Simulating longer vectors of correlated binary random variables via multinomial sampling

The ability to simulate correlated binary data is important for sample size calculation and comparison of methods for analyzing clustered and longitudinal data with dichotomous outcomes. One available approach for simulating vectors of length n of dichotomous random variables is to sample them from multinomial distribution of all possible length n permutations of zeros and ones. However, the multinomial sampling method has only been implemented in a general form (without making the initial restrictive assumptions) for vectors of length 2 and 3 because constructing multinomial distribution is very challenging for longer vectors. This difficulty can be overcome by presenting an algorithm for simulating correlated binary data via multinomial sampling that can be easily used for directly computing the multinomial distribution for any value of n. To demonstrate the approach, vectors of length 4 and 8 are simulated for assessing the power during the planning phase of a study and for evaluating the choice of working correlation structure in an analysis with generalized estimating equations.