TESTS FOR DEPENDENCE IN BINARY REPEATED MEASURES DATA

Abstract

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.