Estimating Variance of Log Standardized Incidence Ratios Assessing Health Care Providers' Performance: Comparative Analysis Using Bayesian, Bootstrap, and Delta Method Approaches.

Background: In health care providers' performance assessment, standardized incidence ratios are essential tools used to assess whether observed event rates deviate from expected values. Accurate estimation of variance in these ratios is crucial as it affects decision-making regarding providers' performance. There is little data on how the choice of these variance estimation methods affects decision-making. Objective: In this study, we compared 3 methods (the delta method, bootstrapping method, and Bayesian approach) to estimate the variance of the logarithm of the standardized incidence ratio. Methods: Using patient-level data from the Australia and New Zealand Dialysis and Transplant Registry for 2012-2023, we used a random effects model to predict treatment at home 1 year after starting treatment. We compared the 3 approaches (with more than 5000 iterations for bootstrapping and Markov chain Monte Carlo sampling) using bias, variance, and mean squared error (MSE) as performance measures. Using the 3 methods, funnel plots were used to compare the hospitals' performance in treating Indigenous and non-Indigenous patients close to home, as a service-level measure of equity. Results: The bias values across all methods were similar, with the Bayesian method narrowly having the lowest bias (0.01922), followed by the delta method (0.01927) and bootstrap method (0.02567). In addition, the Bayesian method exhibited the lowest variance (0.00005), indicating more stable and less dispersed estimates. The delta method had a higher variance (0.00016), while the bootstrap method had the highest variance (0.00027), meaning it introduced more uncertainty. Finally, the Bayesian method had the lowest MSE (0.00042), indicating better overall accuracy, while the bootstrap method had the highest MSE (0.00094), showing it was the least reliable method. Conclusions: We demonstrated that these methods can be used to measure equity for patient-centered outcomes, both within and between service providers simultaneously. The choice of variance estimation method is critical and heavily affects the interpretation of the performance of health service providers. We favor the Bayesian Markov chain Monte Carlo method as it was found to be a better approach.