Multi-parameter regression survival models

It is well known that the proportional hazards (PH) assumption is a simplifying assumption in survival analysis that may not always be appropriate. However, PH models are routinely fitted and inference is made on the data based on such models. A major flaw here is that if the data are non-PH then we will reach incorrect conclusions by making this assumption. For example we may find a covariate to be statistically insigni cant when in fact it is important, but the model fails to pick this up. Even if a PH model does pick up the statistical significance of a non-PH covariate, the nature of the effect of the covariate on survival, as determined by this simplistic model, will clearly be incorrect. We introduce a regression-based extension of PH modelling to try an account for situations such as those described above and offer new, previously unavailable insights, into the data.