Example 1: Two arm | Fixed design | Continuous
example-1.RmdThis example simulates a Phase II/III parallel-group trial evaluating a new treatment against placebo on a continuous primary endpoint (e.g., a biomarker score or symptom scale). With 100 subjects randomised 1:1, we run a two-sample t-test at full enrollment and track the p-value and arm means across simulation replicates. This is the simplest complete rxsim workflow and a good starting point before moving to more complex designs. See Getting Started for an overview of the package.
Scenario
Capture scenario parameters. We will assume piece-wise linear enrollment.
sample_size <- 100
arms <- c("pbo", "trt")
allocation <- c(1,1)
delta <- 0.2
enrollment_fn <- function(n) rexp(n, rate = 1)
dropout_fn <- function(n) rexp(n, rate = 0.01)
scenario <- tidyr::expand_grid(
sample_size = sample_size,
allocation = list(allocation),
delta = delta
)allocation = c(1, 1) specifies balanced randomisation,
equal expected numbers per arm. Using tidyr::expand_grid()
to build the scenario data.frame embeds the design
parameters directly into each analysis result row, making results
self-documenting and easy to compare across parameter sweeps.
Populations
Define population generators.
population_generators <- list(
pbo = function(n) data.frame(
id = 1:n,
value = rnorm(n),
readout_time = 1
),
trt = function(n) data.frame(
id = 1:n,
value = rnorm(n, delta),
readout_time = 1
)
)Each population generator is a function of n that
returns a data.frame with one row per subject.
readout_time = 1 means the endpoint is observed exactly 1
time unit after a subject enrolls. The placebo arm has a mean of 0 and
the treatment arm a mean of delta, a small-to-moderate
standardised effect.
Triggers & Analysis
We want to do a t-test when sample_size subjects have
been enrolled.
analysis_generators <- list(
final = list(
trigger = rlang::exprs(
sum(!is.na(enroll_time)) >= !!sample_size
),
analysis = function(df, timer){
df_enrolled <- df |> subset(!is.na(enroll_time))
tt <- t.test(value ~ arm, data = df_enrolled)
data.frame(
scenario,
n_total = nrow(df_enrolled),
mean_pbo = mean(df_enrolled$value[df_enrolled$arm == "pbo"]),
mean_trt = mean(df_enrolled$value[df_enrolled$arm == "trt"]),
p_value = unname(tt$p.value),
stringsAsFactors = FALSE
)
}
)
)The trigger fires when the cumulative count of enrolled subjects
(sum(!is.na(enroll_time))) reaches
sample_size. Inside the analysis function,
subset(!is.na(enroll_time)) drops subjects who have been
allocated but not yet enrolled. rxsim pre-generates the full allocation
list so filtering is essential. The two-sample t-test then compares
endpoint values between the two enrolled arms.
Trial
Make multiple trial replicates.
trials <- replicate_trial(
trial_name = "test_trial",
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
To simulate all replicates:
run_trials(trials)
#> [[1]]
#> <Trial>
#> Public:
#> clone: function (deep = FALSE)
#> initialize: function (name, seed = NULL, timer = NULL, population = list(),
#> locked_data: list
#> name: test_trial_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: test_trial_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: test_trial_3
#> population: list
#> results: list
#> run: function ()
#> seed: NULL
#> timer: Timer, R6Bind one row per replicate into one data frame.
