87 26 36.00 33.0000 40.0000 94 27 37.00 34.0000 41.0000 91 28 38.00 35.0000 42.0000 89 29 40.00 36.0000 46.0000 87 30 42.00 37.0000 50.0000 96 31 44.00 39.0000 55.0000 88 32 45.00 40.0000 60.0000 91 33 47.00 41.0000 90.0000 83 Best result for 34 subpopulations * Optimal r1 value: 57 * Optimal r2 value: 61 * Minimum variance of subpopulation sizes achieved: 1769.583 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 2.00 2.0000 2.0000 66 3 3.00 3.0000 3.0000 141 4 4.00 4.0000 4.0000 106 5 5.00 5.0000 5.0000 224 6 6.00 6.0000 6.0000 102 7 7.00 7.0000 7.0000 149 8 8.00 8.0000 8.0000 136 9 9.00 9.0000 9.0000 89 10 10.00 10.0000 10.0000 182 11 11.00 11.0000 11.0000 62 12 12.00 12.0000 12.0000 145 13 14.00 13.0000 14.0000 122 14 15.00 15.0000 15.0000 138 15 16.00 16.0000 16.0000 79 16 18.00 17.0000 18.0000 130 17 20.00 19.0000 20.0000 127 18 21.00 21.0000 22.0000 81 19 23.00 22.0000 24.0000 95 20 25.00 24.0000 25.0000 94 21 28.00 26.0000 28.0000 62 22 28.00 27.0000 30.0000 91 23 30.00 29.0000 32.0000 72 24 33.50 31.0000 35.0000 74 25 35.00 33.0000 38.0000 69 26 37.50 35.0000 40.0000 76 27 40.00 36.0000 42.0000 61 28 40.00 37.0000 44.0000 62 29 41.50 39.0000 45.0000 62 30 42.00 40.0000 47.0000 61 31 45.00 41.0000 55.0000 63 32 46.50 42.0000 60.0000 66 33 50.00 44.0000 71.0000 61 34 50.00 45.0000 90.0000 62 Best result for 35 subpopulations * Optimal r1 value: 57 * Optimal r2 value: 60 * Minimum variance of subpopulation sizes achieved: 1787.316 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 2.00 2.0000 2.0000 66 3 3.00 3.0000 3.0000 141 4 4.00 4.0000 4.0000 106 5 5.00 5.0000 5.0000 224 6 6.00 6.0000 6.0000 102 7 7.00 7.0000 7.0000 149 8 8.00 8.0000 8.0000 136 9 9.00 9.0000 9.0000 89 10 10.00 10.0000 10.0000 182 11 11.00 11.0000 11.0000 62 12 12.00 12.0000 12.0000 145 13 14.00 13.0000 14.0000 122 14 15.00 15.0000 15.0000 138 15 16.00 16.0000 16.0000 79 16 18.00 17.0000 18.0000 130 17 20.00 19.0000 20.0000 127 18 21.00 21.0000 22.0000 81 19 23.00 22.0000 24.0000 95 20 25.00 24.0000 25.0000 94 21 28.00 26.0000 28.0000 62 22 28.00 27.0000 30.0000 91 23 30.00 29.0000 31.0000 60 24 30.00 30.0000 32.0000 60 25 33.50 31.0000 35.0000 74 26 35.00 33.0000 38.0000 69 27 37.50 35.0000 40.0000 76 28 40.00 36.0000 42.0000 61 29 40.00 37.0000 44.0000 62 30 41.50 39.0000 45.0000 62 31 42.00 40.0000 47.0000 61 32 45.00 41.0000 55.0000 63 33 46.50 42.0000 60.0000 66 34 50.00 44.0000 70.0000 60 35 50.00 45.0000 90.0000 62 Best result for 36 subpopulations * Optimal r1 value: 59 * Optimal r2 value: 62 * Minimum variance of subpopulation sizes achieved: 1683.454 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 2.00 2.0000 2.0000 66 3 3.00 3.0000 3.0000 141 4 4.00 4.0000 4.0000 106 5 5.00 5.0000 5.0000 224 6 6.00 6.0000 6.0000 102 7 7.00 7.0000 7.0000 149 8 8.00 8.0000 8.0000 136 9 9.00 9.0000 9.0000 89 10 10.00 10.0000 10.0000 182 11 11.00 11.0000 11.0000 62 12 12.00 12.0000 12.0000 145 