Advice on Survival Analysis - Cox model

[Eddy Simms]

I have the survival time for two groups and 7 units and I suspect that there is an interaction between some of the units and group. Univariate analysis shows there to be a difference in the survival curves for group and unit, but the KM plot shows that the assumption of proportional hazards does not hold for unit, and this is confirmed by:
stcox i.unit
. estat phtest, det
Test of proportional-hazards assumption
Time: Time
----------------------------------------------------------------
| rho chi2 df Prob>chi2
------------+---------------------------------------------------
1b.unit | . . 1 .
2.unit | -0.07373 1.47 1 0.2258
3.unit | -0.09501 2.41 1 0.1206
4.unit | -0.10126 2.78 1 0.0954
5.unit | -0.02570 0.18 1 0.6686
6.unit | -0.21703 13.39 1 0.0003
7.unit | -0.06441 1.11 1 0.2915
------------+---------------------------------------------------
global test | 16.11 6 0.0132
----------------------------------------------------------------
and
stcox i.group i.unit
. estat phtest
Test of proportional-hazards assumption

Time: Time
----------------------------------------------------------------
| chi2 df Prob>chi2
------------+---------------------------------------------------
global test | 17.85 7 0.0127
----------------------------------------------------------------

but when I include the interaction term
stcox i.group##i.unit
. estat phtest
Test of proportional-hazards assumption

Time: Time
----------------------------------------------------------------
| chi2 df Prob>chi2
------------+---------------------------------------------------
global test | 14.19 13 0.3607
----------------------------------------------------------------

there is no problem with the assumption of proportional hazards, and comparing the two models with lrtest shows the interaction term to be significant.

My query is - can I use the interaction model in a Cox regression when one of the main terms violates the PH assumption and my model comparison is based on this assumption, or should I go straight to a parametric regression, streg, where I will have to base the selection of the distribution on Information Criteria as I have no theoretical basis for choosing a distribution. Or is there an alternative approach that I could use?

Eddy

[Clyde Schechter]

Yes. In fact, often the way to resolve a problem with non-proportional hazards is to introduce interaction terms! What these results are telling you is that the effect of group is heterogeneous: there is not a single hazard ratio that appropriately describes it. The same is true for unit. But when you fine-grain down to groups and units combined with the interaction, each of those subsets is sufficiently homogeneous as to support a single hazard ratio consistently;. Indeed, it is entirely possible that the heterogeneity of effect within group is due entirely to the differences among the units embedded within the group. In that situation, the interaction is actually a perfect way to obtain conformity to the proportional hazards assumption that actually reflects the real data generating process.

[Eddy Simms]

Thank you for your clear explanation. I managed to miss that in my text books.