Influence diagnostics in linear and nonlinear mixed-effects models with censored data

HIV RNA viral load measures are often subjected to some upper and lower detection limits depending on the quantification assays, and consequently the responses are either left or right censored. Linear and nonlinear mixed-effects models, with modifications to accommodate censoring (LMEC and NLMEC), are routinely used to analyze this type of data. Recently, Vaida and Liu (2009) proposed an exact EM-type algorithm for LMEC/NLMEC, called the SAGE algorithm (Meng and Van Dyk, 1997), that uses closed-form expressions at the E-step, as opposed to Monte Carlo simulations. Motivated by this algorithm, we propose here an exact ECM algorithm (Meng and Rubin, 1993) for LMEC/NLMEC, which enables us to develop local influence analysis for mixed-effects models on the basis of conditional expectation of the complete-data log-likelihood function. This is because the observed data log-likelihood function associated with the proposed model is somewhat complex which makes it difficult to directly apply the approach of Cook, 1977, Cook, 1986. Some useful perturbation schemes are also discussed. Finally, the results obtained from the analyses of two HIV AIDS studies on viral loads are presented to illustrate the newly developed methodology.