gms | German Medical Science

Time-dependent exposures occur in various epidemiological fields, i.e. participants enter the study unexposed and may change their exposure status and get exposed. Ignoring the time-dependent nature of these exposures leads to time-dependent bias [Ref. 1], which, in a broader sense, is remarkably common in medical journals [Ref. 2]. If time to death is the final outcome, this bias is also called 'survival bias' or 'immortal time bias' [Ref. 3], since the exposed subjects must survive the time between cohort entry and the first day of exposure.

The impact of time-dependent exposures on the time until study endpoint may correctly be analysed with data of a full cohort. An alternative way to take the time-dependency of the exposure into account is matching for time to exposure. To evaluate how this approach creates biased hazard ratios, it is compared to the correct method as well as to the approach, in which the time-dependent nature of the exposure is ignored.

Using data of the SIR-3 study (Germany, 2000–2001) on the impact of nosocomial infections in patients admitted to intensive care units (ICU), the correctly estimated hazard ratio of nosocomial pneumonia (NP) on discharge is HR=0.64 (95-% CI: 0.55–0.73). Thus, exposure to NP leads to a prolongation of ICU stay. If unexposed patients are matched for time to exposure, the HR is only slightly biased (HR=0.54). If the time-dependent nature of NP is ignored, the hazard ratio is substantially underestimated (HR=0.38). Including further matching variables like age, gender, ICU, date of admission does not redeem the matching-bias. Simulations show that the HR is always underestimated. For a true HR>1 this may even lead to a reversed effect. The bias decreases if fewer patients are exposed.

Whenever the impact of a time-dependent exposure on the time until study endpoint (e.g. death, discharge from ICU) is considered, the time-dependent nature has to be taken into account. The best choice is to include it as a time-dependent exposure when data of the full cohort is available. In case that only one (or two) unexposed patients per exposed patient are collected (e.g. due to economic reasons), the time-dependent nature should be taken into account by matching for exposure time. The bias may be tolerable if the exposure is very rare.