Survival models with two phases and length biased sampling

Abstract

A survival model is presented in which all patients go through a first phase of disease; some then die and the remainder progress to a second phase of disease. The data observed are the path taken and the total sojourn time in the system but not the time, if ever, at which the second phase is entered. The sojourn time in each phase is assumed to be exponentially distributed with possibly different rates for the two phases. Themodel describes serious diseases that progress through one or two phases, and can be extended to multiple phases. The model is extended to account for several length-biased sampling situations. Censoring is considered in all models. Maximum like lihood estimates for the parameters involved exist, are consistent and are a symptotically normal. One of the proposed models is applied to data from the Veterans Administration involving a study of coronary arterial occlusive disease.

Keywords:

• parametric survival analysis
• hazard rate
• maximtun likelihood estimation
• censoring
• piecevise exponential distribution