13 14.00 13.0000 14.0000 122 14 15.00 15.0000 15.0000 138 15 16.00 16.0000 16.0000 79 16 18.00 17.0000 18.0000 130 17 20.00 19.0000 20.0000 127 18 21.00 21.0000 22.0000 81 19 23.00 22.0000 24.0000 95 20 25.00 24.0000 25.0000 94 21 25.00 25.0000 26.0000 73 22 28.00 26.0000 28.0000 62 23 28.00 27.0000 30.0000 91 24 30.00 29.0000 32.0000 72 25 33.50 31.0000 35.0000 74 26 35.00 32.0000 36.0000 65 27 35.00 33.0000 38.0000 69 28 37.50 35.0000 40.0000 76 29 40.00 36.0000 43.0000 64 30 40.00 37.0000 44.0000 62 31 40.00 38.0000 45.0000 75 32 42.00 40.0000 48.0000 63 33 45.00 41.0000 55.0000 63 34 46.50 42.0000 60.0000 66 35 50.00 43.0000 70.0000 63 36 50.00 45.0000 90.0000 62 Best result for 37 subpopulations * Optimal r1 value: 58 * Optimal r2 value: 60 * Minimum variance of subpopulation sizes achieved: 1733.368 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 2.00 2.0000 2.0000 66 3 3.00 3.0000 3.0000 141 4 4.00 4.0000 4.0000 106 5 5.00 5.0000 5.0000 224 6 6.00 6.0000 6.0000 102 7 7.00 7.0000 7.0000 149 8 8.00 8.0000 8.0000 136 9 9.00 9.0000 9.0000 89 10 10.00 10.0000 10.0000 182 11 11.00 11.0000 11.0000 62 12 12.00 12.0000 12.0000 145 13 14.00 13.0000 14.0000 122 14 15.00 15.0000 15.0000 138 15 16.00 16.0000 16.0000 79 16 18.00 17.0000 18.0000 130 17 20.00 19.0000 20.0000 127 18 21.00 21.0000 22.0000 81 19 23.00 22.0000 24.0000 95 20 25.00 24.0000 25.0000 94 21 25.00 25.0000 26.0000 73 22 28.00 26.0000 28.0000 62 23 28.00 27.0000 30.0000 91 24 30.00 29.0000 31.0000 60 25 30.00 30.0000 32.0000 60 26 33.50 31.0000 35.0000 74 27 35.00 32.0000 36.0000 65 28 35.00 33.0000 38.0000 69 29 37.50 35.0000 40.0000 76 30 40.00 36.0000 42.0000 61 31 40.00 37.0000 44.0000 62 32 41.50 39.0000 45.0000 62 33 42.00 40.0000 47.0000 61 34 45.00 41.0000 55.0000 63 35 46.50 42.0000 60.0000 66 36 50.00 44.0000 70.0000 60 37 50.00 45.0000 90.0000 62 Best result for 38 subpopulations * Optimal r1 value: 59 * Optimal r2 value: 60 * Minimum variance of subpopulation sizes achieved: 1702.475 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 2.00 2.0000 2.0000 66 3 3.00 3.0000 3.0000 141 4 4.00 4.0000 4.0000 106 5 5.00 5.0000 5.0000 224 6 6.00 6.0000 6.0000 102 7 7.00 7.0000 7.0000 149 8 8.00 8.0000 8.0000 136 9 9.00 9.0000 9.0000 89 10 10.00 10.0000 10.0000 182 11 11.00 11.0000 11.0000 62 12 12.00 12.0000 12.0000 145 13 14.00 13.0000 14.0000 122 14 15.00 15.0000 15.0000 138 15 16.00 16.0000 16.0000 79 16 18.00 17.0000 18.0000 130 17 20.00 19.0000 20.0000 127 18 21.00 21.0000 22.0000 81 19 23.00 22.0000 24.0000 95 20 25.00 24.0000 25.0000 94 21 25.00 25.0000 26.0000 73 22 28.00 26.0000 28.0000 62 23 28.00 27.0000 30.0000 91 24 30.00 29.0000 31.0000 60 25 30.00 30.0000 32.0000 60 26 33.50 31.0000 35.0000 74 27 35.00 32.0000 36.0000 65 28 35.00 33.0000 38.0000 69 29 37.50 35.0000 40.0000 76 30 40.00 36.0000 42.0000 61 31 40.00 37.0000 44.0000 62 32 40.00 38.0000 45.0000 75 33 42.00 40.0000 47.0000 