Selection of statistical tests considering competing risks: the importance of understanding the assumptions in each test

TO THE EDITOR:

I appreciate Arcuri et al¹ for the opportunity to address this important issue in our study of cytomegalovirus (CMV) reactivation on leukemia relapse.² They raised a concern regarding the potential spurious and secondary nature of the protective effect of CMV reactivation on relapse due to our statistical approach using the Fine and Gray method. Through simulation results, they advocated the use of a cause-specific Cox model, treating competing events as censoring to demonstrate our findings.

First, I would like to clarify that we used cause-specific Cox models with CMV reactivation and acute graft-versus-host disease (GVHD) treated as time-dependent covariates in our original article.² We found a protective effect of CMV reactivation on relapse using the Cox model (Table S2 in the original article). Although I initially considered these data sufficient for the sensitivity analysis, I followed the suggestions of Arcuri et al and performed an additional analysis. As a result, I also observed a significant association between CMV reactivation and decreased risk of subsequent relapse from the landmark point using the cause-specific Cox regression model (hazard ratio [HR], 0.85; 95% confidence interval, 0.75-0.96; P = .010).

Understanding the discrepancy in how these approaches handle competing events is important when selecting a statistical method. In the Fine and Gray model, patients who experience death without relapse are retained in the number at risk and are considered to have zero risk of relapse. The cause-specific Cox proportional hazard regression model treats deaths without relapse as censored observations, assuming that they have the potential to experience relapse at a rate comparable with that of other individuals who are still at risk. The simulations by Arcuri et al assume that the relapse risk in patients with nonrelapse death is the same as in others. However, the graft-versus-leukemia (GVL) effect is proportional to the severity of acute GVHD^3-5 and patients with severe acute GVHD often experience early mortality before relapse.⁶ Given the strong association between GVHD and CMV reactivation,⁷ patients who develop nonrelapse death with concurrent CMV reactivation could potentially exhibit a more robust GVHD–related GVL effect if they survive. Additionally, in cases of high CMV viral load reactivation, donor immune cells might effectively eliminate CMV-infected leukemia cells, and the risk of nonrelapse death is higher in patients with a high CMV viral load and CMV end-organ disease.^8,9 Consequently, I believe that the true risk of relapse lies between the estimated values derived from these 2 statistical models. Taken together, it is important to validate the protective effect of CMV reactivation on relapse using both statistical approaches, aligning with the viewpoint of Arcuri et al.

Finally, I would like to comment on their simulation because the relapse and nonrelapse mortality (NRM) rates differed significantly from those in our cohort despite similar HR for NRM. After adjusting the annual relapse and NRM risks to 6% and 5%, respectively, the observed 4-year relapse and NRM rates were 19.1% (actual cohort, 19.6%) and 18.9% (actual cohort, 17.9%), respectively. I used the code provided by Arcuri et al, with the exception of this adjustment.¹ As a result, both the Fine and Gray model and the cause-specific Cox model detected a protective effect of CMV reactivation on relapse in 6.8% and 4.2% of 1000 simulations, respectively, which did not indicate a large difference among the models (close to the alpha error at 5%). In contrast, 99.2% of the simulations detected significant differences in the NRM. Subsequently, the annual relapse and NRM risks were adjusted to 10% and 20%, respectively. In this scenario, the median 4-year relapse and NRM rates were calculated to be 22.0% and 51.8%, respectively. Notably, CMV reactivation demonstrated a significant reduction in the risk of relapse using the Fine and Gray model and Cox model in 49.4% and 3.9% of the set of 1000 runs, respectively. These simulations used identical HR for NRM, highlighting that the discrepancy between the 2 statistical approaches becomes more pronounced when the absolute difference in competing events between groups is high and it needs caution in such a scenario unlike in our cohort.

Acknowledgment: Y.A. is a recipient of the Japan Society for the Promotion of Science Postdoctoral Fellowship for Research Abroad.

Contribution: Y.A. designed the study, analyzed the data, and wrote the manuscript.

Conflict-of-interest disclosure: Y.A. declares no competing financial interests.

Correspondence: Yu Akahoshi, Division of Hematology, Jichi Medical University Saitama Medical Center 1-847 Amanuma, Omiya-ku, Saitama-city, Saitama 330-8503, Japan; email: akahoshiu@gmail.com.