Analysis of repeated measures data with clumping at zero

Longitudinal or repeated measures data with clumping at zero occur in many applications within the realm of biometrics, including health policy research, epidemiology, nutrition, and meteorology. These data exhibit correlation because they are measured on the same subject over time or because subjects may be considered repeated measures within a larger unit such as a family. They present special challenges because of the extreme non-normality of the distributions involved. Econometric approaches for cross-sectional data that exhibit clumping at zero are compared with a mixture model for cross-sectional data. Assumptions made by the models with regard to distributional assumptions, the relationship between the occurrence of a non-zero value and the intensity of the non-zero value, and how the observed distribution arises have important implications for the interpretation of these models. A model for repeated measures data with clumping at zero, using a mixed-effects mixture model with correlated random effects, is presented. The model contains components to model the probability of a non-zero value and the mean of nonzero values, allowing for repeated measurements using random effects and allowing for correlation between the two components. It is shown that this model can be fit using recently developed methods and SAS software for fitting generalized linear mixed models. Methods for describing the effect of predictor variables on the probability of non-zero values, on the mean of non-zero values, and on the overall mean amount are given. This interpretation is made for the case where random effects are held at zero; it also applies to the mixture model for cross-sectional data. The proposed methods are illustrated with analyses of two datasets. The first dataset is from the San Luis Valley Diabetes Study. In this study the number of minutes of vigorous activity 20--74 year-old male and female non-Hispanic white and Hispanic participants engaged in each week was collected up to four times over a 14-year period. The second dataset is from the Medical Expenditure Panel Survey. Data were collected on the total medical expenditures during 1996 for all of the members within the households surveyed.