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We develop flexible multi-parameter regression survival models for intervalcensored survival data arising in longitudinal prospective studies andlongitudinal randomised controlled clinical trials. A multi-parameter Weibullregression survival model, which is wholly parametric, and has non-proportionalhazards, is the main focus of the paper. We describe the basic model, developthe interval-censored likelihood and extend the model to include gamma frailtyand a dispersion model. We evaluate the models by means of a simulation studyand a detailed re-analysis of data from the Signal Tandmobiel$^{\circledR}$study. The results demonstrate that the multi-parameter regression model withfrailty is computationally efficient and provides an excellent fit to the data.

A Multi-parameter regression model for interval censored survival data