A mechanistic nonlinear model for censored and mismeasured covariates in longitudinal models, with application in AIDS studies

Abstract

When modeling longitudinal data, the true values of time-varying covariates may be unknown because of 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 mismeasured values based on this empirical model. 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 mismeasured values. Such a mechanistic model is based on solid scientific or biological arguments, so the predicted censored or mismeasured 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 lower detection limit. Simulation results confirm that the proposed models and methods offer substantial advantages over existing empirical covariate models for censored and mismeasured covariates.

Mixed Effects Models with Censored Covariates, with Applications in HIV/AIDS Studies

“…In all cases, a common approach is to model the covariate process based on the observed covariate data and then use the fitted covariate model to "predict" the censored or missing covariate values. As noted in the previous section, a mechanistic or scientific covariate model may make better "predictions" than empirical covariate models, as shown in Zhang and Wu [8].…”

“…Let x , be the censoring components of the covariate vector x . By treating (a , b , x , ) as "missing data", Zhang et al [7] proposed a Monte Carlo EM algorithm in which the Estep is implemented with a Gibbs sampler combined with rejection sampling methods. The Monte Carlo EM algorithm is still computationally intensive but is feasible.…”

“…We first consider generalized linear mixed models (GLMMs) with a left censored and time-dependent covariate in a longitudinal study, following Zhang et al [7]. Let be the response of interest measured for individual at time , = 1, 2, .…”

“…The unknown parameters ( , ) are estimated using a Monte Carlo EM algorithm as described in Zhang et al [7]. Figure 1 shows the NLME and ELM models fit to the observed viral loads of two randomly selected subjects, where the times are rescaled to be in [0, 1].…”

“…Longitudinal data with left censoring have received increasing attention in the literature in recent years (e.g., [1][2][3][4][5][6][7][8]). A common approach is to assume an empirical model for the covariate of interest based on the observed data, such as a linear mixed effects model.…”