Parametric survival analysis: testing proportionality.

[Craig Knott]

I have a parametric survival model with the baseline hazard specified according to a Weibull distribution. I'm looking to test the assumption that hazard ratios are proportionate over time through the inclusion of a covariate*time interaction variable, but am wondering whether there's any particular reason I should choose one function of time over another when deriving such a variable.

I've seen some individuals opt to use linear time when using an exponential or Gompertz baseline function, and log time when using a Weibull function: https://lra.le.ac.uk/bitstream/2381/...HER_MJ_PhD.pdf

Elsewhere I've seen it mentioned that 'for proportional hazards models such as the Weibull, there is no method for the detection for non-proportional hazards': http://pan.oxfordjournals.org/content/18/2/189.abstract

In case it makes any difference, my covariate is a continuous variable scaled to log base 2.

Thoughts?

[Steve Samuels]

I don't think that there is a way to test proportionality in streg itself. But the Weibull is a special case of the proportional hazard models fit by stcox. (A distribution is Weibull if a log (-log) plot of the estimated baseline survival function against log time is linear-have you examined this?). To test for proportionality, do stcox and follow by the stphtest post-estimation commands. As you want a parametric model, a preferable approach is to use Paul Lambert's stpm2 (SSC). The Weibull is a special case (a linear function for the integrated hazard, so the Weibull assumption itself can be fitted and tested. Moreover, stpm2, like stcox, has a tvc() option for testing proportionality; the function of time is a restricted cubic spline, more general than either a log or linear function. Thus the statement you quote in your second reference is incorrect.

Reference: Lambert, P. C. and Royston, P. (2009). Further development of flexible parametric models for survival analysis. The Stata Journal, 9:265–290.

Available at :http://www.stata-journal.com/article...article=st0165