No abstract

SummaryFor longitudinal data, mixed models include random subject effects to indicate how subjects influence their responses over repeated assessments. The error variance and the variance of the random effects are usually considered to be homogeneous. These variance terms characterize the within-subjects (i.e., error variance) and between-subjects (i.e., random-effects variance) variation in the data. In studies using ecological momentary assessment (EMA), up to 30 or 40 observations are often obtained for each subject, and interest frequently centers around changes in the variances, both within and between subjects. In this article, we focus on an adolescent smoking study using EMA where interest is on characterizing changes in mood variation. We describe how covariates can influence the mood variances, and also extend the standard mixed model by adding a subject-level random effect to the within-subject variance specification. This permits subjects to have influence on the mean, or location, and variability, or (square of the) scale, of their mood responses. Additionally, we allow the location and scale random effects to be correlated. These mixed-effects location scale models have useful applications in many research areas where interest centers on the joint modeling of the mean and variance structure.

The significance of the group effect did vary as a function of the assumed relationship between missingness and smoking. The 'conservative' missing = smoking assumption suggested a beneficial group effect on smoking cessation, which was confirmed via a sensitivity analysis only if an extreme odds ratio of 5 between missingness and smoking was assumed. This type of sensitivity analysis is crucial in determining the role that missing data play in arriving at a study's conclusions.

Ecological Momentary Assessment (EMA) and/or Experience Sampling (ESM) methods are increasingly used in health studies to study subjective experiences within changing environmental contexts. In these studies, up to thirty or forty observations are often obtained for each subject. Because there are so many measurements per subject, one can characterize a subject’s mean and variance, and specify models for both. In this article, we focus on an adolescent smoking study using EMA where interest is on characterizing changes in mood variation. We describe how covariates can influence the mood variances, and also extend the statistical model by adding a subject-level random effect to the within-subject variance specification. This permits subjects to have influence on the mean, or location, and variability, or (square of the) scale, of their mood responses. These mixed-effects location scale models have useful applications in many research areas where interest centers on the joint modeling of the mean and variance structure.

Random-coefficient pattern-mixture models (RCPMMs) have been proposed for longitudinal data when drop-out is thought to be non-ignorable. An RCPMM is a random-effects model with summaries of drop-out time included among the regressors. The basis of every RCPMM is extrapolation. We review RCPMMs, describe various extrapolation strategies, and show how analyses may be simplified through multiple imputation. Using simulated and real data, we show that alternative RCPMMs that fit equally well may lead to very different estimates for parameters of interest. We also show that minor model misspecification can introduce biases that are quite large relative to standard errors, even in fairly small samples. For many scientific applications, where the form of the population model and nature of the drop-out are unknown, interval estimates from any single RCPMM may suffer from undercoverage because uncertainty about model specification is not taken into account.