A generalized estimating equation approach to modelling incompatible data formats with covariate measurement error: application to human immunodeficiency virus immune markers

The integration of technological advances into research studies often raises an issue of incompatibility of data. This problem is common to longitudinal and multicentre studies, taking the form of changes in the definitions, acquisition of data or measuring instruments of some study variables. In our case of studying the relationship between a marker of immune response to human immunodeficiency virus and human immunodeficiency virus infection status, using data from the Multi‐Center AIDS Cohort Study, changes in the manufactured tests used for both variables occurred throughout the study, resulting in data with different manufactured scales. In addition, the latent nature of the immune response of interest necessitated a further consideration of a measurement error component. We address the general issue of incompatibility of data, together with the issue of covariate measurement error, in a unified, generalized linear model setting with inferences based on the generalized estimating equation framework. General conditions are constructed to ensure consistent estimates and their variances for the primary model of interest, with the asymptotic behaviour of resulting estimates examined under a variety of modelling scenarios. The approach is illustrated by modelling a repeated ordinal response with incompatible formats, as a function of a covariate with incompatible formats and measurement error, based on the Multi‐Center AIDS Cohort Study data.