We are writing in response to Hu and Wang’s letter, titled “Statistical Methodological Limitations and Improvement Suggestions in the Study of Vitamin D Deficiency and Cardiovascular Mortality After Heart Transplantation,” regarding proposed methodological issues in our analyses. While we acknowledge that there are limitations to our chosen statistical methodology and appreciate the authors’ suggested alternative methods, we stand behind our original conclusions. We also want to reaffirm that the mediation effect of CAV on the relationship between vitamin D deficiency and mortality remains uncertain; future studies will be needed to build on our findings and address the limitations associated with our models and small sample size.

We agree that it is important to consider events per variable (EPV) when choosing Cox proportional hazards regression models and that model overfitting and high variance is a potential concern. Therefore, we carefully selected our variables during the model fitting process, including only those covariates that were significantly associated with our outcome or were deemed clinically relevant confounders that were important to adjust for. We fit different models with varying numbers of covariates during our stepwise model selection process and observed similar results (i.e., vitamin D deficiency was significantly associated with higher risk of adverse cardiac outcomes) so chose to include 14 covariates in our final models. We acknowledge that a high number of model covariates carries the risk of overfitting, but we felt it was equally important to adjust for all clinically relevant confounders. The following tables illustrate our stepwise model-building process for the outcome of all-cause death.

Model 2: Model 1 + Comorbidities (EPV = 6.8)

Covariate	HR	95% CI	P -value
VDD	1.93		0.018
Male	1.31	0.69-2.48	0.414
Black	1.99	1.11-3.56	0.021
Age (years)	0.99	0.97-1.01	0.483
BMI (kg/m 2)	0.92	0.87-0.97	0.001
Ejection fraction	0.99	0.97-1.01	0.259
History of smoking	1.27	0.75-2.14	0.38
Hypertension	1.07	0.57-2.02	0.836
Diabetes	0.98	0.57-1.68	0.945
Hypercholesterolemia	0.95	0.54-1.64	0.847
eGFR	0.98	0.97-0.99	0.004

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