replicate_results <- collect_results(trials)
replicate_results
#> replicate timepoint analysis sample_size allocation delta n_total
#> 1 1 87.36847 final 100 1, 1 0.2 100
#> 2 1 347.10044 final 100 1, 1 0.2 100
#> 3 1 364.07755 final 100 1, 1 0.2 100
#> 4 1 448.68714 final 100 1, 1 0.2 100
#> 5 1 469.18697 final 100 1, 1 0.2 100
#> 6 1 487.15448 final 100 1, 1 0.2 100
#> 7 1 538.98616 final 100 1, 1 0.2 100
#> 8 1 606.20122 final 100 1, 1 0.2 100
#> 9 1 658.76511 final 100 1, 1 0.2 100
#> 10 1 794.98780 final 100 1, 1 0.2 100
#> 11 1 944.07711 final 100 1, 1 0.2 100
#> 12 1 1181.37320 final 100 1, 1 0.2 100
#> 13 1 1212.56973 final 100 1, 1 0.2 100
#> 14 1 1232.97050 final 100 1, 1 0.2 100
#> 15 1 1264.36967 final 100 1, 1 0.2 100
#> 16 1 1365.41125 final 100 1, 1 0.2 100
#> 17 1 1414.98418 final 100 1, 1 0.2 100
#> 18 1 1580.61613 final 100 1, 1 0.2 100
#> 19 1 1905.27865 final 100 1, 1 0.2 100
#> 20 1 1928.66156 final 100 1, 1 0.2 100
#> 21 1 1948.35656 final 100 1, 1 0.2 100
#> 22 1 2080.41273 final 100 1, 1 0.2 100
#> 23 1 2116.29566 final 100 1, 1 0.2 100
#> 24 1 2471.76965 final 100 1, 1 0.2 100
#> 25 1 2506.45921 final 100 1, 1 0.2 100
#> 26 1 2624.28188 final 100 1, 1 0.2 100
#> 27 1 2670.38674 final 100 1, 1 0.2 100
#> 28 1 2721.59496 final 100 1, 1 0.2 100
#> 29 1 2730.16239 final 100 1, 1 0.2 100
#> 30 1 2897.71439 final 100 1, 1 0.2 100
#> 31 1 2943.10416 final 100 1, 1 0.2 100
#> 32 1 2970.64127 final 100 1, 1 0.2 100
#> 33 1 3098.51997 final 100 1, 1 0.2 100
#> 34 1 3101.99965 final 100 1, 1 0.2 100
#> 35 1 3117.23713 final 100 1, 1 0.2 100
#> 36 1 3264.59026 final 100 1, 1 0.2 100
#> 37 1 3324.84528 final 100 1, 1 0.2 100
#> 38 1 3376.45601 final 100 1, 1 0.2 100
#> 39 1 3382.96904 final 100 1, 1 0.2 100
#> 40 1 3392.33000 final 100 1, 1 0.2 100
#> 41 1 3653.75656 final 100 1, 1 0.2 100
#> 42 1 3778.41117 final 100 1, 1 0.2 100
#> 43 1 3954.92212 final 100 1, 1 0.2 100
#> 44 1 3993.06729 final 100 1, 1 0.2 100
#> 45 1 4028.10899 final 100 1, 1 0.2 100
#> 46 1 4041.70989 final 100 1, 1 0.2 100
#> 47 1 4165.86312 final 100 1, 1 0.2 100
#> 48 1 4195.93190 final 100 1, 1 0.2 100
#> 49 1 4258.85114 final 100 1, 1 0.2 100
#> 50 1 4480.33893 final 100 1, 1 0.2 100
#> 51 1 4485.70500 final 100 1, 1 0.2 100
#> 52 1 4538.39996 final 100 1, 1 0.2 100
#> 53 1 4621.85701 final 100 1, 1 0.2 100
#> 54 1 4980.81111 final 100 1, 1 0.2 100
#> 55 1 5022.77206 final 100 1, 1 0.2 100
#> 56 1 5025.26114 final 100 1, 1 0.2 100
#> 57 1 5283.65388 final 100 1, 1 0.2 100
#> 58 1 5322.97061 final 100 1, 1 0.2 100
#> 59 1 5454.57682 final 100 1, 1 0.2 100
#> 60 1 5667.53959 final 100 1, 1 0.2 100
#> 61 1 5807.36313 final 100 1, 1 0.2 100
#> 62 1 5822.36146 final 100 1, 1 0.2 100
#> 63 1 6024.11144 final 100 1, 1 0.2 100
#> 64 1 6033.82973 final 100 1, 1 0.2 100
#> 65 1 6099.33001 final 100 1, 1 0.2 100
