gms | German Medical Science

Infectious diseases are an increasing challenge for health care systems not only in 2020. It is worth investigating the effect of these (rare) diseases on the medical and economic burden. We consider patients, who are admitted to the hospital. During their stay, some of these patients acquire an infection impacting their health and time in the hospital. Usually, cohort studies are considered, aiming to analyze the effect of the time-dependent exposure, represented by the infection, on the length of hospital stay. These studies are subject to censoring constituting a further challenge even when the outcome occurs fairly often, but the infection is rare.

Collecting data of all cases would entail high costs and effort since such cohort studies often require a lot of individuals to be enrolled. The traditional nested case-control design is often considered for large cohort studies, where the analysis is based on a subset of the full cohort, incorporating all cases, but only some individuals without the outcome. The latter does not lead to a reduction in the number of individuals in this setting since information of all cases still is required. The novel nested exposure case-control design is the more adequate method when analyzing the effect of a rarely time-dependent exposure to a commonly observed outcome. Its sampling mechanism guarantees, that for all exposed cases but only for a subset of the unexposed cases data is collected. Compared to the traditional nested case-control design or the full cohort, fewer individuals have to be considered, which reduces the costs as well as the effort. The estimator of the cumulative baseline hazard as an absolute risk measure, however, requires the information of all cases since the calculation considers the increments of all observed event times and subsequently aggregates over these event times. Different methods to deal with the occurring missing covariate values are developed to obtain an unbiased Breslow-type estimator within the nested exposure case-control design. To this end, the proposed methods include, for instance, a semi-parametric estimator imputing the respective covariate value by a single value, corresponding to the mean (mode). Another approach is, to create an estimator based on multiple imputation. Also, a non-parametric estimator adding some weighting factor to the increments calculated at the observed event times to account for the missing cases is considered.

The different methods are compared in simulation studies, and with the true cumulative baseline hazard, the estimates obtained when using the full gold-standard Cox cohort or the traditional nested case-control design.

Additionally, the methods are applied to a real-life data set on hospital-acquired infection in German hospitals and compared to the common costly Cox model. The aim of the project is, to state a method that estimates the cumulative baseline hazard in nested exposure case-control designs. That method should retain the advantage of the reduced number of individuals and deal with the missing covariate inf

The authors declare that they have no competing interests.

The authors declare that an ethics committee vote is not required.