sim_pw_surv() enables simulation of a clinical trial with
essentially arbitrary patterns of enrollment, failure rates and censoring.
The piecewise exponential distribution allows a simple method to specify
a distribution and enrollment pattern where the enrollment, failure,
and dropout rate changes over time.
While the main purpose may be to generate a trial that can be analyzed
at a single point in time or using group sequential methods,
the routine can also be used to simulate an adaptive trial design.
Enrollment, failure, and dropout rates are specified by treatment group,
stratum and time period.
Fixed block randomization is used; blocks must include treatments provided
in failure and dropout specification.
Default arguments are set up to allow very simple implementation of
a non-proportional hazards assumption for an unstratified design.
Usage
sim_pw_surv(
n = 100,
stratum = data.frame(stratum = "All", p = 1),
block = c(rep("control", 2), rep("experimental", 2)),
enroll_rate = data.frame(rate = 9, duration = 1),
fail_rate = data.frame(stratum = rep("All", 4), period = rep(1:2, 2), treatment =
c(rep("control", 2), rep("experimental", 2)), duration = rep(c(3, 1), 2), rate =
log(2)/c(9, 9, 9, 18)),
dropout_rate = data.frame(stratum = rep("All", 2), period = rep(1, 2), treatment =
c("control", "experimental"), duration = rep(100, 2), rate = rep(0.001, 2))
)Arguments
- n
Number of observations. If length(n) > 1, the length is taken to be the number required.
- stratum
A data frame with stratum specified in
stratum, probability (incidence) of each stratum inp.- block
Vector of treatments to be included in each block. Also used to calculate the attribute "ratio" (for more details see the section Value below).
- enroll_rate
Enrollment rates; see details and examples.
- fail_rate
Failure rates; see details and examples; note that treatments need to be the same as input in block.
- dropout_rate
Dropout rates; see details and examples; note that treatments need to be the same as input in block.
Value
A data frame with the following variables for each observation:
stratum: Stratum for the observation.enroll_time: Enrollment time for the observation.treatment: Treatment group; this will be one of the values in the inputblock.fail_time: Failure time generated usingrpwexp().dropout_time: Dropout time generated usingrpwexp().cte: Calendar time of enrollment plus the minimum of failure time and dropout time.fail: Indicator thatctewas set using failure time; i.e., 1 is a failure, 0 is a dropout.
The data frame also has the attribute "ratio", which is calculated as the
number of "experimental" treatments divided by the number of "control"
treatments from the input argument block.
Examples
library(dplyr)
# Example 1
sim_pw_surv(n = 20)
#> stratum enroll_time treatment fail_time dropout_time cte fail
#> 1 All 0.04593469 experimental 0.3408276 98.58106 0.3867623 1
#> 2 All 0.04842350 control 10.6974702 126.02694 10.7458937 1
#> 3 All 0.14582853 control 12.2867886 222.00638 12.4326171 1
#> 4 All 0.36172506 experimental 48.4943098 3940.42836 48.8560349 1
#> 5 All 0.37138895 control 5.5165464 747.72368 5.8879353 1
#> 6 All 0.43100250 control 46.7612306 1035.36115 47.1922331 1
#> 7 All 0.50269713 experimental 4.6297940 591.70021 5.1324911 1
#> 8 All 0.64269364 experimental 25.3045387 1074.12731 25.9472323 1
#> 9 All 0.77982087 control 12.3506497 280.66035 13.1304706 1
#> 10 All 0.79589330 experimental 8.2785049 460.90846 9.0743982 1
#> 11 All 0.81015489 control 27.5026277 159.48258 28.3127826 1
#> 12 All 0.89218614 experimental 1.6351292 480.78425 2.5273153 1
#> 13 All 1.00490722 control 24.6939029 2312.83176 25.6988101 1
#> 14 All 1.11772985 control 2.0823743 195.25467 3.2001042 1
#> 15 All 1.40185144 experimental 19.0080405 80.18976 20.4098919 1
#> 16 All 1.44496111 experimental 0.7551894 278.42173 2.2001505 1
#> 17 All 1.68591991 control 2.5583299 204.01239 4.2442498 1
#> 18 All 1.76044835 experimental 32.7148660 1376.63546 34.4753143 1
#> 19 All 1.94917066 experimental 0.1472751 176.17803 2.0964457 1
#> 20 All 1.98601442 control 10.4512454 2664.66156 12.4372598 1
# Example 2
# 3:1 randomization
sim_pw_surv(
n = 20,
block = c(rep("experimental", 3), "control")
)
#> stratum enroll_time treatment fail_time dropout_time cte fail
#> 1 All 0.3217242 experimental 9.4928294 742.229574 9.814554 1
#> 2 All 0.3565670 experimental 12.4943694 685.656819 12.850936 1
#> 3 All 0.3830329 control 7.9711034 3357.369819 8.354136 1
#> 4 All 0.4244951 experimental 41.0686377 1134.605316 41.493133 1
#> 5 All 0.4762787 experimental 116.8281381 1848.415820 117.304417 1
#> 6 All 0.4887699 control 28.9180215 146.013236 29.406791 1
#> 7 All 0.6136093 experimental 1.1196077 162.507928 1.733217 1
#> 8 All 0.6891445 experimental 44.2434604 4.963087 5.652231 0