#> 66 1 6240.00557 final 100 1, 1 0.2 100
#> 67 1 6313.79473 final 100 1, 1 0.2 100
#> 68 1 6398.47626 final 100 1, 1 0.2 100
#> 69 1 6843.06418 final 100 1, 1 0.2 100
#> 70 1 6893.26695 final 100 1, 1 0.2 100
#> 71 1 6937.06974 final 100 1, 1 0.2 100
#> 72 1 6940.14080 final 100 1, 1 0.2 100
#> 73 1 6951.95172 final 100 1, 1 0.2 100
#> 74 1 7300.51551 final 100 1, 1 0.2 100
#> 75 1 7357.70574 final 100 1, 1 0.2 100
#> 76 1 7422.76732 final 100 1, 1 0.2 100
#> 77 1 7434.85486 final 100 1, 1 0.2 100
#> 78 1 7455.60494 final 100 1, 1 0.2 100
#> 79 1 7516.69768 final 100 1, 1 0.2 100
#> 80 1 7811.33067 final 100 1, 1 0.2 100
#> 81 1 7857.91280 final 100 1, 1 0.2 100
#> 82 1 7997.65149 final 100 1, 1 0.2 100
#> 83 1 8034.86411 final 100 1, 1 0.2 100
#> 84 1 8063.25236 final 100 1, 1 0.2 100
#> 85 1 8163.50249 final 100 1, 1 0.2 100
#> 86 1 8287.81000 final 100 1, 1 0.2 100
#> 87 1 8329.31008 final 100 1, 1 0.2 100
#> 88 1 8368.84116 final 100 1, 1 0.2 100
#> 89 1 8400.65785 final 100 1, 1 0.2 100
#> 90 1 8571.29608 final 100 1, 1 0.2 100
#> 91 1 8584.67803 final 100 1, 1 0.2 100
#> 92 1 8625.88371 final 100 1, 1 0.2 100
#> 93 1 8644.56538 final 100 1, 1 0.2 100
#> 94 1 8700.35951 final 100 1, 1 0.2 100
#> 95 1 8828.78289 final 100 1, 1 0.2 100
#> 96 1 8850.81043 final 100 1, 1 0.2 100
#> 97 1 9065.76198 final 100 1, 1 0.2 100
#> 98 1 9187.05539 final 100 1, 1 0.2 100
#> 99 2 83.92580 final 100 1, 1 0.2 100
#> 100 2 162.86506 final 100 1, 1 0.2 100
#> 101 2 164.52703 final 100 1, 1 0.2 100
#> 102 2 409.86390 final 100 1, 1 0.2 100
#> 103 2 410.46923 final 100 1, 1 0.2 100
#> 104 2 711.15813 final 100 1, 1 0.2 100
#> 105 2 775.96471 final 100 1, 1 0.2 100
#> 106 2 859.67365 final 100 1, 1 0.2 100
#> 107 2 1025.88990 final 100 1, 1 0.2 100
#> 108 2 1131.25232 final 100 1, 1 0.2 100
#> 109 2 1156.72552 final 100 1, 1 0.2 100
#> 110 2 1221.70859 final 100 1, 1 0.2 100
#> 111 2 1376.43033 final 100 1, 1 0.2 100
#> 112 2 1382.39410 final 100 1, 1 0.2 100
#> 113 2 1383.07312 final 100 1, 1 0.2 100
#> 114 2 1452.59714 final 100 1, 1 0.2 100
#> 115 2 1458.82499 final 100 1, 1 0.2 100
#> 116 2 1487.90153 final 100 1, 1 0.2 100
#> 117 2 1574.45724 final 100 1, 1 0.2 100
#> 118 2 1687.75601 final 100 1, 1 0.2 100
#> 119 2 1885.57444 final 100 1, 1 0.2 100
#> 120 2 1930.83150 final 100 1, 1 0.2 100
#> 121 2 2103.96690 final 100 1, 1 0.2 100
#> 122 2 2266.56908 final 100 1, 1 0.2 100
#> 123 2 2482.22496 final 100 1, 1 0.2 100
#> 124 2 2829.74784 final 100 1, 1 0.2 100
#> 125 2 2876.89371 final 100 1, 1 0.2 100
#> 126 2 2904.98490 final 100 1, 1 0.2 100
#> 127 2 2982.17747 final 100 1, 1 0.2 100
#> 128 2 3051.66387 final 100 1, 1 0.2 100
#> 129 2 3207.73134 final 100 1, 1 0.2 100
#> 130 2 3233.42137 final 100 1, 1 0.2 100
#> 131 2 3329.18229 final 100 1, 1 0.2 100
#> 132 2 3335.55715 final 100 1, 1 0.2 100
