Multi-parameter regression survival models

The proportional hazards (PH) assumption in survival analysis may not always be appropriate. If data do not obey the assumption then we will reach incorrect conclusions by making it. For example we may find a covariate to be statistically insignificant when in fact it is important, but on a non-PH scale. Even if a PH model does pick up the statistical significance of such a 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 parametric PH modelling which we call multi-parameter regression, MPR, modelling.