Example 3: Two arm | Fixed design | Two correlated continuous endpoints | t-test
example-3.Rmd
# Core package that provides Timer, Population, Trial, gen_timepoints, add_timepoints, ...
library(rxsim)
# Utilities
library(dplyr)
#>
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#>
#> filter, lag
#> The following objects are masked from 'package:base':
#>
#> intersect, setdiff, setequal, union
library(MASS) # for mvrnorm (simulate correlated endpoints)
#>
#> Attaching package: 'MASS'
#> The following object is masked from 'package:dplyr':
#>
#> selectMany trials evaluate co-primary or key secondary endpoints simultaneously. Ignoring endpoint correlation when planning a study leads to incorrect power estimates. This example shows how to simulate two correlated continuous endpoints (e.g., a primary efficacy score and a key secondary biomarker) and apply multiplicity adjustment via Holm’s procedure. See Example 1 for the simpler single-endpoint baseline.
Scenario
We consider a two-arm, fixed design with two correlated continuous endpoints per subject. Enrollment is piece-wise linear; analysis happens once at the final time.
# Total target sample size
sample_size <- 100
# Arms and allocation (balanced)
arms <- c("pbo", "trt")
allocation <- c(1, 1)
# Piece-wise linear enrollment and dropout rates (per unit time)
# (You can tweak these to match your program's cadence.)
enrollment <- list(
end_time = c(4, 8, 12, 16),
rate = c(5, 10, 15, 20)
)
dropout <- list(
end_time = c(4, 8, 12, 16),
rate = c(1, 2, 4, 8)
)
# Endpoint model parameters
# Endpoint correlation structure (common across arms for simplicity)
rho <- 0.60 # correlation between endpoint1 and endpoint2
sd1 <- 1.00 # SD of endpoint1
sd2 <- 1.00 # SD of endpoint2
# Mean structure per arm
mu1_pbo <- 0.00 # Control mean for endpoint1
mu2_pbo <- 0.00 # Control mean for endpoint2
# Treatment effects (mean shifts)
delta1 <- 0.30 # Treatment - control difference for endpoint1
delta2 <- 0.20 # Treatment - control difference for endpoint2
mu1_trt <- mu1_pbo + delta1
mu2_trt <- mu2_pbo + delta2
# Construct covariance matrix
Sigma <- matrix(
c(sd1^2, rho*sd1*sd2,
rho*sd1*sd2, sd2^2),
nrow = 2, byrow = TRUE
)
scenario <- tidyr::expand_grid(
sample_size = sample_size,
allocation = list(allocation),
rho = rho,
delta1 = delta1,
delta2 = delta2
)rho = 0.60 represents a moderate positive correlation
between the two endpoints — plausible when both reflect the same
underlying biological process. The covariance matrix Sigma
is constructed from the marginal SDs and correlation using the standard
identity cov(y1, y2) = rho × sd1 × sd2. Treatment shifts are delta1 =
0.30 SD for the primary endpoint and delta2 = 0.20 SD for the secondary,
reflecting a scenario where the primary endpoint is more sensitive to
treatment.
Time points
Generate timeline of discrete timepoints and add them to a
Timer.
timepoints <- gen_timepoints(
sample_size = sample_size,
arms = arms,
allocation = allocation,
enrollment = enrollment,
dropout = dropout
)
t <- Timer$new(name = "trial_timer_two_endpoints")
add_timepoints(t, timepoints)
final_time <- t$get_end_timepoint()
final_time
#> [1] 12gen_timepoints() converts piecewise-constant enrollment
and dropout rate lists into a deterministic set of calendar timepoints —
in contrast to the stochastic rexp calls used in Examples 1 and 2.
t$get_end_timepoint() returns the latest timepoint at which
all expected enrollment and follow-up will have completed, providing the
calendar time for the single final analysis.
Arms (Populations)
For each arm we simulate two correlated endpoints
per subject using MASS::mvrnorm. We keep
50 subjects per arm (consistent with
sample_size = 100 and equal allocation).
# Create closure to capture parameters
mk_population_generator <- function(mu_y1, mu_y2) {
function(n) {
xy <- MASS::mvrnorm(
n = n,
mu = c(mu_y1, mu_y2),
Sigma = Sigma
)
data.frame(
id = seq_len(n),
y1 = xy[, 1],
y2 = xy[, 2],
readout_time = 1
)
}
}
population_generators <- list(
pbo = mk_population_generator(mu1_pbo, mu2_pbo),
trt = mk_population_generator(mu1_trt, mu2_trt)
)MASS::mvrnorm draws n samples from a
multivariate normal with the given mean vector and covariance matrix
Sigma. The closure pattern
(mk_population_generator) captures the arm-specific means
at definition time, so each call to
population_generators$pbo(n) or
population_generators$trt(n) produces data under the
correct arm parameters. Endpoint correlation flows entirely through the
shared Sigma matrix — changing rho in the
scenario automatically updates both arms.