#> 133 2 3383.11618 final 100 1, 1 0.2 100
#> 134 2 3397.06429 final 100 1, 1 0.2 100
#> 135 2 3436.36201 final 100 1, 1 0.2 100
#> 136 2 3476.51551 final 100 1, 1 0.2 100
#> 137 2 3781.58448 final 100 1, 1 0.2 100
#> 138 2 3890.17196 final 100 1, 1 0.2 100
#> 139 2 3907.82140 final 100 1, 1 0.2 100
#> 140 2 3957.68072 final 100 1, 1 0.2 100
#> 141 2 4046.83243 final 100 1, 1 0.2 100
#> 142 2 4070.13216 final 100 1, 1 0.2 100
#> 143 2 4236.18139 final 100 1, 1 0.2 100
#> 144 2 4366.13531 final 100 1, 1 0.2 100
#> 145 2 5058.56822 final 100 1, 1 0.2 100
#> 146 2 5195.06935 final 100 1, 1 0.2 100
#> 147 2 5247.85622 final 100 1, 1 0.2 100
#> 148 2 5306.75175 final 100 1, 1 0.2 100
#> 149 2 5447.39854 final 100 1, 1 0.2 100
#> 150 2 5453.48043 final 100 1, 1 0.2 100
#> 151 2 5578.89134 final 100 1, 1 0.2 100
#> 152 2 5613.89604 final 100 1, 1 0.2 100
#> 153 2 5872.18930 final 100 1, 1 0.2 100
#> 154 2 6068.78939 final 100 1, 1 0.2 100
#> 155 2 6175.40092 final 100 1, 1 0.2 100
#> 156 2 6190.98047 final 100 1, 1 0.2 100
#> 157 2 6229.16404 final 100 1, 1 0.2 100
#> 158 2 6323.41052 final 100 1, 1 0.2 100
#> 159 2 6401.16754 final 100 1, 1 0.2 100
#> 160 2 6496.77482 final 100 1, 1 0.2 100
#> 161 2 6560.01235 final 100 1, 1 0.2 100
#> 162 2 6569.19544 final 100 1, 1 0.2 100
#> 163 2 6571.86589 final 100 1, 1 0.2 100
#> 164 2 6807.20046 final 100 1, 1 0.2 100
#> 165 2 6896.87699 final 100 1, 1 0.2 100
#> 166 2 7109.88073 final 100 1, 1 0.2 100
#> 167 2 7124.19290 final 100 1, 1 0.2 100
#> 168 2 7159.79051 final 100 1, 1 0.2 100
#> 169 2 7197.93433 final 100 1, 1 0.2 100
#> 170 2 7316.61338 final 100 1, 1 0.2 100
#> 171 2 7581.32242 final 100 1, 1 0.2 100
#> 172 2 7847.68211 final 100 1, 1 0.2 100
#> 173 2 7902.64242 final 100 1, 1 0.2 100
#> 174 2 8062.46831 final 100 1, 1 0.2 100
#> 175 2 8189.62566 final 100 1, 1 0.2 100
#> 176 2 8233.68681 final 100 1, 1 0.2 100
#> 177 2 8338.28947 final 100 1, 1 0.2 100
#> 178 2 8346.03816 final 100 1, 1 0.2 100
#> 179 2 8349.95850 final 100 1, 1 0.2 100
#> 180 2 8359.23202 final 100 1, 1 0.2 100
#> 181 2 8429.83124 final 100 1, 1 0.2 100
#> 182 2 8441.34870 final 100 1, 1 0.2 100
#> 183 2 8555.06586 final 100 1, 1 0.2 100
#> 184 2 8585.46590 final 100 1, 1 0.2 100
#> 185 2 8614.05634 final 100 1, 1 0.2 100
#> 186 2 8780.06920 final 100 1, 1 0.2 100
#> 187 2 8849.20991 final 100 1, 1 0.2 100
#> 188 2 8851.85363 final 100 1, 1 0.2 100
#> 189 2 8867.06403 final 100 1, 1 0.2 100
#> 190 2 8968.75154 final 100 1, 1 0.2 100
#> 191 2 9149.58844 final 100 1, 1 0.2 100
#> 192 2 9263.90968 final 100 1, 1 0.2 100
#> 193 2 9389.80570 final 100 1, 1 0.2 100
#> 194 2 9399.46535 final 100 1, 1 0.2 100
#> 195 2 9476.42755 final 100 1, 1 0.2 100
#> 196 2 9483.19609 final 100 1, 1 0.2 100
#> 197 2 9531.04625 final 100 1, 1 0.2 100
#> 198 2 9574.95081 final 100 1, 1 0.2 100
