Application of multistate models in hospital epidemiology: advances and challenges.

Survival analysis has established itself as a major statistical technique in medical research. Applications in hospital epidemiology, however, are only beginning to emerge. One reason for this delay is that usually complete follow-up of patients in hospital is feasible. This overview discusses where survival techniques provide additional insight into hospital epidemiology, and where they are, in fact, needed even in the absence of right-censoring.

Incidence densities in a competing events analysis.

Epidemiologists often study the incidence density (ID; also known as incidence rate), which is the number of observed events divided by population-time at risk. Its computational simplicity makes it attractive in applications, but a common concern is that the ID is misleading if the underlying hazard is not constant in time. Another difficulty arises if competing events are present, which seems to have attracted less attention in the literature. However, there are situations in which the presence of competing events obscures the analysis more than nonconstant hazards do. The authors illustrate such a situation using data on infectious complications in patients receiving stem cell transplants, showing that a certain transplant type reduces the infection ID but eventually increases the cumulative infection probability because of its effect on the competing event. The authors investigate the extent to which IDs allow for a reasonable analysis of competing events. They suggest a simple multistate-type graphic based on IDs, which immediately displays the competing event situation. The authors also suggest a more formal summary analysis in terms of a best approximating effect on the cumulative event probability, considering another data example of US women infected with human immunodeficiency virus. Competing events and even more complex event patterns may be adequately addressed with the suggested methodology.

Proportional subdistribution hazards modeling offers a summary analysis, even if misspecified.

Competing risks model time-to-first-event and the event type. Our motivating data example is the ONKO-KISS study on the occurrence of infections in neutropenic patients after stem-cell transplantation with first-event-types 'infection' and 'end of neutropenia'. The standard approach to study the effects of covariates in competing risks is to assume each event-specific hazard (ESH) to follow a proportional hazards model. However, a summarizing probability interpretation of the different event-specific effects of one covariate can be challenging. This difficulty has led to the development of the proportional subdistribution hazards model of a competing event of interest. However, one model specification usually precludes the other. Assuming proportional ESHs, we find that the subdistribution log-hazard ratio may show a pronounced time-dependency, even changing sign. Still, the subdistribution analysis is useful by estimating the least false parameter (LFP), a time-averaged effect on the cumulative event probabilities. In examples, we find that the LFP offers a robust summary of the effects on the ESHs for different observation periods, ranging from heavy censoring to no censoring at all. In particular, if there is no effect on the competing ESH, the subdistribution log-hazard ratio is close to the event-specific log-hazard ratio of interest. We reanalyze an interpretationally challenging example from the ONKO-KISS study and conduct a simulation study, where we find that the LFP is reliably estimated by the subdistribution analysis even for moderate sample sizes.