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How to simulate binary data

Source: vignettes/datasim_bin.Rmd
datasim_bin.Rmd

datasim_bin()

The function datasim_bin() enables data simulation of a platform trial with binary endpoint and an arbitrary number of treatment arms entering at different time points.

Assumptions

  • equal sample sizes across all treatment arms, different sample size for the control group (resulting from allocation ratio 1:1:…:1 in each period)
  • block randomization is used, a factor to multiply the number of active arms with in order to get the block size in each period can be specified as input argument (period_blocks, default=2)

Notation

Paper Software
\(N\) n_total
\(K\) num_arms
\(d\) d
\(n\) n_arm
\(\eta_0\) p0
\(\lambda\) lambda
\(N_p\) N_peak

Usage

Input

The user specifies the number of treatment arms in the trial, the sample size per treatment arm (assumed equal) and the timing of adding arms in terms of patients recruited to the trial so far.

  • num_arms Number of treatment arms in the trial
  • n_arm Sample size per arm (assumed equal)
  • d Vector with timings of adding new arms in terms of number of patients recruited to the trial so far (of length num_arms)
  • period_blocks - number to multiply the number of active arms with in order to get the block size per period (block size = period_blocks \(\cdot\) #active arms)
  • p0 - response in the control arm
  • OR- vector with odds ratios for each treatment arm (of length num_arms)
  • lambda - vector with strength of time trend in each arm (of length num_arms+1, as time trend in the control is also allowed)
  • trend - indicates the time trend pattern (“linear”, “stepwise” or “inv_u”)
  • N_peak - point at which the inverted-u time trend switches direction in terms of overall sample size
  • full - Boolean. Indicates whether the full dataset should be returned. Default=FALSE

Output

Per default (using full=FALSE), the function outputs a dataframe with simulated trial data needed for the analysis. If the parameter full is set to TRUE, the output is a list containing an extended version of the dataframe (also including lambdas and underlying responses) and all input parameters.

Examples 

# Dataset with trial data only (default) 

head(datasim_bin(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
                 p0 = 0.7, OR = rep(1.8, 3), 
                 lambda = rep(0.15, 4), trend="stepwise"))
  j response treatment period
1 1        1         1      1
2 2        1         1      1
3 3        1         0      1
4 4        1         0      1
5 5        0         1      1
6 6        0         0      1
# Full dataset

head(datasim_bin(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
                 p0 = 0.7, OR = rep(1.8, 3), 
                 lambda = rep(0.15, 4), trend="stepwise", full = T)$Data)
  j response treatment period         p lambda0 lambda1 lambda2 lambda3
1 1        0         1      1 0.8076923    0.15    0.15    0.15    0.15
2 2        1         0      1 0.7000000    0.15    0.15    0.15    0.15
3 3        0         0      1 0.7000000    0.15    0.15    0.15    0.15
4 4        1         1      1 0.8076923    0.15    0.15    0.15    0.15
5 5        1         0      1 0.7000000    0.15    0.15    0.15    0.15
6 6        1         1      1 0.8076923    0.15    0.15    0.15    0.15