Pooling results from multiple imputations using Rubin's Rule
pool_results(dat, cox.fit, conf.level = 0.95)a data.frame of pooled hazard ratio and confidence interval estimate using Rubin's Rule
a list of data.frames from multiple imputation using one alpha or kappa parameter
a coxph object which is used to compute HRs for each imputed datasets
confidence level for the returned confidence interval, default to be 0.95.
The Rubin's rule is applied to the Cox PH model results across imputed datasets as:
Compute pooled HR: $$\bar{HR}_\lambda = \exp\Bigg(\frac{1}{M} \sum_{m=1}^{M} \log(HR_m)\Bigg)$$
Compute pooled variance: $$\bar{\sigma}_\lambda^2 = \frac{1}{M} \sum_{m=1}^{M} \sigma_m^2 + \frac{1 + \frac{1}{M}}{M-1} \sum_{m=1}^{M} \big(\log(HR_m) - \overline{\log(HR_\lambda)}\big)^2$$
Compute CI: $$\bar{HR}_\lambda \times \exp\big(\pm t_{\alpha/2} \sqrt{\bar{\sigma}_\lambda^2}\big)$$