Models for Multivariate Random Length Data with Applications in Clinical Trials

Abstract

This paper focuses on the development of models for multivariate random length data encountered in clinical or medical trials. When a patient's data consist of multiple responses of a certain quantitative variable and a random number of such responses, an observation of a multivariate random vector with random length is obtained. The trial therapy is likely to affect both the magnitude of each response and the number of responses through some underlying mechanism. The approach in this paper to analyzing these complex data is by proposing statistical models that meaningfully describe the relationships between the quantitative variables and the number of responses. Multiple population models for multivariate random length data with and without covariates are introduced in this paper. Maximum likelihood equation (MLE) methods are used for parameter estimation. The asymptotic efficiency of the MLEs is obtained via information matrices of the parameters. Data from the TYPE II coronary intervention study are analyzed using the multiple population model without covariates.