#> 199 2 9650.05829 final 100 1, 1 0.2 100
#> 200 3 96.44952 final 100 1, 1 0.2 100
#> 201 3 641.30535 final 100 1, 1 0.2 100
#> 202 3 642.31945 final 100 1, 1 0.2 100
#> 203 3 674.93478 final 100 1, 1 0.2 100
#> 204 3 769.22693 final 100 1, 1 0.2 100
#> 205 3 842.08596 final 100 1, 1 0.2 100
#> 206 3 875.35735 final 100 1, 1 0.2 100
#> 207 3 907.68533 final 100 1, 1 0.2 100
#> 208 3 997.34185 final 100 1, 1 0.2 100
#> 209 3 1072.05718 final 100 1, 1 0.2 100
#> 210 3 1163.39035 final 100 1, 1 0.2 100
#> 211 3 1191.59587 final 100 1, 1 0.2 100
#> 212 3 1562.07009 final 100 1, 1 0.2 100
#> 213 3 1899.90611 final 100 1, 1 0.2 100
#> 214 3 1940.35632 final 100 1, 1 0.2 100
#> 215 3 2154.49290 final 100 1, 1 0.2 100
#> 216 3 2447.37535 final 100 1, 1 0.2 100
#> 217 3 2822.93260 final 100 1, 1 0.2 100
#> 218 3 2941.35975 final 100 1, 1 0.2 100
#> 219 3 3110.94827 final 100 1, 1 0.2 100
#> 220 3 3148.98925 final 100 1, 1 0.2 100
#> 221 3 3217.53725 final 100 1, 1 0.2 100
#> 222 3 3337.18543 final 100 1, 1 0.2 100
#> 223 3 3367.90075 final 100 1, 1 0.2 100
#> 224 3 3529.54127 final 100 1, 1 0.2 100
#> 225 3 3561.12345 final 100 1, 1 0.2 100
#> 226 3 3709.40028 final 100 1, 1 0.2 100
#> 227 3 3840.98646 final 100 1, 1 0.2 100
#> 228 3 3981.35337 final 100 1, 1 0.2 100
#> 229 3 4027.76788 final 100 1, 1 0.2 100
#> 230 3 4160.72530 final 100 1, 1 0.2 100
#> 231 3 4186.89686 final 100 1, 1 0.2 100
#> 232 3 4399.55299 final 100 1, 1 0.2 100
#> 233 3 4557.13615 final 100 1, 1 0.2 100
#> 234 3 4638.33157 final 100 1, 1 0.2 100
#> 235 3 4639.82467 final 100 1, 1 0.2 100
#> 236 3 4671.16697 final 100 1, 1 0.2 100
#> 237 3 4728.99685 final 100 1, 1 0.2 100
#> 238 3 4770.76598 final 100 1, 1 0.2 100
#> 239 3 4982.05892 final 100 1, 1 0.2 100
#> 240 3 4984.32119 final 100 1, 1 0.2 100
#> 241 3 5183.69330 final 100 1, 1 0.2 100
#> 242 3 5246.51642 final 100 1, 1 0.2 100
#> 243 3 5277.27244 final 100 1, 1 0.2 100
#> 244 3 5387.88795 final 100 1, 1 0.2 100
#> 245 3 5407.20693 final 100 1, 1 0.2 100
#> 246 3 5452.74780 final 100 1, 1 0.2 100
#> 247 3 5468.71062 final 100 1, 1 0.2 100
#> 248 3 5542.58750 final 100 1, 1 0.2 100
#> 249 3 5763.47315 final 100 1, 1 0.2 100
#> 250 3 5771.96148 final 100 1, 1 0.2 100
#> 251 3 5984.73519 final 100 1, 1 0.2 100
#> 252 3 6004.08873 final 100 1, 1 0.2 100
#> 253 3 6300.91345 final 100 1, 1 0.2 100
#> 254 3 6311.73592 final 100 1, 1 0.2 100
#> 255 3 6313.31644 final 100 1, 1 0.2 100
#> 256 3 6417.45507 final 100 1, 1 0.2 100
#> 257 3 6569.04139 final 100 1, 1 0.2 100
#> 258 3 6679.38170 final 100 1, 1 0.2 100
#> 259 3 6809.27436 final 100 1, 1 0.2 100
#> 260 3 6813.54794 final 100 1, 1 0.2 100
#> 261 3 6849.44519 final 100 1, 1 0.2 100
#> 262 3 6970.02494 final 100 1, 1 0.2 100
#> 263 3 6987.69901 final 100 1, 1 0.2 100
#> 264 3 7057.59733 final 100 1, 1 0.2 100
