Some comments on efficiency gains from auxiliary information for right-censored data

Heavily right-censored time to event, or survival, data arise frequently in research areas such as medicine and industrial reliability. Recently, there have been suggestions that auxiliary outcomes which are more fully observed may be used to “enhance” or increase the efficiency of inferences for a primary survival time variable. However, efficiency gains from this approach have mostly been very small. Most of the situations considered have involved semiparametric models, so in this note we consider two very simple fully parametric models. In the one case involving a correlated auxiliary variable that is always observed, we find that efficiency gains are small unless the response and auxiliary variable are very highly correlated and the response is heavily censored. In the second case, which involves an intermediate stage in a three-stage model of failure, the efficiency gains can be more substantial. We suggest that careful study of specific situations is needed to identify opportunities for “enhanced” inferences, but that substantial gains seem more likely when auxiliary information involves structural information about the failure process.