Prediction of short-term survival with an application in primary biliary cirrhosis

Many long-term follow-up studies for survival accumulate repeated measurements of prognostic factors. Survival models which include only covariate values at baseline do not use all available information, and do not relate to survival predictions for times other than at that baseline. Time-dependent covariate models (which update covariate values as measurements occur through time) might be used, though limitations of software for estimating the underlying hazard functions and difficulty in relating hazard function changes to survival prediction present serious drawbacks. By dividing each patient's follow-up into successive intervals of equal length (using a length of interest for prediction) and with measurements available at the start of each, we describe how an analysis taking person-intervals as the observation units can be undertaken using readily available software to produce short-term survival models. We show that this approach is related to both the baseline and time-dependent covariate models. The method is illustrated using data from a long-term study of patients with primary biliary cirrhosis, where interest is in short-term survival predictions to aid the decision when to undertake liver transplantation.