#> 265 3 7120.24351 final 100 1, 1 0.2 100
#> 266 3 7148.95843 final 100 1, 1 0.2 100
#> 267 3 7367.40178 final 100 1, 1 0.2 100
#> 268 3 7413.14504 final 100 1, 1 0.2 100
#> 269 3 7447.56728 final 100 1, 1 0.2 100
#> 270 3 7511.52748 final 100 1, 1 0.2 100
#> 271 3 7545.62878 final 100 1, 1 0.2 100
#> 272 3 7575.01451 final 100 1, 1 0.2 100
#> 273 3 7653.02453 final 100 1, 1 0.2 100
#> 274 3 7718.38987 final 100 1, 1 0.2 100
#> 275 3 7742.26552 final 100 1, 1 0.2 100
#> 276 3 7810.47626 final 100 1, 1 0.2 100
#> 277 3 7929.15282 final 100 1, 1 0.2 100
#> 278 3 8138.48451 final 100 1, 1 0.2 100
#> 279 3 8213.91817 final 100 1, 1 0.2 100
#> 280 3 8356.04399 final 100 1, 1 0.2 100
#> 281 3 8394.89321 final 100 1, 1 0.2 100
#> 282 3 8567.68352 final 100 1, 1 0.2 100
#> 283 3 8612.32526 final 100 1, 1 0.2 100
#> 284 3 8683.38045 final 100 1, 1 0.2 100
#> 285 3 8693.11929 final 100 1, 1 0.2 100
#> 286 3 8832.87024 final 100 1, 1 0.2 100
#> 287 3 8900.00150 final 100 1, 1 0.2 100
#> 288 3 8988.58802 final 100 1, 1 0.2 100
#> 289 3 9110.43423 final 100 1, 1 0.2 100
#> 290 3 9272.97598 final 100 1, 1 0.2 100
#> 291 3 9283.41623 final 100 1, 1 0.2 100
#> 292 3 9313.77786 final 100 1, 1 0.2 100
#> 293 3 9394.88550 final 100 1, 1 0.2 100
#> 294 3 9562.00349 final 100 1, 1 0.2 100
#> 295 3 9594.28157 final 100 1, 1 0.2 100
#> 296 3 9701.40004 final 100 1, 1 0.2 100
#> 297 3 9706.49654 final 100 1, 1 0.2 100
#> 298 3 9730.28383 final 100 1, 1 0.2 100
#> mean_pbo mean_trt p_value
#> 1 -0.02475451 0.32833062 0.05877739
#> 2 -0.02475451 0.32833062 0.05877739
#> 3 -0.02475451 0.32833062 0.05877739
#> 4 -0.02475451 0.32833062 0.05877739
#> 5 -0.02475451 0.32833062 0.05877739
#> 6 -0.02475451 0.32833062 0.05877739
#> 7 -0.02475451 0.32833062 0.05877739
#> 8 -0.02475451 0.32833062 0.05877739
#> 9 -0.02475451 0.32833062 0.05877739
#> 10 -0.02475451 0.32833062 0.05877739
#> 11 -0.02475451 0.32833062 0.05877739
#> 12 -0.02475451 0.32833062 0.05877739
#> 13 -0.02475451 0.32833062 0.05877739
#> 14 -0.02475451 0.32833062 0.05877739
#> 15 -0.02475451 0.32833062 0.05877739
#> 16 -0.02475451 0.32833062 0.05877739
#> 17 -0.02475451 0.32833062 0.05877739
#> 18 -0.02475451 0.32833062 0.05877739
#> 19 -0.02475451 0.32833062 0.05877739
#> 20 -0.02475451 0.32833062 0.05877739
#> 21 -0.02475451 0.32833062 0.05877739
#> 22 -0.02475451 0.32833062 0.05877739
#> 23 -0.02475451 0.32833062 0.05877739
#> 24 -0.02475451 0.32833062 0.05877739
#> 25 -0.02475451 0.32833062 0.05877739
#> 26 -0.02475451 0.32833062 0.05877739
#> 27 -0.02475451 0.32833062 0.05877739
#> 28 -0.02475451 0.32833062 0.05877739
#> 29 -0.02475451 0.32833062 0.05877739
#> 30 -0.02475451 0.32833062 0.05877739
#> 31 -0.02475451 0.32833062 0.05877739
#> 32 -0.02475451 0.32833062 0.05877739
#> 33 -0.02475451 0.32833062 0.05877739
