Missing information caused by death leads to bias in relative risk estimates

In most clinical and epidemiologic studies, information on disease status is usually collected at regular follow-up visits. Often, this information can only be retrieved in individuals who are alive at follow-up, and studies frequently right censor individuals with missing information because of death in the analysis. Such ad hoc analyses can lead to seriously biased hazard ratio estimates of potential risk factors. We systematically investigate this bias.

We illustrate under which conditions the bias can occur. Considering three numerical studies, we characterize the bias, its magnitude, and direction as well as its real-world relevance.

Depending on the situation studied, the bias can be substantial and in both directions. It is mainly caused by differential mortality: if deaths without occurrence of the disease are more pronounced, the risk factor effect is overestimated. However, if the risk for dying after being diseased is prevailing, the effect is mostly underestimated and might even change signs.

The bias is a result of both, a too coarse follow-up and an ad hoc Cox analysis in which the data sample is restricted to the observed and known event history. This is especially relevant for studies in which a considerable number of death cases are expected.