Trial Parameters
Define enrollment/dropout profiles and parameters.
arms <- c("pbo", "trt")
allocation <- c(1, 1)
enrollment_fn <- function(n) rexp(n, rate = 1)
dropout_fn <- function(n) rexp(n, rate = 0.01)Note that enrollment_fn and dropout_fn here
are stochastic functions passed to replicate_trial(), which
uses them in gen_plan() to generate per-replicate
enrollment and dropout times. They are separate from the
piecewise-constant enrollment and dropout
lists used by gen_timepoints() above — those lists drive
the deterministic timer, while these functions drive per-subject event
times within each simulated replicate.
Trigger & Analysis
This is a fixed design: perform analysis
once.
We run two independent two-sample t-tests (one per endpoint).
analysis_generators <- list(
final = list(
trigger = rlang::exprs(
sum(!is.na(enroll_time)) >= !!sample_size
),
analysis = function(df, timer) {
df_e <- df |> subset(!is.na(enroll_time))
p1 <- t.test(y1 ~ arm, data = df_e)$p.value
p2 <- t.test(y2 ~ arm, data = df_e)$p.value
padj <- p.adjust(c(p1, p2), method = "holm")
data.frame(
scenario,
p_y1 = unname(p1),
p_y2 = unname(p2),
p_holm_y1 = unname(padj[1]),
p_holm_y2 = unname(padj[2]),
n_total = nrow(df_e),
n_pbo = sum(df_e$arm == "pbo"),
n_trt = sum(df_e$arm == "trt"),
stringsAsFactors = FALSE
)
}
)
)The two t-tests are run independently on the enrolled subset,
producing unadjusted p-values p_y1 and p_y2.
p.adjust(..., method = "holm") applies Holm’s stepwise
procedure: padj[1] corresponds to the endpoint with the
smaller raw p-value (most significant) and padj[2] to the
larger. The adjusted values account for the familywise error rate across
the two endpoints, so p_holm_y1 >= p_y1 always
holds.
Trial
Create and run the trial. (We supply a seed for
reproducibility inside the trial engine—e.g., enrollment/dropout
sampling.)
trials <- replicate_trial(
trial_name = "two_endpoints_fixed_design",
sample_size = sample_size,
arms = arms,
allocation = allocation,
enrollment = enrollment_fn,
dropout = dropout_fn,
analysis_generators = analysis_generators,
population_generators = population_generators,
n = 3
)Simulate
run_trials(trials)
#> [[1]]
#> <Trial>
#> Public:
#> clone: function (deep = FALSE)
#> initialize: function (name, seed = NULL, timer = NULL, population = list(),
#> locked_data: list
#> name: two_endpoints_fixed_design_1
#> population: list
#> results: list
#> run: function ()
#> seed: NULL
#> timer: Timer, R6
#>
#> [[2]]
#> <Trial>
#> Public:
#> clone: function (deep = FALSE)
#> initialize: function (name, seed = NULL, timer = NULL, population = list(),
#> locked_data: list
#> name: two_endpoints_fixed_design_2
#> population: list
#> results: list
#> run: function ()
#> seed: NULL
#> timer: Timer, R6
#>
#> [[3]]
#> <Trial>
#> Public:
#> clone: function (deep = FALSE)
#> initialize: function (name, seed = NULL, timer = NULL, population = list(),
#> locked_data: list
#> name: two_endpoints_fixed_design_3
#> population: list
#> results: list
#> run: function ()
#> seed: NULL
#> timer: Timer, R6Results
One row per replicate, row-bound across all replicates:
replicate_results <- collect_results(trials)
replicate_results
#> replicate timepoint analysis sample_size allocation rho delta1 delta2
#> 1 1 87.36847 final 100 1, 1 0.6 0.3 0.2
#> 2 1 347.10044 final 100 1, 1 0.6 0.3 0.2
#> 3 1 364.07755 final 100 1, 1 0.6 0.3 0.2
#> 4 1 448.68714 final 100 1, 1 0.6 0.3 0.2
#> 5 1 469.18697 final 100 1, 1 0.6 0.3 0.2
#> 6 1 487.15448 final 100 1, 1 0.6 0.3 0.2
#> 7 1 538.98616 final 100 1, 1 0.6 0.3 0.2
#> 8 1 606.20122 final 100 1, 1 0.6 0.3 0.2
#> 9 1 658.76511 final 100 1, 1 0.6 0.3 0.2
#> 10 1 794.98780 final 100 1, 1 0.6 0.3 0.2
#> 11 1 944.07711 final 100 1, 1 0.6 0.3 0.2
#> 12 1 1181.37320 final 100 1, 1 0.6 0.3 0.2
#> 13 1 1212.56973 final 100 1, 1 0.6 0.3 0.2
#> 14 1 1232.97050 final 100 1, 1 0.6 0.3 0.2
#> 15 1 1264.36967 final 100 1, 1 0.6 0.3 0.2
#> 16 1 1365.41125 final 100 1, 1 0.6 0.3 0.2
#> 17 1 1414.98418 final 100 1, 1 0.6 0.3 0.2
#> 18 1 1580.61613 final 100 1, 1 0.6 0.3 0.2
#> 19 1 1905.27865 final 100 1, 1 0.6 0.3 0.2
#> 20 1 1928.66156 final 100 1, 1 0.6 0.3 0.2
#> 21 1 1948.35656 final 100 1, 1 0.6 0.3 0.2
#> 22 1 2080.41273 final 100 1, 1 0.6 0.3 0.2
#> 23 1 2116.29566 final 100 1, 1 0.6 0.3 0.2
#> 24 1 2471.76965 final 100 1, 1 0.6 0.3 0.2
#> 25 1 2506.45921 final 100 1, 1 0.6 0.3 0.2
#> 26 1 2624.28188 final 100 1, 1 0.6 0.3 0.2
#> 27 1 2670.38674 final 100 1, 1 0.6 0.3 0.2
#> 28 1 2721.59496 final 100 1, 1 0.6 0.3 0.2
#> 29 1 2730.16239 final 100 1, 1 0.6 0.3 0.2
#> 30 1 2897.71439 final 100 1, 1 0.6 0.3 0.2
#> 31 1 2943.10416 final 100 1, 1 0.6 0.3 0.2
#> 32 1 2970.64127 final 100 1, 1 0.6 0.3 0.2
#> 33 1 3098.51997 final 100 1, 1 0.6 0.3 0.2
#> 34 1 3101.99965 final 100 1, 1 0.6 0.3 0.2
#> 35 1 3117.23713 final 100 1, 1 0.6 0.3 0.2
#> 36 1 3264.59026 final 100 1, 1 0.6 0.3 0.2
#> 37 1 3324.84528 final 100 1, 1 0.6 0.3 0.2
#> 38 1 3376.45601 final 100 1, 1 0.6 0.3 0.2
