Simulating longer vectors of correlated binary random variables via multinomial sampling

摘要

The importance of simulating correlated binary data in determining sample size is examined as well as a comparison of methods for analyzing clustered and longitudinal data with dichotomous outcomes. The best way to simulate correlated binary data still remains an active area of research in statistical literature. The use of sampling from multinomial distribution for simulating vectors of correlated binary random variables is available only in a general form for vectors of length 2 and 3 since construction of multivariate distribution is very challenging for longer vectors. In order to overcome this problem, an algorithm is presented for simulating correlated binary data via multinomial sampling that can be easily used for directly computing the multinomial distribution for vectors of any length. However, in order to demonstrate the proposed multinomial sampling approach, vectors of length 4 and 8 are simulated and then the power during the planning phase of a study is assessed. Also, the choice of working correlation structure in an analysis with generalized estimating equations is evaluated.