A genetic algorithm for simulating correlated binary data from biomedical research

Correlated binary data arise in a large variety of biomedical research. In order to evaluate methods for their analysis, computer simulations of such data are often required. Existing methods can often not cover the full range of possible correlations between the variables or are not available as implemented software. We propose a genetic algorithm that approaches the desired correlation structure under a given marginal distribution. The procedure generates a large representative matrix from which the probabilities of individual observations can be derived or from which samples can be drawn directly. Our genetic algorithm is evaluated under different specified marginal frequencies and correlation structures, and is compared against two existing approaches. The evaluation checks the speed and precision of the approach as well as its suitability for generating also high-dimensional data. In an example of high-throughput glycan array data, we demonstrate the usability of our approach to simulate the power of global test procedures. An implementation of our own and two other methods were added to the R package `RepeatedHighDim'. The presented algorithm is not restricted to certain correlation structures. In contrast to existing methods it is also evaluated for high-dimensional data.