Abstract

Binomial regression is an estimation technique used for predicting a binary event status at future time points. In survival analysis the outcome is the time between a well-defined time origin (or ) and the occurrence of an event. The key to using binomial regression for time-to-event outcome is the observation that at any time horizon after the time origin the event status is binary, taking the value 1 if the event has occurred, and 0 otherwise. Clearly, the event status at a single time horizon carries much less information than the time-to-event outcome. However, the time process {N _e (t)= I{T ≤ t,ϵ} : t ∈ [0, ∞)} represents the same information as (T, ϵ), where ϵ indicates the type of the event and T the event time. Indeed, there is a one-to-one correspondence between binomial regression models and (Doksum and Gasko, 1990) which holds also in more complex models for event history analysis (Jewell, 2005).