Exposure density sampling: Dynamic matching with respect to a time-dependent exposure

Estimating the potential risk associated with an exposure occurring over time requires complex statistical techniques, since ignoring the time from study entry until the exposure leads to potentially seriously biased effect estimates. A prominent example is estimating the effect of hospital-acquired infections on adverse outcomes in patients admitted to the intensive care unit. Exposure density sampling has been proposed as an approach to dynamic matching with respect to a time-dependent exposure. Firstly, exposure density sampling can be useful to reduce the workload of study follow up, as it includes all exposed but only a subset of the not yet exposed individuals. Secondly, it can help to obtain a comparable control group by including propensity score matching. In the present article, we provide the theoretical justification that data obtained by exposure density sampling can be analyzed as a left-truncated cohort. It is shown that exposure density sampling allows estimation of the effect of a time-dependent exposure as well as further baseline covariates on a subsequent event, with only minor loss in precision as compared with a full cohort analysis. The sampling is applied to a real data example (hospital-acquired infections in intensive care units) and in a simulation study. We also provide an estimate of the loss in precision in terms of an increased standard error in the reduced data set after exposure density sampling as compared with the full cohort.