On the relationship between response to treatment and survival time

In this paper we review several approaches which have been used to investigate the relationship between survival time and response to treatment. We show that the approaches based on summary data are subjected to various types of biases (publication bias, confounding by prognostic features, ecologic bias) and are therefore of doubtful value. We also discuss several approaches based on individual patient data. Comparisons of survival by response are generally subject to length-biased sampling, and are therefore inadequate. The landmark method is adequate when responses occur soon after starting treatment, but not when responses may appear later in the course of the disease. For responses which can occur over extended periods of time, response must be considered as a time-dependent covariate. Using data from randomized trials in advanced colorectal cancer, we show that response is a potent and independent prognostic factor for survival in this disease. Analyses using the landmark method yield results essentially equivalent to those in which response is considered as a time-dependent covariate. The hazard rate of responders is about half that of non-responders, after taking the patient's performance status into account. The issue of response as a surrogate marker for survival is taken up further in a separate paper.