Highlights
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Low EPV (4.9) risks unstable Cox model hazard ratios with 14 covariates.
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CAV mediation (26.5%) lacks robustness from limited event numbers.
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Penalized regression and sensitivity analyses could improve model reliability.
We have carefully read the latest research paper by Gold et al., titled “Cardiac Allograft Vasculopathy Mediates the Relationship Between Vitamin D Deficiency and Cardiovascular Mortality Following Heart Transplantation,” published in your journal. This study proposes a potential mechanism by which VDD may mediate cardiovascular death through cardiac allograft vasculopathy (CAV), a finding of significant clinical importance. However, we have identified key methodological issues in the study that were insufficiently discussed, which may substantially affect the reliability of its conclusions.
The authors adjusted for 14 covariates (age, race, gender, BMI, EF, smoking history, hypertension, diabetes, hypercholesterolemia, eGFR, hsCRP levels, vitamin D use, ACEi/ARB use, and statin use) in their Cox model. According to simulation studies by Peduzzi et al. and Wynants et al., the recommended ratio of events per variable (EPV) should be no less than 10. Although Eric et al. have suggested that the Cox proportional hazards model performs adequately with an EPV of 5–9 when confounding factors are well-controlled, researchers must still interpret results with caution. In this study, there were 68 all-cause deaths, resulting in an EPV of 4.9, which is slightly below 5. A low EPV may lead to model overfitting and high variance in hazard ratio estimates, thereby reducing the model’s generalizability. , Although the authors validated the proportional hazards assumption using Schoenfeld residuals, the low EPV may still cause instability in parameter estimates, particularly in small samples. The authors’ mediation analysis indicated that CAV mediated 26.5% (95% CI: 1.9%-165%) of the association, with an extremely wide confidence interval likely due to the bootstrap method’s inability to stably estimate the mediation effect under low event counts. When event numbers are small, the sampling distribution in bootstrap methods may differ significantly from the original sample, leading to inaccurate confidence interval estimation. The authors’ limited discussion of this statistical uncertainty may undermine the credibility of their conclusions.
We recommend that the authors optimize model complexity by integrating variable selection strategies (e.g., penalized regression) to reduce redundant covariates. Additionally, they should quantify the impact of EPV on the conclusions, such as through sensitivity analyses simulating the stability of parameter estimates under different EPV scenarios. These improvements would not only mitigate the risk of model overfitting caused by the low EPV but also enhance the robustness of the results, providing more reliable statistical support for causal inference regarding the relationship between VDD and cardiovascular mortality.
