Purpose The past two decades witnessed increased use of risk-adjusted standardized measures such as standardized mortality ratios (SMRs) and standardized incidence ratios (SIRs) in institutional comparisons between healthcare units. 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. 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 sampling. While JAGS and Stan are 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 for a binary kidney transplant status across centers in Australia and apply MH steps. 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 centers. Results We found posterior point estimates and uncertainty summaries highly consistent across the MH, R2jags, and Stan implementations, indicating that substantive inference is robust to the choice of sampling algorithm and software platform. Our finding indicated that, stable posterior estimates can be achieved (PSRF <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\approx 1.0\)</EquationSource> </InlineEquation> and ESS <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(> 200\)</EquationSource> </InlineEquation>) for the regression parameters but for covariates with sparse data. Conclusion The results support the conclusion that the custom MH implementation provides valid and reliable posterior inference for the present application despite the reduced computational efficiency for certain parameters relative to R2jags and Stan. It also reinforces its use in stabilizing centers with limited patient volume.

Centers performance for end-stage kidney replacement therapy: a Bayesian hierarchical logistic regression for a binary kidney transplant status

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2026年2月20日

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Solomon Woldeyohannes,
Alan Cass,
Yomei Jones,
Paul Lawton

摘要

Purpose

The past two decades witnessed increased use of risk-adjusted standardized measures such as standardized mortality ratios (SMRs) and standardized incidence ratios (SIRs) in institutional comparisons between healthcare units. 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. 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 sampling. While JAGS and Stan are 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 for a binary kidney transplant status across centers in Australia and apply MH steps. 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 centers.

Results

We found posterior point estimates and uncertainty summaries highly consistent across the MH, R2jags, and Stan implementations, indicating that substantive inference is robust to the choice of sampling algorithm and software platform. Our finding indicated that, stable posterior estimates can be achieved (PSRF \(\approx 1.0\) and ESS \(> 200\) ) for the regression parameters but for covariates with sparse data.

Conclusion

The results support the conclusion that the custom MH implementation provides valid and reliable posterior inference for the present application despite the reduced computational efficiency for certain parameters relative to R2jags and Stan. It also reinforces its use in stabilizing centers with limited patient volume.