test_that("OneParLogNormalPrior reproduces same numbers as in paper by Neuenschwander et al.", {
  mcmc_options <- McmcOptions(
    burnin = 50000,
    step = 2,
    samples = 10000,
    rng_kind = "Wichmann-Hill",
    rng_seed = 1
  )

  # One-parameter model
  dose_grid <- c(
    1,
    2.5,
    5,
    10,
    15,
    20,
    25,
    30,
    40,
    50,
    75,
    100,
    150,
    200,
    250
  )

  # (A) Posterior summaries (original skeleton)
  empty_data <- Data(dose_grid = dose_grid)

  data_obs_a <- Data(
    x = c(
      rep(c(1, 2.5, 5, 10, 25), times = c(3, 4, 5, 4, 2))
    ),
    y = c(
      rep(c(0, 1), times = c(16, 2))
    ),
    cohort = c(
      rep(c(1, 2, 3, 4, 7), times = c(3, 4, 5, 4, 2))
    ),
    doseGrid = dose_grid,
    ID = 1:18
  )

  model_power_a <- OneParLogNormalPrior(
    skel_probs = c(
      0.01,
      0.015,
      0.020,
      0.025,
      0.03,
      0.04,
      0.05,
      0.10,
      0.17,
      0.30,
      0.45,
      0.70,
      0.80,
      0.90,
      0.95
    ),
    dose_grid = dose_grid,
    sigma2 = 1.34^2
  )

  prior_samples <- mcmc(
    data = empty_data,
    model = model_power_a,
    options = mcmc_options
  )

  # NCRM rule with loss function
  ncrm_loss <- NextBestNCRMLoss(
    target = c(0.2, 0.35),
    overdose = c(0.35, 0.6),
    unacceptable = c(0.6, 1),
    max_overdose_prob = 0.25,
    losses = c(1, 0, 1, 2)
  )

  increments_no <- IncrementsRelative(
    intervals = c(0, 250),
    increments = c(2, 2)
  )

  post_samples_a <- mcmc(data_obs_a, model_power_a, mcmc_options)

  dose_rec_loss_a <- nextBest(
    ncrm_loss,
    doselimit = maxDose(
      increments_no,
      data_obs_a
    ),
    samples = post_samples_a,
    model = model_power_a,
    data = data_obs_a
  )

  # (A) Actual table I
  tab1_a_act <- rbind(
    "Skeleton (CRM)" = c(
      0.01,
      0.015,
      0.020,
      0.025,
      0.03,
      0.04,
      0.05,
      0.10,
      0.17,
      0.30,
      0.45,
      0.70,
      0.80,
      0.90,
      0.95
    )[1:10],
    "Mean" = t(dose_rec_loss_a$probs[, 6])[, 1:10],
    "Std. dev." = t(dose_rec_loss_a$probs[, 7])[, 1:10]
  )

  # (B) Actual table I
  data_obs_b <- data_obs_a
  data_obs_b@doseGrid <- dose_grid[1:10]
  data_obs_b@nGrid <- length(data_obs_b@doseGrid)

  model_power_b <- OneParLogNormalPrior(
    skel_probs = c(
      0.063,
      0.125,
      0.188,
      0.250,
      0.313,
      0.375,
      0.438,
      0.500,
      0.563,
      0.625
    ),
    dose_grid = dose_grid[1:10],
    sigma2 = 1.34^2
  )

  post_samples_b <- mcmc(data_obs_b, model_power_b, mcmc_options)

  dose_rec_loss_b <- nextBest(
    ncrm_loss,
    doselimit = maxDose(
      increments_no,
      data_obs_b
    ),
    samples = post_samples_b,
    model = model_power_b,
    data = data_obs_b
  )

  tab1_b_act <- rbind(
    "Skeleton (CRM)" = c(
      0.01,
      0.015,
      0.020,
      0.025,
      0.03,
      0.04,
      0.05,
      0.10,
      0.17,
      0.30,
      0.45,
      0.70,
      0.80,
      0.90,
      0.95
    )[1:10],
    "Mean" = t(dose_rec_loss_b$probs[, 6])[, 1:10],
    "Std. dev." = t(dose_rec_loss_b$probs[, 7])[, 1:10]
  )

  # (A)+ (B) Actual table I
  tab1_act <- list(
    "Posterior summaries (original skeleton)" = as.data.frame(tab1_a_act),
    "Posterior summaries (equidistant skeleton)" = as.data.frame(tab1_b_act)
  )

