The Time-Dependent Bias and its Effect on Extra Length of Stay due to Nosocomial Infection - Barnett, Adrian G.; Beyersmann, Jan; Allignol, Arthur; Rosenthal, Victor D.; Graves, Nicholas; Wolkewitz, Martin (Value in health, 2011)
Many studies disregard the time dependence of nosocomial infection when examining length of hospital stay and the associated financial costs. This leads to the “time-dependent bias,” which biases multiplicative hazard ratios. We demonstrate the time-dependent bias on the additive scale of extra length of stay. To estimate the extra length of stay due to infection, we used a multistate model that accounted for the time of infection. For comparison we used a generalized linear model assuming a gamma distribution, a commonly used model that ignores the time of infection. We applied these two methods to a large prospective cohort of hospital admissions from Argentina, and compared the methods' performance using a simulation study. For the Argentina data the extra length of stay due to nosocomial infection was 11.23 days when ignoring time dependence and only 1.35 days after accounting for the time of infection. The simulations showed that ignoring time dependence consistently overestimated the extra length of stay. This overestimation was similar for different rates of infection and even when an infection prolonged or shortened stay. We show examples where the time-dependent bias remains unchanged for the true discharge hazard ratios, but the bias for the extra length of stay is doubled because length of stay depends on the infection hazard. Ignoring the timing of nosocomial infection gives estimates that greatly overestimate its effect on the extra length of hospital stay.