Mixed-effects models for censored data with autoregressive errors

Mixed-effects models, with modifications to accommodate censored observations (LMEC/NLMEC), are routinely used to analyze measurements, collected irregularly over time, which are often subject to some upper and lower detection limits. This paper presents a likelihood-based approach for fitting LMEC/NLMEC models with autoregressive of order $$ dependence of 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 that arise from the stationarity conditions for the autoregressive parameters in the EM algorithm are handled by a reparameterization scheme, as discussed in Lin and Lee (2007). To examine the performance of the proposed method, we present some simulation studies and analyze a real AIDS case study. The proposed algorithm and methods are implemented in the new R package ARpLMEC.