Enhancing Survival Analysis in Epidemiologic Studies: An Integrated Model for Overall and Conditional Survival

Abstract

Survival analysis is a well-known statistical technique which evaluates the time from an origin to an outcome of interest. The origin might be the date of diagnosis or when an intervention is begun, while the outcome might be death, relapse or cure. Although this addresses the overall survival (OS) experience, there is considerable interest in conditional survival (CS). That is, conditional on surviving to an intermediate milestone of clinical significance, what is the survival experience thereafter? A common approach is to apply standard survival techniques to individuals event-free and uncensored at the milestone. Although valid inferences are forthcoming from this technique, the separate analyses can lead to a fragmented and disconnected analytic strategy especially when there are multiple milestones. In this paper, we demonstrate how both OS and CS statistical inference can be performed in a single piecewise exponential model. Like the proportional hazards model, it avoids making arbitrary assumptions on the overall shape of the hazard function and provides for baseline and time-dependent covariates. We indicate how to formulate the model and derive the OS and CS probabilities. It is shown that the estimators enjoy optimal asymptotic properties and hypotheses can be readily tested using Wald \(\chi^2\) procedures. The advantage is that all OS and CS inferences are performed in a single integrated model leading to a coherent inferential strategy. The methodology is illustrated with an example.