Multiple population models for multivariate random length data--with applications in clinical trials

This paper focuses on the development and study of multiple population models for multivariate random length data, of the type often encountered in clinical trials. If experimental outcomes per subject consist of multiple measurements of a quantitative variable and the number of these measurements, then a multivariate random length vector is observed. For this type of data, the experimental treatment is likely to affect both the quantitative measurements and the number of these measurements. One example of such data is from the National Heart, Lung and Blood Institute Type II coronary intervention study (Brensike et al. (1982; Controlled Clinical Trials 3, 91-111; 1984, Circulation 69, 313-324)). The outcome data consist of vectors of lesion sizes with lengths determined by the number of underlying lesions assessed from the patients' angiograms, where both the numbers and the lesion sizes depend on patients' overall disease status. We propose models which can realistically describe the relationships between the quantitative variables and the number of responses. The asymptotic covariance of the maximum likelihood estimators is obtained. Data from the Type II study are analyzed using this multiple population model.