#> 34 -0.02475451 0.32833062 0.05877739
#> 35 -0.02475451 0.32833062 0.05877739
#> 36 -0.02475451 0.32833062 0.05877739
#> 37 -0.02475451 0.32833062 0.05877739
#> 38 -0.02475451 0.32833062 0.05877739
#> 39 -0.02475451 0.32833062 0.05877739
#> 40 -0.02475451 0.32833062 0.05877739
#> 41 -0.02475451 0.32833062 0.05877739
#> 42 -0.02475451 0.32833062 0.05877739
#> 43 -0.02475451 0.32833062 0.05877739
#> 44 -0.02475451 0.32833062 0.05877739
#> 45 -0.02475451 0.32833062 0.05877739
#> 46 -0.02475451 0.32833062 0.05877739
#> 47 -0.02475451 0.32833062 0.05877739
#> 48 -0.02475451 0.32833062 0.05877739
#> 49 -0.02475451 0.32833062 0.05877739
#> 50 -0.02475451 0.32833062 0.05877739
#> 51 -0.02475451 0.32833062 0.05877739
#> 52 -0.02475451 0.32833062 0.05877739
#> 53 -0.02475451 0.32833062 0.05877739
#> 54 -0.02475451 0.32833062 0.05877739
#> 55 -0.02475451 0.32833062 0.05877739
#> 56 -0.02475451 0.32833062 0.05877739
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#> 67 -0.02475451 0.32833062 0.05877739
#> 68 -0.02475451 0.32833062 0.05877739
#> 69 -0.02475451 0.32833062 0.05877739
#> 70 -0.02475451 0.32833062 0.05877739
#> 71 -0.02475451 0.32833062 0.05877739
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#> 74 -0.02475451 0.32833062 0.05877739
#> 75 -0.02475451 0.32833062 0.05877739
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#> 88 -0.02475451 0.32833062 0.05877739
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#> 90 -0.02475451 0.32833062 0.05877739
#> 91 -0.02475451 0.32833062 0.05877739
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#> 93 -0.02475451 0.32833062 0.05877739
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#> 96 -0.02475451 0.32833062 0.05877739
#> 97 -0.02475451 0.32833062 0.05877739
#> 98 -0.02475451 0.32833062 0.05877739
#> 99 -0.05831826 0.13052493 0.36397787
#> 100 -0.05831826 0.13052493 0.36397787
#> 101 -0.05831826 0.13052493 0.36397787
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#> 123 -0.05831826 0.13052493 0.36397787
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#> 167 -0.05831826 0.13052493 0.36397787
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#> 199 -0.05831826 0.13052493 0.36397787
#> 200 -0.25739017 0.08945477 0.09253380
#> 201 -0.25739017 0.08945477 0.09253380
#> 202 -0.25739017 0.08945477 0.09253380
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#> 215 -0.25739017 0.08945477 0.09253380
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#> 222 -0.25739017 0.08945477 0.09253380
#> 223 -0.25739017 0.08945477 0.09253380
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#> 230 -0.25739017 0.08945477 0.09253380
#> 231 -0.25739017 0.08945477 0.09253380
#> 232 -0.25739017 0.08945477 0.09253380
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#> 234 -0.25739017 0.08945477 0.09253380
#> 235 -0.25739017 0.08945477 0.09253380
