Purpose: To develop statistical Bayesian hierarchical methods for efficient sample size calculations when designing a clinical study yielding multi-cluster outcome data.
Methods and Materials: Computerized decision aid models were developed to predict major complications following angioplastic procedures based on a number of critical pre-procedural variables. We then designed a large complex study to systematically evaluate and compare the predictive ability of both subjective and model-based objective assessment of probability of major in-hospital complications following percutaneous coronary interventions by health providers. The hierarchical data structure consisted of: (1) Strata: PGY4, PGY7, and physician assistant as providers with varied experiences; (2) Clusters: ks providers per stratum; (3) Individuals: ns patients reviewed by each provider. The main outcome event illustrated was mortality in predictive analyses. Cluster specific mortality rates were modeled by a Bayesian beta-binomial model. Pilot information and assumptions were utilized to elicit beta prior distributions. Sample size calculations were based on the approximated average length of 95% posterior intervals of the mean event rate parameter, fixed at 1%. Necessary sample sizes by non-Bayesian and Bayesian methods were compared.
Results: The providers included ks=28 PGY4s, 10 PGY7s, and 12 PAs. Pilot data showed that the mortality rate was 2% (95% confidence interval: 1.3% to 3.4%, with a length of 2%) in the moderate risk group. The variances of the priors decrease from PGY4, PGY7, and to PA, which reflects lower variability for providers with greater clinical experiences. Under the non-Bayesian method, ns=108, 302, and 251 patients per provider were needed (total N=9,056), while under the Bayesian ns=51, 199, 170 needed (total N=5,458), respectively, in a two-year study. Thus, Bayesian method led to a total saving of 3,598 patients evaluated during two years.
Conclusion: Health care utilization and outcome studies call for hierarchical approaches. The developed Bayesian methods are efficient with fewer patients required and may be generalized to the designs of similar multi-cluster radiologic studies.
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