Centers Performance for End-Stage Kidney Replacement Therapy: a Bayesian hierarchical logistic regression for a binary kidney transplant status

Purpose: The past two decades witnessed increased use of risk-adjusted standardized measures such as standardized mortality ratios (SMRs), standardized incidence ratios (SIRs), age-standardized relative survival and excess hazard ratios in institutional comparisons between healthcare units (cen-ters/hospitals/doctors). Estimating the variance of these standardised measures is necessary for creating false discovery rates (FDRs) in studies that use funnel plots for assessing healthcare providers’ performance. The theoretical delta-method, and approximate approaches such as bootstrapping and Bayesian approaches are commonly used. Using Bayesian hierarchical logistic regression for obtaining estimated standardised performance measure, introduces non-conjugacy in the posterior distribution of the fixed and random effects parameters. The non-conjugate parameters require Metropolis-Hastings (MH) steps within the Gibbs sampling algorithm. For this, JAGS and BUGS software are used to specify prior distribution and run MH sampling with accept-reject steps. While JAGS is flexible and reduce programming burden, manual control of the sampling algorithm, can offer advantages in fine-tuning the sampling process, especially for complex hierarchical models or when exploring alternative priors. Methods and analysis: Posterior computation of intractable distributions involves deriving and sampling from full conditionals of model parameters and hyperparameters. Therefore, we derived full conditionals of the parameters of a Bayesian hierarchical logistic regression model and apply Metropolis-Hastings (MH) steps a binary kidney transplant status across centers in Australia. Our model includes centre-level random intercepts and patient-level covariates that spans from 2006 to 2023. Model based predicted probabilities were used to estimate expected kidney transplant counts per centre and log-standardised incidence ratios were used as performance measures for classifying centres. Results: Our finding indicated that, stable posterior estimates were achieved (Gelman-Rubin Statistic values close to one and Effective Sample Size values > 200) for the regression parameters. In addition, autocorrelation plots supported the convergence of the chains for the parameters and trace plots confirmed good mixing among the chains for the respective model parameters. Conclusion: Our approach demonstrates not only the possibility but also the viability of Metropolis-within-Gibbs algorithms for hierarchical healthcare performance assessment, especially when tailored control over the estimation process is desired. In addition, it reinforces its use in stabilizing centres with limited patient volume.