Survival analysis in natural history studies of disease

Clinicians often wish to use data from clinical trials or hospital databases to study disease natural history. Of particular interest are estimated survival and prognostic factors. In this context, it may be appropriate to measure survival from diagnosis or some other time origin, possibly prior to study entry. We describe the application of methods for truncated survival data, and compare these with the standard product limit estimator and proportional hazards models in the measurement of survival from entry. Theoretical considerations suggest that analysis of survival from entry may under- or overestimate the survival distribution of interest, depending on the shape of the true underlying hazard. Analogous results hold for the coefficients from a proportional hazards model. We illustrate our findings with data from a multicenter clinical trial and a hospital database.