61 34 45.00 41.0000 55.0000 63 35 46.50 42.0000 60.0000 66 36 48.00 43.0000 66.0000 60 37 50.00 44.0000 70.0000 60 38 50.00 45.0000 90.0000 62 Best result for 39 subpopulations * Optimal r1 value: 60 * Optimal r2 value: 62 * Minimum variance of subpopulation sizes achieved: 1627.734 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 2.00 2.0000 2.0000 66 3 3.00 3.0000 3.0000 141 4 4.00 4.0000 4.0000 106 5 5.00 5.0000 5.0000 224 6 6.00 6.0000 6.0000 102 7 7.00 7.0000 7.0000 149 8 8.00 8.0000 8.0000 136 9 9.00 9.0000 9.0000 89 10 10.00 10.0000 10.0000 182 11 11.00 11.0000 11.0000 62 12 12.00 12.0000 12.0000 145 13 14.00 13.0000 14.0000 122 14 15.00 15.0000 15.0000 138 15 16.00 16.0000 16.0000 79 16 18.00 17.0000 18.0000 130 17 20.00 19.0000 20.0000 127 18 21.00 21.0000 22.0000 81 19 23.00 22.0000 24.0000 95 20 25.00 24.0000 25.0000 94 21 25.00 25.0000 26.0000 73 22 28.00 26.0000 28.0000 62 23 28.00 27.0000 30.0000 91 24 30.00 29.0000 32.0000 72 25 31.00 30.0000 33.0000 69 26 33.50 31.0000 35.0000 74 27 35.00 32.0000 36.0000 65 28 35.00 33.0000 38.0000 69 29 35.00 34.0000 39.0000 66 30 37.50 35.0000 40.0000 76 31 40.00 36.0000 43.0000 64 32 40.00 37.0000 44.0000 62 33 40.00 38.0000 45.0000 75 34 42.00 40.0000 48.0000 63 35 45.00 41.0000 55.0000 63 36 46.50 42.0000 60.0000 66 37 50.00 43.0000 70.0000 63 38 50.00 44.0000 80.0000 63 39 50.00 45.0000 90.0000 62 Best result for 40 subpopulations * Optimal r1 value: 56 * Optimal r2 value: 57 * Minimum variance of subpopulation sizes achieved: 1856.513 * Subpopulation summary information Covariate Summary Sample Subpopulation Median Minimum Maximum size 1 1.00 0.0000 1.0000 176 2 2.00 2.0000 2.0000 66 3 3.00 3.0000 3.0000 141 4 4.00 4.0000 4.0000 106 5 5.00 5.0000 5.0000 224 6 6.00 6.0000 6.0000 102 7 7.00 7.0000 7.0000 149 8 8.00 8.0000 8.0000 136 9 9.00 9.0000 9.0000 89 10 10.00 10.0000 10.0000 182 11 11.00 11.0000 11.0000 62 12 12.00 12.0000 12.0000 145 13 14.00 13.0000 14.0000 122 14 15.00 15.0000 15.0000 138 15 16.00 16.0000 16.0000 79 16 18.00 17.0000 18.0000 130 17 20.00 19.0000 20.0000 127 18 21.00 21.0000 22.0000 81 19 22.00 22.0000 23.0000 59 20 24.00 23.0000 24.0000 61 21 25.00 24.0000 25.0000 94 22 28.00 26.0000 28.0000 62 23 28.00 27.0000 29.0000 59 24 29.00 28.0000 30.0000 78 25 30.00 29.0000 31.0000 60 26 30.00 30.0000 32.0000 60 27 33.50 31.0000 35.0000 74 28 35.00 33.0000 38.0000 69 29 36.00 35.0000 39.0000 57 30 40.00 36.0000 42.0000 61 31 40.00 37.0000 43.0000 57 32 40.00 38.0000 44.0000 59 33 41.50 39.0000 45.0000 62 34 42.00 40.0000 46.0000 58 35 45.00 41.0000 53.0000 58 36 45.00 42.0000 55.0000 57 37 48.00 43.0000 60.0000 59 38 50.00 44.0000 66.0000 57 39 50.00 45.0000 80.0000 58 40 55.00 46.0000 90.0000 46 Overall best result * Number of subpopulations: 13 * Best r1 value: 65 * Best r2 value: 186 * Minimum variance of subpopulation sizes achieved: 560.2308 > > proc.time() user system elapsed 61.07 5.35 66.67