Likelihood based inference for autoregressive censored mixed-effects models, with applications to hiv viral loads dataset

Abstract

In AIDS clinical trials, the HIV-1 RNA measurements are often subject to some upper and lower detection limits, depending on the quantification assays. Linear and nonlinear mixedeffects models, with modifications to accommodate censored observations, are routinely used to analyze this type of data (VAIDA; LIU, 2009). This work presents a likelihood based approach for fitting Linear and nonlinear mixedeffects models, with modifications to accommodate censored observations and considering an structure autoregressive of order p (AR(p)) dependence on the error term. An EM-type algorithm is developed for computing the maximum likelihood estimates, obtaining as a byproduct the standard errors of the fixed effects and the likelihood value. Moreover, the constraints on the parameter space arising, from the stationarity conditions for the autoregressive parameters, in the EM algorithm are handled by a reparametrization scheme, as discussed by Lin e Lee (2007). Finally, the proposed algorithm is implemented in the R package ARpMMEC, which is available. It presents an application to real data and developed three simulation studies that show the relevance and applicability of the proposed model.