Size-biased sensitivity analysis for matched pairs design to assess the impact of healthcare-associated infections

Abstract:Healthcare-associated infections are serious adverse events that occur during a hospital admission. Quantifying the impact of these infections on inpatient length of stay and cost has important policy implications due to the Hospital-Acquired Conditions Reduction Program in the United States. However, most studies on this topic are flawed because they do not account for when a healthcare-associated infection occurred during a hospital admission. Such an approach leads to selection bias because patients with longer hospital stays are more likely to experience an infection due to their increased exposure time. Time of infection is often not incorporated into the estimation strategy because this information is unknown, yet there are no methods that account for the selection bias in this scenario. To address this problem, we propose a sensitivity analysis for matched pairs designs for assessing the effect of healthcare-associated infections on length of stay and cost when time of infection is unknown. The approach models the probability of infection, or the assignment mechanism, as proportional to a power function of the uninfected length of stay, where the sensitivity parameter is the value of the power. The general idea is to incorporate the degree of exposure into the probability of an infection occurring. Under this size-biased assignment mechanism, we develop hypothesis tests under a sharp null hypothesis of constant multiplicative effects. The approach is demonstrated on a pediatric cohort of inpatient encounters and compared to benchmark estimates that properly account for time of infection. The results reaffirm the severe degree of bias when not accounting for time of infection and also show that the proposed sensitivity analysis captures the benchmark estimates for plausible and theoretically justified values of the sensitivity parameter.