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Trend analysis with response incompatible formats and measurement error

The increasing popularity of longitudinal studies, along with the rapid advances in science and technology, has created a potential incompatibility between data formats, which leads to an inference problem when applying conventional statistical methods. This inference problem is further compounded by measurement error, since incompatible data format often arise in the context of measuring latent constructs. Without a systematic study of the impact of scale differences, ad-hoc approaches generally lead to inconsistent estimates and thus, invalid statistical inferences. In this paper, we examine the asymptotic properties and identify conditions that guarantee consistent estimation within the context of a trend analysis with response incompatible formats and measurement error. For model estimation, we introduce two competing methods that use a generalized estimating equation approach to provide inferences for the parameters of interest, and highlight the relative strengths of each method. The approach is illustrated by data obtained from a multi-centre AIDS cohort study (MACS), where a trend analysis of an immunologic marker of HIV infection is of interest.