8.3 Interactions and stratification

An interaction between treatment and another covariate lets the treatment effect differ between groups (effect modification). In veteran, adding the treatment-by-cell-type interaction raises the log partial likelihood from \(-474.9\) to \(-471.6\), a statistic of \(6.6\) on \(3\) degrees of freedom, \(p = 0.08\): weak evidence at most that the treatment works differently for different tumours. Subgroup analyses of this kind should be pre-specified and interpreted cautiously, since with many subgroups some will appear to differ by chance.

A stratified Cox model gives each stratum its own baseline hazard \(h_{0s}(t)\), with common coefficients for the other covariates: \[ h(t \mid x, s) = h_{0s}(t)e^{\beta ^{\mathsf T}x} . \] It is used for a factor whose effect is not proportional, or which is a nuisance whose effect need not be estimated, such as the centre in a multicentre trial. Stratifying veteran by cell type gives a treatment hazard ratio of \(1.26\) and \(0.965\) per Karnofsky point, close to the unstratified values; the price is that no hazard ratio is estimated for the stratification factor itself.

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