#> 39 1 3382.96904 final 100 1, 1 0.6 0.3 0.2
#> 40 1 3392.33000 final 100 1, 1 0.6 0.3 0.2
#> 41 1 3653.75656 final 100 1, 1 0.6 0.3 0.2
#> 42 1 3778.41117 final 100 1, 1 0.6 0.3 0.2
#> 43 1 3954.92212 final 100 1, 1 0.6 0.3 0.2
#> 44 1 3993.06729 final 100 1, 1 0.6 0.3 0.2
#> 45 1 4028.10899 final 100 1, 1 0.6 0.3 0.2
#> 46 1 4041.70989 final 100 1, 1 0.6 0.3 0.2
#> 47 1 4165.86312 final 100 1, 1 0.6 0.3 0.2
#> 48 1 4195.93190 final 100 1, 1 0.6 0.3 0.2
#> 49 1 4258.85114 final 100 1, 1 0.6 0.3 0.2
#> 50 1 4480.33893 final 100 1, 1 0.6 0.3 0.2
#> 51 1 4485.70500 final 100 1, 1 0.6 0.3 0.2
#> 52 1 4538.39996 final 100 1, 1 0.6 0.3 0.2
#> 53 1 4621.85701 final 100 1, 1 0.6 0.3 0.2
#> 54 1 4980.81111 final 100 1, 1 0.6 0.3 0.2
#> 55 1 5022.77206 final 100 1, 1 0.6 0.3 0.2
#> 56 1 5025.26114 final 100 1, 1 0.6 0.3 0.2
#> 57 1 5283.65388 final 100 1, 1 0.6 0.3 0.2
#> 58 1 5322.97061 final 100 1, 1 0.6 0.3 0.2
#> 59 1 5454.57682 final 100 1, 1 0.6 0.3 0.2
#> 60 1 5667.53959 final 100 1, 1 0.6 0.3 0.2
#> 61 1 5807.36313 final 100 1, 1 0.6 0.3 0.2
#> 62 1 5822.36146 final 100 1, 1 0.6 0.3 0.2
#> 63 1 6024.11144 final 100 1, 1 0.6 0.3 0.2
#> 64 1 6033.82973 final 100 1, 1 0.6 0.3 0.2
#> 65 1 6099.33001 final 100 1, 1 0.6 0.3 0.2
#> 66 1 6240.00557 final 100 1, 1 0.6 0.3 0.2
#> 67 1 6313.79473 final 100 1, 1 0.6 0.3 0.2
#> 68 1 6398.47626 final 100 1, 1 0.6 0.3 0.2
#> 69 1 6843.06418 final 100 1, 1 0.6 0.3 0.2
#> 70 1 6893.26695 final 100 1, 1 0.6 0.3 0.2
#> 71 1 6937.06974 final 100 1, 1 0.6 0.3 0.2
#> 72 1 6940.14080 final 100 1, 1 0.6 0.3 0.2
#> 73 1 6951.95172 final 100 1, 1 0.6 0.3 0.2
#> 74 1 7300.51551 final 100 1, 1 0.6 0.3 0.2
#> 75 1 7357.70574 final 100 1, 1 0.6 0.3 0.2
#> 76 1 7422.76732 final 100 1, 1 0.6 0.3 0.2
#> 77 1 7434.85486 final 100 1, 1 0.6 0.3 0.2
#> 78 1 7455.60494 final 100 1, 1 0.6 0.3 0.2
#> 79 1 7516.69768 final 100 1, 1 0.6 0.3 0.2
#> 80 1 7811.33067 final 100 1, 1 0.6 0.3 0.2
#> 81 1 7857.91280 final 100 1, 1 0.6 0.3 0.2
#> 82 1 7997.65149 final 100 1, 1 0.6 0.3 0.2
#> 83 1 8034.86411 final 100 1, 1 0.6 0.3 0.2
#> 84 1 8063.25236 final 100 1, 1 0.6 0.3 0.2
#> 85 1 8163.50249 final 100 1, 1 0.6 0.3 0.2
#> 86 1 8287.81000 final 100 1, 1 0.6 0.3 0.2
#> 87 1 8329.31008 final 100 1, 1 0.6 0.3 0.2
#> 88 1 8368.84116 final 100 1, 1 0.6 0.3 0.2
#> 89 1 8400.65785 final 100 1, 1 0.6 0.3 0.2
#> 90 1 8571.29608 final 100 1, 1 0.6 0.3 0.2
#> 91 1 8584.67803 final 100 1, 1 0.6 0.3 0.2
#> 92 1 8625.88371 final 100 1, 1 0.6 0.3 0.2
#> 93 1 8644.56538 final 100 1, 1 0.6 0.3 0.2
#> 94 1 8700.35951 final 100 1, 1 0.6 0.3 0.2
#> 95 1 8828.78289 final 100 1, 1 0.6 0.3 0.2
#> 96 1 8850.81043 final 100 1, 1 0.6 0.3 0.2
#> 97 1 9065.76198 final 100 1, 1 0.6 0.3 0.2
#> 98 1 9187.05539 final 100 1, 1 0.6 0.3 0.2
#> 99 2 83.92580 final 100 1, 1 0.6 0.3 0.2
#> 100 2 162.86506 final 100 1, 1 0.6 0.3 0.2
#> 101 2 164.52703 final 100 1, 1 0.6 0.3 0.2
#> 102 2 409.86390 final 100 1, 1 0.6 0.3 0.2
#> 103 2 410.46923 final 100 1, 1 0.6 0.3 0.2
#> 104 2 711.15813 final 100 1, 1 0.6 0.3 0.2
#> 105 2 775.96471 final 100 1, 1 0.6 0.3 0.2
#> 106 2 859.67365 final 100 1, 1 0.6 0.3 0.2
#> 107 2 1025.88990 final 100 1, 1 0.6 0.3 0.2
#> 108 2 1131.25232 final 100 1, 1 0.6 0.3 0.2
#> 109 2 1156.72552 final 100 1, 1 0.6 0.3 0.2
#> 110 2 1221.70859 final 100 1, 1 0.6 0.3 0.2
#> 111 2 1376.43033 final 100 1, 1 0.6 0.3 0.2
#> 112 2 1382.39410 final 100 1, 1 0.6 0.3 0.2
#> 113 2 1383.07312 final 100 1, 1 0.6 0.3 0.2
#> 114 2 1452.59714 final 100 1, 1 0.6 0.3 0.2
#> 115 2 1458.82499 final 100 1, 1 0.6 0.3 0.2
#> 116 2 1487.90153 final 100 1, 1 0.6 0.3 0.2
#> 117 2 1574.45724 final 100 1, 1 0.6 0.3 0.2
#> 118 2 1687.75601 final 100 1, 1 0.6 0.3 0.2
#> 119 2 1885.57444 final 100 1, 1 0.6 0.3 0.2
#> 120 2 1930.83150 final 100 1, 1 0.6 0.3 0.2
#> 121 2 2103.96690 final 100 1, 1 0.6 0.3 0.2
#> 122 2 2266.56908 final 100 1, 1 0.6 0.3 0.2
#> 123 2 2482.22496 final 100 1, 1 0.6 0.3 0.2
#> 124 2 2829.74784 final 100 1, 1 0.6 0.3 0.2
#> 125 2 2876.89371 final 100 1, 1 0.6 0.3 0.2
#> 126 2 2904.98490 final 100 1, 1 0.6 0.3 0.2
#> 127 2 2982.17747 final 100 1, 1 0.6 0.3 0.2
#> 128 2 3051.66387 final 100 1, 1 0.6 0.3 0.2
#> 129 2 3207.73134 final 100 1, 1 0.6 0.3 0.2
#> 130 2 3233.42137 final 100 1, 1 0.6 0.3 0.2
#> 131 2 3329.18229 final 100 1, 1 0.6 0.3 0.2
#> 132 2 3335.55715 final 100 1, 1 0.6 0.3 0.2
#> 133 2 3383.11618 final 100 1, 1 0.6 0.3 0.2
#> 134 2 3397.06429 final 100 1, 1 0.6 0.3 0.2
#> 135 2 3436.36201 final 100 1, 1 0.6 0.3 0.2
#> 136 2 3476.51551 final 100 1, 1 0.6 0.3 0.2
#> 137 2 3781.58448 final 100 1, 1 0.6 0.3 0.2
#> 138 2 3890.17196 final 100 1, 1 0.6 0.3 0.2
#> 139 2 3907.82140 final 100 1, 1 0.6 0.3 0.2
#> 140 2 3957.68072 final 100 1, 1 0.6 0.3 0.2
#> 141 2 4046.83243 final 100 1, 1 0.6 0.3 0.2
#> 142 2 4070.13216 final 100 1, 1 0.6 0.3 0.2
#> 143 2 4236.18139 final 100 1, 1 0.6 0.3 0.2
#> 144 2 4366.13531 final 100 1, 1 0.6 0.3 0.2
#> 145 2 5058.56822 final 100 1, 1 0.6 0.3 0.2
