To the Editor—We congratulate Brown et alReference Brown, Daneman and Stevens ¹ for the excellent review article about the necessary issues that need to be addressed in multivariate analyses of hospital-acquired infection (HAI) risk factors. We agree that 4 statistical issues should be addressed in such an analysis as follows: (1) adjust for the at-risk time, (2) avoid the time-dependent bias in case of time-dependent exposures, (3) include ecological exposure measures, and (4) account for correlated outcomes.

In addition to these challenges, we would like to emphasize the need to account for competing events when evaluating the risk of HAI.Reference Wolkewitz, Cooper, Bonten, Barnett and Schumacher ^{2 ,} Reference Schumacher, Allignol, Beyersmann, Binder and Wolkewitz ³ When studying the time to HAI, patients are usually followed until the occurrence of HAI, discharge, or death without HAI. Due to the definition of HAI, the risk of acquiring HAI after discharge is 0, and it is also 0 after death. Thus, it is recognized that discharge or death without HAI are competing events for HAI.Reference Wolkewitz, Cooper, Bonten, Barnett and Schumacher ^{2 ,} Reference Schumacher, Allignol, Beyersmann, Binder and Wolkewitz ³ In the presence of competing events, 2 different metrics should be distinguished: the (hazard) rate metric, which explores the etiology, and the risk metric, which is related to prediction (Table 1).

TABLE 1 Overview of Rate and Risk Metric Models in Multivariate Analyses of Hospital-Acquired Infection (HAI) Risk Factors

For instance, in a multilevel competing risk analysis,Reference Wolkewitz, Cooper and Palomar-Martinez ⁴ we showed that intensive care unit (ICU) patients who received antibiotic treatment 48 h before and/or after ICU admission had a lower hazard of acquiring a primary or secondary nosocomial bacteremia of any pathogen (hazard ratio [HR], 0.83; 95% CI, 0.77–0.88). For the competing events, antibiotic treatment is also associated with an increased death hazard (HR, 1.08; 95% CI, 1.04–1.13) and a reduced discharge hazard (HR, 0.70; 95% CI, 0.69–0.71), meaning that patients with antibiotic treatment remain at risk longer. These 3 hazard ratios refer to the rate metric. However, the infection hazard ratio cannot be interpreted as a comparison of cumulative infection risk because the cumulative infection risk depends also on all competing event hazards.Reference Wolkewitz, Cooper, Bonten, Barnett and Schumacher ^{2 ,} Reference Schumacher, Allignol, Beyersmann, Binder and Wolkewitz ^{3 ,} Reference Latouche, Allignol, Beyersmann, Labopin and Fine ⁵ This can be seen if the antibiotic treatment is studied on a risk metric where the subdistribution hazard ratio is 1.01 (95% CI, 0.95–1.09). In this case, a simpler risk metric analysis via logistic regression and risk odds ratios yielded similar results.Reference Wolkewitz, Cooper and Palomar-Martinez ⁴ The phenomenon can be explained as follows: Even though patients with antibiotic treatment acquire less nosocomial bacteremia per ICU day at risk (nosocomial bacteremia HR, 0.83), their extended at-risk time in the ICU (discharge HR, 0.70) results eventually in an equal cumulative infection risk. Notably, the discharge hazard is much larger than the death hazard and is therefore the main determinant for the at-risk time.

It is very likely that there is a similar phenomenon in the analysis of Brown et al.Reference Brown, Daneman and Stevens ¹ In their second sensitivity analysis, they reported an amplified effect of direct antibiotic use in terms of an odds ratio of 2.26 (95% CI, 1.71–2.97); this analysis was based on a risk metric (see Table 1). We believe that this amplification can be explained analogously by a competing risk analysis. As in our analysis, we expect that patients with direct antibiotic use remain at risk longer in the hospital (ie, a reducing effect of antibiotic treatment on the discharge hazard occurs without HAI).

As correctly stated by Brown et al, when analyzing cohort studies with time-fixed or time-dependent exposures using the corresponding Cox proportional hazard model (approaches 1 and 2 in Brown et alReference Brown, Daneman and Stevens ¹ ), patients were technically considered censored if they experienced discharge or death without infection. This analysis is valid, but we argue that it is incomplete if the impact of the exposures on discharge or death without infection is not studied. Therefore, an additional analysis regarding the competing events is necessary. This is done by performing additional Cox proportional hazard models with the same exposures but for the competing events as the outcome. Patients who acquire a HAI are then censored at the time of infection onset.Reference Wolkewitz, Cooper and Palomar-Martinez ⁴

Such competing risk analyses are not only very informative, they might also explain phenomena due to the 2 metrics. We believe that competing risk analyses are necessary since ignoring the potential effect of exposures on the competing events can easily lead to incorrect conclusions. For instance, a rate metric analysis showed no effect of burns on HAI in African children but a simple risk metric analyses showed a 3 times higher risk of HAI because children with burns remain at risk much longer in the hospital.Reference Schumacher, Allignol, Beyersmann, Binder and Wolkewitz ³ The type of metric highly matters and influences the conclusion. Thus, only the use of both metrics can provide a complete picture in multivariate analyses of HAI risk factors.Reference Wolkewitz, Cooper and Palomar-Martinez ^{4 ,} Reference Latouche, Allignol, Beyersmann, Labopin and Fine ⁵ However, in the presence of time-dependent exposures, the rate metric approaches are very suitable,Reference Wolkewitz, Vonberg and Grundmann ⁶ but risk metric approaches have still challenging limitations in their interpretation.