How much does hyperkalemia lengthen inpatient stays? About methodological issues in analyzing time-dependant events

Adverse events may increase the hospital length of stay (LOS). As a consequence, computing the mean difference of LOS between two inpatient groups, with or without event, is a convenient way to evaluate their severity. Conversely, some adverse events are time-dependent: this leads to overestimate the consequences of the adverse event when statistical tests are performed. In this paper, we interest on hyperkalemia in the inpatient database of a community hospital (2% of the inpatient stays). The cumulated risk of hyperkalemia appears to be a linear function of the LOS. We compute the LOS difference associated with hyperkalemia by using 17 statistical methods. The raw LOS difference is 8.8 days, but the simulation finds a difference of 2.3 days, while the regressions (with linear or log link, with or without pairing, with or without propensity score) find a difference of 4.4 to 4.6 days. The characteristics of the methods are discussed, but it is not possible to know which one is true. However the raw difference seems to overestimate the truth. This methodological bias is quite frequent and is a challenge in public health, as it participates in false knowledge discovery, which could lead decision makers to focus on wrong issues and make wrong decisions.