  # Expected table I (Neuenschwander et al.)
  tab1 <- structure(
    list(
      dose1 = c(
        3,
        0,
        NA,
        0.01,
        0.069,
        0.055,
        NA,
        0.063,
        0.024,
        0.03
      ),
      dose2.5 = c(
        4,
        0,
        NA,
        0.015,
        0.085,
        0.062,
        NA,
        0.125,
        0.054,
        0.051
      ),
      dose5 = c(
        5,
        0,
        NA,
        0.02,
        0.099,
        0.068,
        NA,
        0.188,
        0.09,
        0.069
      ),
      dose10 = c(
        4,
        0,
        NA,
        0.025,
        0.111,
        0.072,
        NA,
        0.25,
        0.13,
        0.084
      ),
      dose15 = c(
        NA,
        NA,
        NA,
        0.03,
        0.123,
        0.076,
        NA,
        0.313,
        0.176,
        0.097
      ),
      dose20 = c(
        NA,
        NA,
        NA,
        0.04,
        0.144,
        0.082,
        NA,
        0.375,
        0.226,
        0.107
      ),
      dose25 = c(
        2,
        2,
        NA,
        0.05,
        0.163,
        0.087,
        NA,
        0.438,
        0.281,
        0.115
      ),
      dose30 = c(
        NA,
        NA,
        NA,
        0.1,
        0.242,
        0.101,
        NA,
        0.5,
        0.341,
        0.119
      ),
      dose40 = c(
        NA,
        NA,
        NA,
        0.17,
        0.33,
        0.109,
        NA,
        0.563,
        0.405,
        0.12
      ),
      dose50 = c(
        NA,
        NA,
        NA,
        0.3,
        0.465,
        0.108,
        NA,
        0.625,
        0.475,
        0.117
      )
    ),
    class = "data.frame",
    row.names = c(
      "No. of patients",
      "No. of DLTs",
      "A) Posterior summaries (original skeleton)",
      "Skeleton (CRM)",
      "Mean",
      "Std. dev.",
      "B) Posterior summaries (equidistant skeleton)",
      "Skeleton (CRM)",
      "Mean",
      "Std. dev."
    )
  )

  tab1_a_exp <- rbind(
    "Skeleton (CRM)" = tab1[4, ],
    "Mean" = tab1[5, ],
    "Std. dev." = tab1[6, ]
  )

  names(tab1_a_exp) <- colnames(tab1_a_act)

  tab1_b_exp <- rbind(
    "Skeleton (CRM)" = tab1[8, ],
    "Mean" = tab1[9, ],
    "Std. dev." = tab1[10, ]
  )

  names(tab1_b_exp) <- colnames(tab1_b_act)

  # (A)+ (B) Expected table I
  tab1_exp <- list(
    "Posterior summaries (original skeleton)" = tab1_a_exp,
    "Posterior summaries (equidistant skeleton)" = tab1_b_exp
  )

  # test Posterior summaries for probabilities of DLT (CRM)
  # check whether absolute differences between published results and computed
  # results are smaller than chosen tolerance
  tolerance <- 0.01
  # original skeleton
  diff_org_mean <- abs(
    tab1_act$"Posterior summaries (original skeleton)"[2, ] -
      tab1_exp$"Posterior summaries (original skeleton)"[2, ]
  ) <
    tolerance

  diff_org_sd <- abs(
    tab1_act$"Posterior summaries (original skeleton)"[3, ] -
      tab1_exp$"Posterior summaries (original skeleton)"[3, ]
  ) <
    tolerance

  # if all computed results (mean or sd) have deviation smaller than
  # tolerance from corresponding published result, set result as TRUE
  result_org <- ifelse(all(diff_org_mean) & all(diff_org_sd), TRUE, FALSE)

  # silent if all absolute differences are < tolerance
  expect_true(result_org)

  # equidistant skeleton
  diff_equi_mean <- abs(
    tab1_act$"Posterior summaries (equidistant skeleton)"[2, ] -
      tab1_exp$"Posterior summaries (equidistant skeleton)"[2, ]
  ) <
    tolerance

  diff_equi_sd <- abs(
    tab1_act$"Posterior summaries (equidistant skeleton)"[3, ] -
      tab1_exp$"Posterior summaries (equidistant skeleton)"[3, ]
  ) <
    tolerance

  result_equi <- ifelse(all(diff_equi_mean) & all(diff_equi_sd), TRUE, FALSE)

  # silent if all absolute differences are < tolerance
  expect_true(result_equi)
})