Hierarchical Generalized Linear Models in the Analysis of Variations in Health Care Utilization

References

• Albert , J. H. 1988 . “Bayesian Estimation of Poisson Means Using a Hierarchical Log-Linear Model,” . In Bayesian Statistics 3 , Edited by: Bernardo , J. M. , DeGroot , M. H. , Lindley , D. V. and Smith , A. F. M. 519 – 531 . Oxford , , U.K. : Clarendon Press .
   Google Scholar
• Albert , J. H. and Chib , S. 1996 . “Bayesian Tests and Model Diagnostics in Conditionally Independent Hierarchical Models,” . Journal of the American Statistical Association , 92 : 916 – 925 .
   Web of Science ®Google Scholar
• Bennet , J. E. , Racine-Poon , A. and Wakefield , J. C. 1996 . “MCMC for Nonlinear Hierarchical Models,” . In Markov Chain Monte Carlo in Practice , Edited by: Gilks , W. R. , Richardson , S. and Spiegelhalter , D. J. 339 – 358 . London : Chapman and Hall .
   Google Scholar
• Besag , J. , Green , P. , Higdon , D. and Mengersen , K. 1995 . “Bayesian Computation and Stochastic Systems,” . Statistical Science , 10 : 3 – 41 .
   Web of Science ®Google Scholar
• Breslow , N. and Clayton , D. 1993 . “Approximate Inference in Generalized Linear Models,” . Journal of the American Statistical Association , 88 : 9 – 25 .
   Web of Science ®Google Scholar
• Bryk , A. S. and Raudenbush , S. W. 1992 . Hierarchical Linear Models: Application and Data Analysis Methods , Newbury Park , CA : Sage .
   Google Scholar
• Bryk , A. S. , Raudenbush , S. W. and Congdon , R. T. 1998 . Hierarchical Linear Modeling, Version 4.03 , Chicago , IL : Scientific Software International .
   Google Scholar
• Calvin , J. A. and Sedransk , J. 1991 . “Bayesian and Frequentist Predictive Inference for the Patterns of Care Studies,” . Journal of the American Statistical Association , 86 : 36 – 48 .
   Web of Science ®Google Scholar
• Christiansen , C. L. and Morris , C. N. 1997 . “Hierarchical Poisson Regression Modeling,” . Journal of the American Statistical Association , 92 : 618 – 632 .
   Web of Science ®Google Scholar
• Cowles , M. K. and Carlin , B. P. 1996 . “Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review,” . Journal of the American Statistical Association , 91 : 883 – 904 .
   Web of Science ®Google Scholar
• Daniels , M. J. and Gatsonis , C. G. 1997 . “Hierarchical Polytomous Regression Models With Applications to Health Services Research,” . Statistics in Medicine , 16 : 2311 – 2326 .
   PubMed Web of Science ®Google Scholar
• Dartmouth Medical School, Center for the Evaluative Clinical Sciences . 1996 . The Dartmouth Atlas of Health Care in the United States , Chicago : American Hospital Publishing .
   Google Scholar
• DiCiccio , T. J. , Kass , R. E. , Raftery , A. and Wasserman , L. 1997 . “Computing Bayes Factors by Combining Simulation and Asymptotic Approximations,” . Journal of the American Statistical Association , 92 : 903 – 915 .
   Web of Science ®Google Scholar
• Diehr , P. 1984 . “Small Area Statistics: Large Statistical Problems,” . American Journal of Public Health , 74 : 313 – 314 .
   PubMed Web of Science ®Google Scholar
• Diehr , P. , Cain , K. , Connell , F. and Volinn , E. 1990 . “What Is Too Much Variation? The Null Hypothesis in Small Area Analysis,” . Health Services Research , 24 : 741 – 771 .
   PubMed Web of Science ®Google Scholar
• Escobar , M. D. and West , M. 1995 . “Bayesian Density Estimation and Inference Using Mixtures,” . Journal of the American Statistical Association , 90 : 577 – 588 .
   Web of Science ®Google Scholar
• Gatsonis , C. , Epstein , A. , Newhouse , J. , Normand , S. and McNeil , B. 1995 . “Variations in the Utilization of Coronary Angiography for Elderly Patients With an Acute Myocardial Infarction: An Analysis Using Hierarchical Logistic Regression,” . Medical Care , 33 : 625 – 642 .
   PubMed Web of Science ®Google Scholar
• Gatsonis , C. , Normand , S. L. , Liu , C. and Morris , C. 1993 . “Geographic Variation of Procedure Utilization: A Hierarchical Model Approach,” . Medical Care , 31 : YS54 – YS59 .
   PubMed Web of Science ®Google Scholar
• Gelfand , A. E. , Dey , D. K. and Chang , H. 1995 . “Model Determination Using Predictive Distributions With Implementation via Sampling-Based Methods,” . In Bayesian Statistics 4 , Edited by: Bernardo , J. M. , Berger , J. O. , David , A. P. and Smith , A. F. M. 147 – 167 . Oxford , , U.K. : Clarendon Press .
   Google Scholar
• Gelfand , A. E. and Ghosh , S. K. 1998 . “Model Choice: A Minimum Posterior Predictive Loss Approach,” . Biometrika , 85 : 1 – 12 .
   Web of Science ®Google Scholar
• Gelfand , A. E. , Sahu , S. K. and Carlin , B. P. 1995 . “Efficient Parameterizations for Normal Linear Mixed Models,” . Biometrika , 82 : 479 – 488 .
   Web of Science ®Google Scholar
• Gelfand , A. E. and Smith , A. F. M. 1990 . “Sampling-Based Approaches to Calculating Marginal Densities,” . Journal of the American Statistical Association , 85 : 398 – 409 .
   Web of Science ®Google Scholar
• Gelman , A. , Meng , X-L. and Stern , H. 1996 . “Posterior Predictive Assessment of Model Fitness via Realized Discrepancies,” . Statistica Sinica , 6 : 733 – 807 .
   Web of Science ®Google Scholar
• Gelman , A. and Rubin , D. B. 1992 . “Inference From Iterative Simulation Using Multiple Sequences,” . Statistical Science , 7 : 457 – 472 .
   Google Scholar
• Ghosh , M. , Natarajan , K. , Stroud , T. W. F. and Carlin , B. P. 1998 . “Generalized Linear Models for Small-Area Estimation,” . Journal of the American Statistical Association ,
   Google Scholar
• Gilks , W. R. , Wang , C. C. , Yvonnet , B. and Coursaget , P. 1993 . “Random Effect Models for Longitudinal Data Using Gibbs Sampling,” . Biometrics , 49 : 441 – 454 .
   PubMed Web of Science ®Google Scholar
• Goldstein , H. 1995 . Multilevel Statistical Models , London : Edward Arnold .
   Google Scholar
• Goldstein , H. and Spiegelhalter , D. 1996 . “League Tables and Their Limitations: Statistical Issues in Comparisons of Institutional Performance,” . