The two‐way proportional hazards model

Summary. Survival analysis problems often involve dual timescales, most commonly calendar date and lifetime, the latter being the elapsed time since an initiating event such as a heart transplant. In our main example attention is focused on the hazard rate of ‘death’ as a function of calendar date. Three different estimates are discussed, one each from proportional hazards analyses on the lifetime and the calendar date scales, and one from a symmetric approach called here the ‘two‐way proportional hazards model’, a multiplicative hazards model going back to Lexis in the 1870s. The three are connected through a Poisson generalized linear model for the Lexis diagram. The two‐way model is shown to combine the information from the two ‘one‐way’ proportional hazards analyses efficiently, at the cost of more extensive parametric modelling.