#> 146 2 5195.06935 final 100 1, 1 0.6 0.3 0.2
#> 147 2 5247.85622 final 100 1, 1 0.6 0.3 0.2
#> 148 2 5306.75175 final 100 1, 1 0.6 0.3 0.2
#> 149 2 5447.39854 final 100 1, 1 0.6 0.3 0.2
#> 150 2 5453.48043 final 100 1, 1 0.6 0.3 0.2
#> 151 2 5578.89134 final 100 1, 1 0.6 0.3 0.2
#> 152 2 5613.89604 final 100 1, 1 0.6 0.3 0.2
#> 153 2 5872.18930 final 100 1, 1 0.6 0.3 0.2
#> 154 2 6068.78939 final 100 1, 1 0.6 0.3 0.2
#> 155 2 6175.40092 final 100 1, 1 0.6 0.3 0.2
#> 156 2 6190.98047 final 100 1, 1 0.6 0.3 0.2
#> 157 2 6229.16404 final 100 1, 1 0.6 0.3 0.2
#> 158 2 6323.41052 final 100 1, 1 0.6 0.3 0.2
#> 159 2 6401.16754 final 100 1, 1 0.6 0.3 0.2
#> 160 2 6496.77482 final 100 1, 1 0.6 0.3 0.2
#> 161 2 6560.01235 final 100 1, 1 0.6 0.3 0.2
#> 162 2 6569.19544 final 100 1, 1 0.6 0.3 0.2
#> 163 2 6571.86589 final 100 1, 1 0.6 0.3 0.2
#> 164 2 6807.20046 final 100 1, 1 0.6 0.3 0.2
#> 165 2 6896.87699 final 100 1, 1 0.6 0.3 0.2
#> 166 2 7109.88073 final 100 1, 1 0.6 0.3 0.2
#> 167 2 7124.19290 final 100 1, 1 0.6 0.3 0.2
#> 168 2 7159.79051 final 100 1, 1 0.6 0.3 0.2
#> 169 2 7197.93433 final 100 1, 1 0.6 0.3 0.2
#> 170 2 7316.61338 final 100 1, 1 0.6 0.3 0.2
#> 171 2 7581.32242 final 100 1, 1 0.6 0.3 0.2
#> 172 2 7847.68211 final 100 1, 1 0.6 0.3 0.2
#> 173 2 7902.64242 final 100 1, 1 0.6 0.3 0.2
#> 174 2 8062.46831 final 100 1, 1 0.6 0.3 0.2
#> 175 2 8189.62566 final 100 1, 1 0.6 0.3 0.2
#> 176 2 8233.68681 final 100 1, 1 0.6 0.3 0.2
#> 177 2 8338.28947 final 100 1, 1 0.6 0.3 0.2
#> 178 2 8346.03816 final 100 1, 1 0.6 0.3 0.2
#> 179 2 8349.95850 final 100 1, 1 0.6 0.3 0.2
#> 180 2 8359.23202 final 100 1, 1 0.6 0.3 0.2
#> 181 2 8429.83124 final 100 1, 1 0.6 0.3 0.2
#> 182 2 8441.34870 final 100 1, 1 0.6 0.3 0.2
#> 183 2 8555.06586 final 100 1, 1 0.6 0.3 0.2
#> 184 2 8585.46590 final 100 1, 1 0.6 0.3 0.2
#> 185 2 8614.05634 final 100 1, 1 0.6 0.3 0.2
#> 186 2 8780.06920 final 100 1, 1 0.6 0.3 0.2
#> 187 2 8849.20991 final 100 1, 1 0.6 0.3 0.2
#> 188 2 8851.85363 final 100 1, 1 0.6 0.3 0.2
#> 189 2 8867.06403 final 100 1, 1 0.6 0.3 0.2
#> 190 2 8968.75154 final 100 1, 1 0.6 0.3 0.2
#> 191 2 9149.58844 final 100 1, 1 0.6 0.3 0.2
#> 192 2 9263.90968 final 100 1, 1 0.6 0.3 0.2
#> 193 2 9389.80570 final 100 1, 1 0.6 0.3 0.2
#> 194 2 9399.46535 final 100 1, 1 0.6 0.3 0.2
#> 195 2 9476.42755 final 100 1, 1 0.6 0.3 0.2
#> 196 2 9483.19609 final 100 1, 1 0.6 0.3 0.2
#> 197 2 9531.04625 final 100 1, 1 0.6 0.3 0.2
#> 198 2 9574.95081 final 100 1, 1 0.6 0.3 0.2
#> 199 2 9650.05829 final 100 1, 1 0.6 0.3 0.2
#> 200 3 96.44952 final 100 1, 1 0.6 0.3 0.2
#> 201 3 641.30535 final 100 1, 1 0.6 0.3 0.2
#> 202 3 642.31945 final 100 1, 1 0.6 0.3 0.2
#> 203 3 674.93478 final 100 1, 1 0.6 0.3 0.2
#> 204 3 769.22693 final 100 1, 1 0.6 0.3 0.2
#> 205 3 842.08596 final 100 1, 1 0.6 0.3 0.2
#> 206 3 875.35735 final 100 1, 1 0.6 0.3 0.2
#> 207 3 907.68533 final 100 1, 1 0.6 0.3 0.2
#> 208 3 997.34185 final 100 1, 1 0.6 0.3 0.2
#> 209 3 1072.05718 final 100 1, 1 0.6 0.3 0.2
#> 210 3 1163.39035 final 100 1, 1 0.6 0.3 0.2
#> 211 3 1191.59587 final 100 1, 1 0.6 0.3 0.2
#> 212 3 1562.07009 final 100 1, 1 0.6 0.3 0.2
#> 213 3 1899.90611 final 100 1, 1 0.6 0.3 0.2
#> 214 3 1940.35632 final 100 1, 1 0.6 0.3 0.2
#> 215 3 2154.49290 final 100 1, 1 0.6 0.3 0.2
#> 216 3 2447.37535 final 100 1, 1 0.6 0.3 0.2
#> 217 3 2822.93260 final 100 1, 1 0.6 0.3 0.2
#> 218 3 2941.35975 final 100 1, 1 0.6 0.3 0.2
#> 219 3 3110.94827 final 100 1, 1 0.6 0.3 0.2
#> 220 3 3148.98925 final 100 1, 1 0.6 0.3 0.2
#> 221 3 3217.53725 final 100 1, 1 0.6 0.3 0.2
#> 222 3 3337.18543 final 100 1, 1 0.6 0.3 0.2
#> 223 3 3367.90075 final 100 1, 1 0.6 0.3 0.2
#> 224 3 3529.54127 final 100 1, 1 0.6 0.3 0.2
#> 225 3 3561.12345 final 100 1, 1 0.6 0.3 0.2
#> 226 3 3709.40028 final 100 1, 1 0.6 0.3 0.2
#> 227 3 3840.98646 final 100 1, 1 0.6 0.3 0.2
#> 228 3 3981.35337 final 100 1, 1 0.6 0.3 0.2
#> 229 3 4027.76788 final 100 1, 1 0.6 0.3 0.2
#> 230 3 4160.72530 final 100 1, 1 0.6 0.3 0.2
#> 231 3 4186.89686 final 100 1, 1 0.6 0.3 0.2
#> 232 3 4399.55299 final 100 1, 1 0.6 0.3 0.2
#> 233 3 4557.13615 final 100 1, 1 0.6 0.3 0.2
#> 234 3 4638.33157 final 100 1, 1 0.6 0.3 0.2
#> 235 3 4639.82467 final 100 1, 1 0.6 0.3 0.2
#> 236 3 4671.16697 final 100 1, 1 0.6 0.3 0.2
#> 237 3 4728.99685 final 100 1, 1 0.6 0.3 0.2
#> 238 3 4770.76598 final 100 1, 1 0.6 0.3 0.2
#> 239 3 4982.05892 final 100 1, 1 0.6 0.3 0.2
#> 240 3 4984.32119 final 100 1, 1 0.6 0.3 0.2
#> 241 3 5183.69330 final 100 1, 1 0.6 0.3 0.2
#> 242 3 5246.51642 final 100 1, 1 0.6 0.3 0.2
#> 243 3 5277.27244 final 100 1, 1 0.6 0.3 0.2
#> 244 3 5387.88795 final 100 1, 1 0.6 0.3 0.2
#> 245 3 5407.20693 final 100 1, 1 0.6 0.3 0.2
#> 246 3 5452.74780 final 100 1, 1 0.6 0.3 0.2
#> 247 3 5468.71062 final 100 1, 1 0.6 0.3 0.2
#> 248 3 5542.58750 final 100 1, 1 0.6 0.3 0.2
#> 249 3 5763.47315 final 100 1, 1 0.6 0.3 0.2
#> 250 3 5771.96148 final 100 1, 1 0.6 0.3 0.2
#> 251 3 5984.73519 final 100 1, 1 0.6 0.3 0.2
