Latent Class Linear Mixed Models: a general approach implemented via SAS macro with a tutorial for clinical researchers

Linear mixed models provide a flexible, intuitive method for analyzing repeated-measures data when the population being studied can be thought of as either a single population or as a set of known subpopulations. However, in many cases, the underlying subpopulations are not known. Furthermore, the factors that determine the subpopulations can be extremely complex or unmeasurable. In such cases, a different approach is required in order to more accurately analyze the data. The Latent Class Linear Mixed Model (LCLMM) combines the features of the linear mixed model (LMM) with an additional component, which partitions the population into subpopulations or latent classes. This model has usually been specified with relatively simple, restrictive assumptions. In this dissertation, the methods related to the LCLMM are extended to provide a more general model specification. Fixed-effects may be specified as a combination of class-specific effects and across-class effects. Variances may be specified as being class-specific or equal across classes, a general correlation structure for the random effects is permitted, and multiple residual error variances may be fit. The bound proposed by Hathaway [1985] on the variances to ensure consistency is examined in the context of mixtures of linear mixed models. Class membership probabilities may be specified in one of two ways - via a logistic regression model or using our proposed method in which class membership is estimated based on the relative fit of the underlying linear mixed models. These methods are implemented in a new SAS[registered trademark] macro which offers several options for estimation. In addition to an EM algorithm, gradient-based methods, including quasi-Newton, as well as Hessian-based methods, such as Newton-Raphson, are available to the user. Parameter standard errors are estimated, and predictions of the random effects are derived and calculated. Practical issues, including choosing the number of latent classes and estimation method, are discussed and guidelines are provided based on simulation studies. The stability and advantage of the proposed methods are also examined via simulation study. Finally, our methods are applied to several simple simulated datasets as well as to three real-world applications to illustrate their usefulness for practical applications