A Model for Binary Time Series Data with Serial Odds Ratio Patterns

Abstract

SUMMARY Moment methods for analysing repeated binary responses using the marginal odds ratio as a measure of association have recently been proposed by several researchers. Using the generalized estimating equation (GEE) methodology, they estimated the regression parameters associated with the expected value of an individual's vector of binary responses. In addition, they estimated the marginal odds ratio between pairs of binary responses. In this paper, we discuss a model for binary time series data where the repeated responses on each individual may be unequally spaced in time. This model allows both the number of observations per individual and the times of measurement to vary between individuals. Our approach is to model the association between the binary responses using serial odds ratio patterns. This model can be thought of as a binary time series analogue of the exponential correlation pattern so commonly assumed for continuous time series data. Parameter estimates are obtained by using the GEE methodology. The model is illustrated with data from an arthritis clinical trial where the response variable is a binary self-assessment measurement.