Tests for Dependence in Binary Repeated Measures Data

If we observe repeated binary outcomes over time then there may be dependence in outcomes and a test for dependence may be sought for such data. However, tests for dependence in models for repeated measures remain a challenge where covariates are associated with previous outcomes and both covariates and previous outcomes are included simultaneously in a model. This paper displays the nature of such problems (i.e. dependence among outcomes may depend on the association between covariates and previous outcomes) inherent in models for repeated binary outcomes that can distort the estimates and may produce misleading results. In the context of application of regressive models, this paper discusses conditions for which the regressive models can be safely employed. All these are shown on the basis of simple relationships between the conditional, marginal and joint probability mass functions for the bivariate binary outcomes which can be extended to the multivariate data stemmed from repeated measures. Some test procedures are suggested and applications are demonstrated using both simulations and real life data. Both the applications clearly indicate the utility of the proposed tests.