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.