#> 236 -0.25739017 0.08945477 0.09253380
#> 237 -0.25739017 0.08945477 0.09253380
#> 238 -0.25739017 0.08945477 0.09253380
#> 239 -0.25739017 0.08945477 0.09253380
#> 240 -0.25739017 0.08945477 0.09253380
#> 241 -0.25739017 0.08945477 0.09253380
#> 242 -0.25739017 0.08945477 0.09253380
#> 243 -0.25739017 0.08945477 0.09253380
#> 244 -0.25739017 0.08945477 0.09253380
#> 245 -0.25739017 0.08945477 0.09253380
#> 246 -0.25739017 0.08945477 0.09253380
#> 247 -0.25739017 0.08945477 0.09253380
#> 248 -0.25739017 0.08945477 0.09253380
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#> 250 -0.25739017 0.08945477 0.09253380
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#> 252 -0.25739017 0.08945477 0.09253380
#> 253 -0.25739017 0.08945477 0.09253380
#> 254 -0.25739017 0.08945477 0.09253380
#> 255 -0.25739017 0.08945477 0.09253380
#> 256 -0.25739017 0.08945477 0.09253380
#> 257 -0.25739017 0.08945477 0.09253380
#> 258 -0.25739017 0.08945477 0.09253380
#> 259 -0.25739017 0.08945477 0.09253380
#> 260 -0.25739017 0.08945477 0.09253380
#> 261 -0.25739017 0.08945477 0.09253380
#> 262 -0.25739017 0.08945477 0.09253380
#> 263 -0.25739017 0.08945477 0.09253380
#> 264 -0.25739017 0.08945477 0.09253380
#> 265 -0.25739017 0.08945477 0.09253380
#> 266 -0.25739017 0.08945477 0.09253380
#> 267 -0.25739017 0.08945477 0.09253380
#> 268 -0.25739017 0.08945477 0.09253380
#> 269 -0.25739017 0.08945477 0.09253380
#> 270 -0.25739017 0.08945477 0.09253380
#> 271 -0.25739017 0.08945477 0.09253380
#> 272 -0.25739017 0.08945477 0.09253380
#> 273 -0.25739017 0.08945477 0.09253380
#> 274 -0.25739017 0.08945477 0.09253380
#> 275 -0.25739017 0.08945477 0.09253380
#> 276 -0.25739017 0.08945477 0.09253380
#> 277 -0.25739017 0.08945477 0.09253380
#> 278 -0.25739017 0.08945477 0.09253380
#> 279 -0.25739017 0.08945477 0.09253380
#> 280 -0.25739017 0.08945477 0.09253380
#> 281 -0.25739017 0.08945477 0.09253380
#> 282 -0.25739017 0.08945477 0.09253380
#> 283 -0.25739017 0.08945477 0.09253380
#> 284 -0.25739017 0.08945477 0.09253380
#> 285 -0.25739017 0.08945477 0.09253380
#> 286 -0.25739017 0.08945477 0.09253380
#> 287 -0.25739017 0.08945477 0.09253380
#> 288 -0.25739017 0.08945477 0.09253380
#> 289 -0.25739017 0.08945477 0.09253380
#> 290 -0.25739017 0.08945477 0.09253380
#> 291 -0.25739017 0.08945477 0.09253380
#> 292 -0.25739017 0.08945477 0.09253380
#> 293 -0.25739017 0.08945477 0.09253380
#> 294 -0.25739017 0.08945477 0.09253380
#> 295 -0.25739017 0.08945477 0.09253380
#> 296 -0.25739017 0.08945477 0.09253380
#> 297 -0.25739017 0.08945477 0.09253380
#> 298 -0.25739017 0.08945477 0.09253380collect_results() returns a data.frame with
replicate, timepoint, and
analysis columns prepended to your analysis columns. The
p_value column varies across replicates because each
replicate draws fresh random data.