• Clustered data;
  • EM algorithm;
  • Excessive zeros;
  • Mixture models;
  • Two-part models

Summary.  This article considers clinical trials in which the efficacy measure is taken from several sites within each patient, such as the alveolar bone height of the tooth sites, or bone mineral densities of the lumbar spine sites. Since usually only a small portion of these sites will exhibit changes, the conventional method using per patient average gives a diluted result due to excessive no changes in the data. Different methods have been proposed for this type of data in the case where the observations are mutually independent. This includes the popular “two-part model” (Lachenbruch, 2001, Statistics in Medicine20, 1215–1234; 2002, Statistical Methods in Medical Research11, 297–302), which is related to the “composite approach” for discrete and continuous data in Shih and Quan (1997, Statistics in Medicine16, 1225–1239; 2001, Statistica Sinica11, 53–62). In this article, we model the data with excessive zeros (no changes) in clustered data using a mixture of distributions, and taking into account possible measurement errors. This mixture model includes the two-part model as a special case when one component of the mixture degenerates.