There are few publications on analyses of event data treating the
potential time-dependent structure of covariates as such.
The most common approach is to apply modified versions of the
Cox model, probably because this is already available in
packages like BMDP or SAS.
Obviously, a time-dependent Cox model can handle time-varying covariates.
But the resulting estimate of the effect is a constant,
a smoothed average over follow-up time.
The competitor, the linear additive regression model by Aalen (1989, 1993) is able to deal with time-dependent structures of covariates and to estimate time-dependent effects, too. Just a few papers do compare Aalen's linear additive model with the multiplicative Cox model, but comparisons have only been reported for applications with data fixed at baseline values. Hence, we re-analyzed text-book and own data by use of both competing approaches and found quite differing results (4). Furthermore, within the "Sonderforschungsbereichs 386", we developed DynaSURV, a collection of SAS macros to analyze dynamic survival data, including estimators and diagnostics for the linear Aalen model, and for any mixture of time-dependent and fixed covariates. DynaSURV (released for public use at time of the conference) is an experimental tool kit whose main building blocks are
- estimation of cumulated regression functions,
- graphical display of cumulated regression functions,
- computation and plot of (pointwise) confidence intervals,
- testing on significance (of the regression function),
- kernel smoothing of regression functions and/or effect of covariates,
- diagnostic tools (Schoenfeld-, score-, martingale residuals).
Despite advantages like estimation of dynamic covariate effects, the Aalen model has some restrictions, e.g. on the number of time-dependent covariates involved. Thus we next incorporate into DynaSURV some extensions, e.g. the partly parametric additive risk model (McKeague & Sasieni, 1994). This model provides advantages similar to the Aalen approach but is more flexible with respect to number and type of covariates.