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Abstract:
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In the conventional joint model (JM) of a longitudinal and time-to-event outcome, a linear mixed model (LMM) assuming normal random error is typically used to model the longitudinal process. However, in many circumstances, the normality assumption cannot be satisfied and the LMM is not the appropriate submodel. In addition, as LMM models the conditional mean of the longitudinal outcome, it is not appropriate if clinical interest lies in making inference or prediction about medians, lower, or upper ends of the response distribution. Quantile regression (QR), on the other hand, provides a flexible, distribution-free way to study covariate effects at different quantiles of the longitudinal outcome that is robust to deviations from assumed normality or errors, and to outlying observations. In this paper, we present and advocate the linear quantile mixed model (LQMM) for the longitudinal process in the JM framework. Our development is motivated by large prospective study of Huntington's Disease where primary clinical interest is in utilizing longitudinal motor scores and other early covariates to predict the risk of developing HD. To this end, we develop a Gibbs sampler based on the loc
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