A parametric estimation procedure for relapse time distributions.



Liselotte Åhlström
Astra Hässle AB
Mölndal 		Olle Nerman and Marita Olsson
Mathematical Statistics
Chalmers and Göteborg University

Abstract

In certain clinical trials where the distribution of relapse-times is considered, there are two modes of detection; a relapse is detected either at one of a number of predetermined examinations, or at a spontaneous visit initiated by the patient. In the first case we get an interval-censored observation of X=time to relapse,, and in the second case we observe Y=time to symptoms. Typical diseases for which these clinical trials are used, are cancer and ulcer.

In order to estimate X, the time to relapse, from the data obtained in such a clinical trial, we suggest to model the joint distribution of (X,Y) with a bivariate phase-type distribution. This model can also be regarded as a hidden Markov model of the progression of the disease. The fact that we use a parametric model of the joint distribution of (X,Y) means that we can extract information about X also from the observations of Y, which is not possible in a non-parametric model for X. Furthermore, this model allows natural distributional forms for X and Y (e.g. gamma distributions), and smooth dependencies between the distributions of X and Y-X.

KEY WORDS: EM algorithm, hidden Markov process, interval-censoring, phase-type distribution, relapse clinical trial.