title: Analyzing repeated measures semi-continuous data, with application to an alcohol dependence study.
abstract: Two-part random effects models (Olsen and Schafer,(1) Tooze et al.(2)) have been applied to repeated measures of semi-continuous data, characterized by a mixture of a substantial proportion of zero values and a skewed distribution of positive values. In the original formulation of this model, the natural logarithm of the positive values is assumed to follow a normal distribution with a constant variance parameter. In this article, we review and consider three extensions of this model, allowing the positive values to follow (a) a generalized gamma distribution, (b) a log-skew-normal distribution, and (c) a normal distribution after the Box-Cox transformation. We allow for the possibility of heteroscedasticity. Maximum likelihood estimation is shown to be conveniently implemented in SAS Proc NLMIXED. The performance of the methods is compared through applications to daily drinking records in a secondary data analysis from a randomized controlled trial of topiramate for alcohol dependence treatment. We find that all three models provide a significantly better fit than the log-normal model, and there exists strong evidence for heteroscedasticity. We also compare the three models by the likelihood ratio tests for non-nested hypotheses (Vuong(3)). The results suggest that the generalized gamma distribution provides the best fit, though no statistically significant differences are found in pairwise model comparisons.
authors.affiliation: Department of Preventive Medicine, Northwestern University, Chicago, USA lei.liu@northwestern.edu.
authors.forename: Lei
authors.initials: L
authors.lastname: Liu
authors.affiliation: Department of Biological Statistics and Computational Biology, Cornell University, Ithaca, USA.
authors.forename: Robert L
authors.initials: RL
authors.lastname: Strawderman
authors.affiliation: Department of Psychiatry and Neurobehavioral Sciences, University of Virginia, Charlottesville, USA.
authors.forename: Bankole A
authors.initials: BA
authors.lastname: Johnson
authors.affiliation: Laboratoire de Statistique Théorique et Appliquée Université Pierre et Marie Curie, Paris VI, France.
authors.forename: John M
authors.initials: JM
authors.lastname: O'Quigley
mesh_terms: D000427:Alcohol Deterrents / Q000627:therapeutic use; D000437:Alcoholism / Q000188:drug therapy*; D056808:Biostatistics; D003627:Data Interpretation, Statistical; D005632:Fructose / Q000031:analogs & derivatives / Q000627:therapeutic use; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D015233:Models, Statistical; D016016:Proportional Hazards Models; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data; D000077236:Topiramate
chemical_list: D000427:Alcohol Deterrents; D000077236:Topiramate; D005632:Fructose