To the Editor—We thank Dr. Wolkewitz for his thoughtful comments and clear breakdown of cumulative risk-based and rate-based measures of association in hospital acquired infection (HAI) research. We agree that a thorough understanding of the distinction between rate-based and cumulative risk-based metrics is essential for researchers performing studies of HAI risk factors.

Another way of thinking about this distinction is through the lens of the study question, which is often either etiologic or prognostic in nature.Reference Noordzij, Leffondre, van Stralen, Zoccali, Dekker and Jager ¹ The objective of an etiologic research question is to assess the causal association between a risk factor and a given outcome. That is, if a given exposure were introduced experimentally, would a given patient be more or less likely to experience the outcome.Reference Little and Rubin ² On the other hand, prognostic research aims to predict the probability that a patient subgroup experiences an outcome on or before a given time point in a hospital stay, irrespective of whether a given risk factor caused an increased rate of disease.

In HAI research, patient subgroups with longer hospital stays may be more likely to develop an HAI during a given stay only because of the longer average duration of their stay. Whereas a risk-based approach would capture this as a difference in cumulative risk of HAI, a rate-based approach would find that the rate of HAI is no different. Epidemiologists interested in questions regarding etiology may be more likely to gravitate toward rate-based approaches, which have been subject to criticism by advocates of causal inference methods,Reference Hernán ³ while clinicians interested in prognostic questions may be more likely to veer toward cumulative risk-based approaches. Because of our primary interest in developing strategies for the prevention of HAI, which exclude modifying length of hospital stay, our research has tended to focus on rate-based approaches.Reference Brown, Daneman and Stevens ^{4 ,} Reference Brown, Jones and Daneman ⁵

In certain circumstances, a comparison of each approach may certainly be useful, while in others, it may not be worth the additional analytic burden. What is important is to understand and interpret the insights derived from cumulative risk-based and rate-based approaches correctly; to conflate the 2 approaches is to muddy the epidemiologic waters.