Abstract:
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When modeling longitudinal data, the true values of time-varying covariates may be unknown due to detection-limit censoring or measurement error. A common approach in the literature is to empirically model the covariate process based on observed data, and then predict the censored values or mis-measured values. Such an empirical model can be misleading, especially for censored values since the (unobserved) censored values may behave very differently than observed values due to the underlying data-generation mechanisms or disease status. In this paper, we propose a mechanistic nonlinear covariate model based on the underlying data-generation mechanisms to address censored values and mis-measured values. Such a mechanistic model is based on solid scientific or biological arguments, so the predicted censored or mis-measured values are more reasonable. We use a Monte Carlo EM algorithm for likelihood inference, and apply the methods to an AIDS dataset, where viral load is censored by a detection limit. Simulation results confirm that the proposed models, methods offer substantial advantages over existing empirical covariate models for censored and mis-measured covariates.
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