Mixed Effects Models With Censored Response

The lecture deals with inference methods for linear and nonlinear mixed-effects models with censored responses, such as those that occur with longitudinal biomarkers below the detection limit (e.g. HIV viral load).

In the parametric framework, a double integral via random effects and the censorship probability complicates the calculation of maximum and restricted maximum likelihood.

Several approaches are presented: multiple imputation of censored values ​​and exact maximum likelihood estimation using EM algorithms.

A Monte Carlo EM (Vaida, Fitzgerald, DeGruttola, 2007) and a closed EM approach (Vaida, Liu, 2009) are explained, the latter based on moments of the truncated multinormal distribution.

The methods cover a broad class of mixed effects models (including Laird–Ware, complex variance structures, heteroskedasticity, autocorrelation, multilevel) and are demonstrated in two biostatistical case studies of longitudinal HIV viral load.

Florin Vaida is a Professor at the Herbert Wertheim School of Public Health & Human Longevity Science, UC San Diego.