Bias due to censoring of deaths when calculating extra length of stay for patients acquiring a hospital infection

Shahina Rahman, Maja von Cube, Martin Schumacher, Martin Wolkewitz

In many studies the information of patients who are dying in the hospital is censored when examining the change in length of hospital stay (cLOS) due to hospital-acquired infections (HIs). While appropriate estimators of cLOS are available in literature, the existence of the bias due to censoring of deaths was neither mentioned nor discussed by the according authors. Using multi-state models, we systematically evaluate the bias when estimating cLOS in such a way. We first evaluate the bias in a mathematically closed form assuming a setting with constant hazards. To estimate the cLOS due to HIs non-parametrically, we relax the assumption of constant hazards and consider a time-inhomogeneous Markov model. In our analytical evaluation we are able to discuss challenging effects of the bias on cLOS. These are in regard to direct and indirect differential mortality. Moreover, we can make statements about the magnitude and direction of the bias. For real-world relevance, we illustrate the bias on a publicly available prospective cohort study on hospital-acquired pneumonia in intensive-care. Based on our findings, we can conclude that censoring the death cases in the hospital and considering only patients discharged alive should be avoided when estimating cLOS. Moreover, we found that the closed mathematical form can be used to describe the bias for settings with constant hazards.