#> 252 3 6004.08873 final 100 1, 1 0.6 0.3 0.2
#> 253 3 6300.91345 final 100 1, 1 0.6 0.3 0.2
#> 254 3 6311.73592 final 100 1, 1 0.6 0.3 0.2
#> 255 3 6313.31644 final 100 1, 1 0.6 0.3 0.2
#> 256 3 6417.45507 final 100 1, 1 0.6 0.3 0.2
#> 257 3 6569.04139 final 100 1, 1 0.6 0.3 0.2
#> 258 3 6679.38170 final 100 1, 1 0.6 0.3 0.2
#> 259 3 6809.27436 final 100 1, 1 0.6 0.3 0.2
#> 260 3 6813.54794 final 100 1, 1 0.6 0.3 0.2
#> 261 3 6849.44519 final 100 1, 1 0.6 0.3 0.2
#> 262 3 6970.02494 final 100 1, 1 0.6 0.3 0.2
#> 263 3 6987.69901 final 100 1, 1 0.6 0.3 0.2
#> 264 3 7057.59733 final 100 1, 1 0.6 0.3 0.2
#> 265 3 7120.24351 final 100 1, 1 0.6 0.3 0.2
#> 266 3 7148.95843 final 100 1, 1 0.6 0.3 0.2
#> 267 3 7367.40178 final 100 1, 1 0.6 0.3 0.2
#> 268 3 7413.14504 final 100 1, 1 0.6 0.3 0.2
#> 269 3 7447.56728 final 100 1, 1 0.6 0.3 0.2
#> 270 3 7511.52748 final 100 1, 1 0.6 0.3 0.2
#> 271 3 7545.62878 final 100 1, 1 0.6 0.3 0.2
#> 272 3 7575.01451 final 100 1, 1 0.6 0.3 0.2
#> 273 3 7653.02453 final 100 1, 1 0.6 0.3 0.2
#> 274 3 7718.38987 final 100 1, 1 0.6 0.3 0.2
#> 275 3 7742.26552 final 100 1, 1 0.6 0.3 0.2
#> 276 3 7810.47626 final 100 1, 1 0.6 0.3 0.2
#> 277 3 7929.15282 final 100 1, 1 0.6 0.3 0.2
#> 278 3 8138.48451 final 100 1, 1 0.6 0.3 0.2
#> 279 3 8213.91817 final 100 1, 1 0.6 0.3 0.2
#> 280 3 8356.04399 final 100 1, 1 0.6 0.3 0.2
#> 281 3 8394.89321 final 100 1, 1 0.6 0.3 0.2
#> 282 3 8567.68352 final 100 1, 1 0.6 0.3 0.2
#> 283 3 8612.32526 final 100 1, 1 0.6 0.3 0.2
#> 284 3 8683.38045 final 100 1, 1 0.6 0.3 0.2
#> 285 3 8693.11929 final 100 1, 1 0.6 0.3 0.2
#> 286 3 8832.87024 final 100 1, 1 0.6 0.3 0.2
#> 287 3 8900.00150 final 100 1, 1 0.6 0.3 0.2
#> 288 3 8988.58802 final 100 1, 1 0.6 0.3 0.2
#> 289 3 9110.43423 final 100 1, 1 0.6 0.3 0.2
#> 290 3 9272.97598 final 100 1, 1 0.6 0.3 0.2
#> 291 3 9283.41623 final 100 1, 1 0.6 0.3 0.2
#> 292 3 9313.77786 final 100 1, 1 0.6 0.3 0.2
#> 293 3 9394.88550 final 100 1, 1 0.6 0.3 0.2
#> 294 3 9562.00349 final 100 1, 1 0.6 0.3 0.2
#> 295 3 9594.28157 final 100 1, 1 0.6 0.3 0.2
#> 296 3 9701.40004 final 100 1, 1 0.6 0.3 0.2
#> 297 3 9706.49654 final 100 1, 1 0.6 0.3 0.2
#> 298 3 9730.28383 final 100 1, 1 0.6 0.3 0.2
#> p_y1 p_y2 p_holm_y1 p_holm_y2 n_total n_pbo n_trt
#> 1 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 2 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 3 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 4 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 5 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 6 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 7 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 8 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 9 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 10 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 11 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 12 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 13 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 14 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 15 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 16 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 17 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 18 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 19 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 20 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 21 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 22 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 23 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 24 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 25 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 26 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 27 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 28 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 29 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 30 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 31 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 32 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 33 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 34 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 35 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 36 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 37 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 38 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 39 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 40 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 41 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 42 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 43 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 44 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 45 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 46 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 47 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 48 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 