# How to simulate binary data

    library(NCC)

## 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        0         0      1
    2 2        1         1      1
    3 3        1         1      1
    4 4        1         0      1
    5 5        1         0      1
    6 6        0         1      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         0      1 0.7000000    0.15    0.15    0.15    0.15
    2 2        0         1      1 0.8076923    0.15    0.15    0.15    0.15
    3 3        1         1      1 0.8076923    0.15    0.15    0.15    0.15
    4 4        1         0      1 0.7000000    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