The Lognormal Distribution as a Model for Survival Time in Cancer, With an Emphasis on Prognostic Factors

Despite their long history, parametric survival‐time models have largely been neglected in the modern biostatistical and medical literature in favour of the Cox proportional hazards model. Here, I present a case for the use of the lognormal distribution in the analysis of survival times of breast and ovarian cancer patients, specifically in modelling the effects of prognostic factors. The lognormal provides a completely specified probability distribution for the observations and a sensible estimate of the variation explained by the model, a quantity that is controversial for the Cox model. I show how imputation of censored observations under the model may be used to inspect the data using familiar graphical and other technques. Results from the Cox and lognormal models are compared and shown apparently to differ to some extent. However, it is hard to judge which model gives the more accurate estimates. It is concluded that provided the lognormal model fits the data adequately, it may be a useful approach to the analysis of censored survival data.