Thomas H. Scheike 
Dept of Biostatistics
University of Copenhagen

Dynamic regression models in Survival Analysis

Abstract

The talk will present an overview of recent work on how to  deal with
time-varying effects in survival analysis. I consider both the
proportional Cox regression model and the additive risk model by
Aalen.

The Cox model is the standard tool to describe treatment effects in
survival analysis.  A basic assumption behind this analysis that is
often violated  is that the treatment effect is constant over time.
Estimation of time-varying (non-parametric) effects in the  Cox model
is made difficult by the non-linearity of the  Cox model and makes the
choice of smoothing parameters necessary.  I will present an iterative
estimation procedure that is efficient and  amounts to smoothing of
scaled Schoenfeld residuals in each step.

The additive risk model by Aalen provides an alternative to the  Cox
model, that is particularly appealing when the interest is on
estimating time-varying effects.   Time-varying effects can be
estimated without any smoothing and  explicit estimators exist. The
semi-parametric submodel of the Aalen model have the same pleasant
properties, and I will show how  to test if effects are time-varying
in this model.