#> 9 All 0.7894425 experimental 4.5214569 456.380132 5.310899 1
#> 10 All 1.0188476 control 5.8872020 1544.620162 6.906050 1
#> 11 All 1.0209447 experimental 6.9775576 276.484136 7.998502 1
#> 12 All 1.2873632 experimental 14.8730426 426.240944 16.160406 1
#> 13 All 1.4099907 experimental 0.1715598 30.568471 1.581550 1
#> 14 All 1.4468614 experimental 10.0687941 3025.328402 11.515656 1
#> 15 All 1.4532458 control 2.4995260 1411.869284 3.952772 1
#> 16 All 1.5900233 experimental 17.4354083 1147.682266 19.025432 1
#> 17 All 1.6577903 experimental 99.0519123 76.763221 78.421012 0
#> 18 All 1.8990358 experimental 19.0166778 440.688450 20.915714 1
#> 19 All 2.1388782 control 19.5929947 286.458360 21.731873 1
#> 20 All 2.2620772 experimental 3.6437051 1873.164324 5.905782 1
# Example 3
# Simulate 2 stratum; will use defaults for blocking and enrollRates
sim_pw_surv(
n = 20,
# 2 stratum,30% and 70% prevalence
stratum = data.frame(stratum = c("Low", "High"), p = c(.3, .7)),
fail_rate = data.frame(
stratum = c(rep("Low", 4), rep("High", 4)),
period = rep(1:2, 4),
treatment = rep(c(
rep("control", 2),
rep("experimental", 2)
), 2),
duration = rep(c(3, 1), 4),
rate = c(.03, .05, .03, .03, .05, .08, .07, .04)
),
dropout_rate = data.frame(
stratum = c(rep("Low", 2), rep("High", 2)),
period = rep(1, 4),
treatment = rep(c("control", "experimental"), 2),
duration = rep(1, 4),
rate = rep(.001, 4)
)
)
#> stratum enroll_time treatment fail_time dropout_time cte fail
#> 1 High 0.05272381 experimental 9.066633 494.34540 9.119357 1
#> 2 Low 0.13566515 experimental 78.546249 128.42704 78.681914 1
#> 3 High 0.26260540 experimental 54.966515 21.84553 22.108138 0
#> 4 High 0.33482645 control 7.189508 2008.07518 7.524335 1
#> 5 Low 0.48250535 control 14.974977 517.85966 15.457482 1
#> 6 High 0.68305515 control 7.064524 513.65581 7.747579 1
#> 7 High 0.81710026 control 21.438898 1164.23533 22.255998 1
#> 8 High 1.07033538 control 19.713971 2212.00385 20.784306 1
#> 9 Low 1.41332672 control 19.401860 2560.64452 20.815187 1
#> 10 High 1.61703621 experimental 17.517759 699.12197 19.134795 1
#> 11 High 1.61704018 experimental 7.688537 788.59361 9.305577 1
#> 12 Low 1.68979094 experimental 8.225572 89.70154 9.915363 1
#> 13 Low 1.73695233 control 4.916503 1871.11105 6.653455 1
#> 14 Low 1.78646504 control 6.955286 276.59924 8.741751 1
#> 15 High 1.79986228 experimental 16.726290 382.11254 18.526153 1
#> 16 Low 1.80771972 experimental 40.504842 653.13538 42.312562 1
#> 17 Low 1.90859178 experimental 4.846215 170.22468 6.754807 1
#> 18 High 1.99798037 control 43.722842 23.72062 25.718601 0
#> 19 High 2.00729138 control 15.319417 661.56404 17.326709 1
#> 20 High 2.02787066 experimental 22.863487 134.13149 24.891357 1
# Example 4
# If you want a more rectangular entry for a data.frame
fail_rate <- bind_rows(
data.frame(stratum = "Low", period = 1, treatment = "control", duration = 3, rate = .03),
data.frame(stratum = "Low", period = 1, treatment = "experimental", duration = 3, rate = .03),
data.frame(stratum = "Low", period = 2, treatment = "experimental", duration = 3, rate = .02),
data.frame(stratum = "High", period = 1, treatment = "control", duration = 3, rate = .05),
data.frame(stratum = "High", period = 1, treatment = "experimental", duration = 3, rate = .06),
data.frame(stratum = "High", period = 2, treatment = "experimental", duration = 3, rate = .03)
)
dropout_rate <- bind_rows(
data.frame(stratum = "Low", period = 1, treatment = "control", duration = 3, rate = .001),
data.frame(stratum = "Low", period = 1, treatment = "experimental", duration = 3, rate = .001),
data.frame(stratum = "High", period = 1, treatment = "control", duration = 3, rate = .001),
data.frame(stratum = "High", period = 1, treatment = "experimental", duration = 3, rate = .001)
)
sim_pw_surv(
n = 12,
stratum = data.frame(stratum = c("Low", "High"), p = c(.3, .7)),
fail_rate = fail_rate,
dropout_rate = dropout_rate
)
#> stratum enroll_time treatment fail_time dropout_time cte fail
#> 1 Low 0.1321033 experimental 49.865443 1562.73537 49.997547 1
#> 2 High 0.3007465 experimental 18.103313 117.95707 18.404059 1
#> 3 High 0.4960628 control 13.752074 908.18929 14.248136 1
#> 4 High 0.5495319 experimental 36.791951 599.65573 37.341483 1
#> 5 Low 0.7205039 experimental 22.158442 1352.21930 22.878946 1
#> 6 High 0.8137968 control 34.253180 930.71607 35.066977 1
#> 7 High 0.8824684 control 8.837317 13.13534 9.719785 1
#> 8 High 0.9442470 experimental 53.139230 1493.85426 54.083477 1
#> 9 High 0.9865067 experimental 57.256334 1265.50109 58.242841 1
#> 10 Low 1.2318692 control 41.671776 403.53936 42.903645 1
#> 11 High 1.2658735 control 56.696444 46.61400 47.879875 0
#> 12 Low 1.4219050 control 98.788315 553.18286 100.210220 1