49 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 50 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 51 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 52 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 53 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 54 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 55 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 56 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 57 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 58 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 59 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 60 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 61 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 62 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 63 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 64 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 65 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 66 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 67 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 68 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 69 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 70 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 71 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 72 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 73 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 74 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 75 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 76 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 77 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 78 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 79 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 80 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 81 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 82 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 83 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 84 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 85 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 86 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 87 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 88 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 89 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 90 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 91 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 92 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 93 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 94 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 95 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 96 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 97 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 98 0.07643188 0.6506456 0.15286377 0.6506456 100 50 50
#> 99 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 100 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 101 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 102 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 103 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 104 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 105 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 106 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 107 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 108 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 109 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 110 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 111 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 112 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 113 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 114 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 115 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 116 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 117 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 118 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 119 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 120 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 121 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 122 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 123 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 124 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 125 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 126 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 127 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 128 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 129 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 130 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 131 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 132 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 133 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 134 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 135 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 136 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 137 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 138 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 139 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 140 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 141 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 142 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 143 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 144 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 145 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 146 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 147 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 148 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 149 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 150 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 151 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 152 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 153 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 154 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 155 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 156 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 157 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 158 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 159 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 160 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 161 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 162 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 163 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 164 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 165 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 166 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 167 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 168 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 169 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 170 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 171 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 172 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 173 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 174 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 175 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 176 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 177 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 178 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 179 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 180 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 181 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 182 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 183 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 184 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 185 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 186 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 187 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 188 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 189 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 190 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 191 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 192 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 193 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 194 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 195 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 196 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 197 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 198 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 199 0.01064244 0.2144255 0.02128487 0.2144255 100 50 50
#> 200 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 201 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 202 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 203 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 204 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 205 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 206 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 207 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 208 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 209 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 210 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 211 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 212 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 213 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 214 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 215 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 216 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 217 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 218 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 219 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 220 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 221 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 222 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 223 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 224 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 225 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 226 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 227 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 228 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 229 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 230 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 231 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 232 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 233 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 234 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 235 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 236 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 237 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 238 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 239 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 240 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 241 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 242 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 243 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 244 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 245 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 246 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 247 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 248 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 249 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 250 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 251 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 252 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 253 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 254 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 255 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 256 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 257 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 258 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 259 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 260 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 261 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 262 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 263 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 264 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 265 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 266 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 267 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 268 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 269 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 270 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 271 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 272 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 273 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 274 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 275 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 276 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 277 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 278 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 279 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 280 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 281 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 282 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 283 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 284 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 285 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 286 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 287 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 288 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 289 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 290 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 291 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 292 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 293 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 294 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 295 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 296 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 297 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50
#> 298 0.17952451 0.3090734 0.35904902 0.3590490 100 50 50collect_results() prepends replicate,
timepoint, and analysis columns to the four
p-value columns. p_holm_y1 and p_holm_y2 will
always be ≥ their unadjusted counterparts because Holm correction is
more conservative. Because the two endpoints are positively correlated
(rho = 0.6), replicates that reject for y1 tend to also reject for y2 —
joint rejection probability exceeds what you would expect for
independent endpoints under the same effect sizes.