Markov chains with measurement error: Estimating the 'true' course of a marker of the progression of human immunodeficiency virus disease

A Markov chain is a useful way of describing cohort data Longitudinal observations of a marker of the progression of the human immunodeficiency virus (HIV), such as CD4 cell count, measured on members of a cohort study, can be analysed as a continuous time Markov chain by categorizing the CD4 cell counts into stages. Unfortunately, CD4 cell counts are subject to substantial measurement error and short timescale variability. Thus, fitting a Markov chain to raw CD4 cell count measurements does not determine the transition probabilities for the true or underlying CD4 cell counts; the measurement error results in a process that is too rough. Assuming independent measurement errors, we propose a likelihood-based method for estimating the 'true' or underlying transition probabilities. The Markov structure allows efficient calculation of the likelihood by using hidden Markov model methodology. As an example, we consider CD4 cell count data from 430 HIV-infected participants in the San Francisco Men's Health Study by categorizing the marker data into seven stages; up to 17 observations are available for each individual. We find that including measurement error both produces a significantly better fit and provides a model for CD4 progression that is more biologically reasonable.