Letter to the editor in response to Tang et al.

We want to thank Tang et al. for their interest in our work, “The cochlear dose and the age at radiotherapy predict severe hearing loss after passive scattering proton therapy and cisplatin in children with medulloblastoma.”¹ Their letter noted several statistical concerns, and we appreciate the opportunity to provide clarification.

First, Tang et al. noted the number of covariates included in the multivariable Cox proportional hazards models (Table 3) exceeds the traditional “rule of thumb” of 10 events per variable. It is worth noting that empirical evidence supporting this conventional criterion is rather limited, and some investigators even suggest that the minimum of 10 events per variable is overly conservative.^2,3 While we acknowledge that overfitting is an important consideration, we did not observe strong evidence of violations of underlying statistical assumptions in our published analysis. Notably, the adjusted hazard ratios (aHR) and confidence intervals of the multivariable model in question were largely consistent with unadjusted hazard ratios (uHR) for each variable: mean cochlear dose (aHR: 1.12 [1.06–1.18] vs. uHR: 1.10 [1.05–1.15]), age at radiotherapy (aHR: 0.85 [0.71–1.01] vs. uHR: 0.92 [0.81–1.05]), cisplatin dose (aHR: 1.01 [1.00–1.02] vs. uHR: 1.00 [0.99–1.01]), female gender (aHR: 0.91 [0.33–2.45] vs. uHR: 0.63 [0.27–1.50]), and amifostine (aHR: 0.52 [0.22–1.23] vs. uHR: 0.48 [0.22–1.05]). There is relatively little concern about overfitting in the unadjusted models (eg, 27 events per variable), and given the consistency of the unadjusted and multivariable-adjusted findings, we believe it is reasonable to rule out confounding due to other variables included in the multivariable model.

However, we wholeheartedly agree that externally validating the results of this study in larger patient populations will be an important next step.

Secondly, Tang et al. noted some ambiguity in the variable selection strategy for the multivariable model. While not explicitly stated in the manuscript, variables included in the multivariable model were largely selected a priori based on their reported contribution to hearing impairment in the scientific literature, including cisplatin dose.^4–6 Not only is it important to consider these variables to facilitate comparisons with the existing literature, but failure to account for suspected risk factors may also result in biased effect estimates due to uncontrolled confounding. Tang et al. also correctly note that other variables, including disease risk stratification, mean posterior fossa dose, and mean craniospinal irradiation (CSI) dose, were significantly associated with hearing impairment in unadjusted comparisons but were excluded from multivariable models. These variables were not included in multivariable models due to their correlation with mean cochlear dose (correlation coefficient >0.80). Thus, including any of these variables would have likely introduced multicollinearity in our multivariable models.

In conclusion, we thank Tang et al. for their thoughtful review and comments. We acknowledge the published work has some limitations, perhaps none more notable than the relatively small sample size. While it is important to consider the implications of these limitations, the published work provides important insights into hearing loss in a vulnerable population and encourages future investigations to validate these findings.