Joint models for longitudinal and time‐to‐event data in a case‐cohort design

Studies with longitudinal measurements are common in clinical research. Particular interest lies in studies where the repeated measurements are used to predict a time‐to‐event outcome, such as mortality, in a dynamic manner. If event rates in a study are low, however, and most information is to be expected from the patients experiencing the study endpoint, it may be more cost efficient to only use a subset of the data. One way of achieving this is by applying a case‐cohort design, which selects all cases and only a random samples of the noncases. In the standard way of analyzing data in a case‐cohort design, the noncases who were not selected are completely excluded from analysis; however, the overrepresentation of the cases will lead to bias. We propose to include survival information of all patients from the cohort in the analysis. We approach the fact that we do not have longitudinal information for a subset of the patients as a missing data problem and argue that the missingness mechanism is missing at random. Hence, results obtained from an appropriate model, such as a joint model, should remain valid. Simulations indicate that our method performs similar to fitting the model on a full cohort, both in terms of parameters estimates and predictions of survival probabilities. Estimating the model on the classical version of the case‐cohort design shows clear bias and worse performance of the predictions. The procedure is further illustrated in data from a biomarker study on acute coronary syndrome patients, BIOMArCS.