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