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With interest we read the article by Major et al1 on the effect of rifaximin ‘follow-on’ treatment to prevent recurrent Clostridium difficile infection (rCDI).
Major et al point out the advantage of their study sample being composed of elderly patients who represent the frailties and comorbidities of the target population. The frailty of the sample is reflected by the, compared with other trials on new agents, higher mortality rate, which is considered to increase the generalisability of the results to daily clinical practice.
A main statistical challenge when studying a frail patient population using a non-fatal endpoint is dealing with mortality.2
Patients who died without rCDI are no longer at risk of a recurrent infection. Thus, death is a competing risk of rCDI.
In their analysis, Major et al first exclude patients who have died or have withdrawn from the study before end of follow-up by using generalised estimating equations to estimate the risk difference (RD) of rCDI. Second, they treat them equally as randomly censored by using a Kaplan-Meier estimator (K-M) to estimate the risk of rCDI.
However, in contrast to patients who have withdrawn from the study and remain at risk of rCDI after withdrawal, patients who have died will not experience the event of interest at a later time point. Thus, patients who have died differ fundamentally from patients who have withdrawn from the study or are lost to follow-up.
Using the K-M in the presence of competing risks results in an estimate for a hypothetical patient population immune against the competing risk (ie, does not die). This unrealistic assumption precludes the effect of the treatment for the frail target population. In most cases, the treatment effect in the artificially constructed hypothetical patient population underlying the K-M differs from the treatment effect in the real target population. As a consequence, the results of the analyses are not generalisable to clinical practice despite having initially a study sample that is a good representation of the target population.3
To demonstrate the potential interpretational pitfalls, we consider two hypothetical data scenarios reflecting the data situation of Major et al: Common to both scenarios, we assume no effect of treatment on the death rate (cause-specific HR (csHR)=1) and a reducing effect on the recurrence rate (csHR=0.33). In scenario 1, we modelled a rather low death rate and in scenario 2 a rather high one (table 1). Thus, we observe more death cases in scenario 2 and therefore fewer patients who factually benefit from the treatment.
The RD based on the cumulative-incidence function (CIF) reflects this difference between scenarios 1 and 2 (table 1, figure 1). In contrast, the RD based on the K-M remains the same in both scenarios, failing to take the frailty of the patient population in scenario 2 into account.
Interestingly, despite a decreased absolute risk of recurrence due to an increased death rate, the relative risk of recurrence remains the same in both scenarios. In the special case of no effect on the competing event, the relative risk of rCDI is also independent of the competing event.
Nevertheless, potential effects of the treatment on the competing events are not detectable when using the K-M. A competing risks analysis investigating effects on all possible outcomes provides a full picture of the possible treatment effects without loss of information. Thus, despite presuming that the trial of Major et al may be comparable with scenario 1, where the difference between the K-M and the CIF is small, we highly recommend a competing risks analysis of their trial.
In conclusion, we recommend to collect all time-related outcome events (such as recurrence and death) and perform a competing-risk analysis which includes the evaluation of potential time-varying treatment effects over the course of time.4
Patient consent for publication Not required.
Contributors MKvC performed the simulation study and wrote the letter. MS critically revised the letter and provided major comments. MS and MW formulated the main problem. MW supervised the writing process and provided major comments. All authors read and approved the final manuscript.
Funding MKvC has received support from the Innovative Medicines Initiative Joint Undertaking under grant agreement no. 115737-2 (Combatting bacterial resistance in Europe - molecules against Gram negative infections [COMBACTE-MAGNET]). MW has been funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, grant No WO 1746/1-1).
Competing interests None declared.
Provenance and peer review Not commissioned; externally peer reviewed.
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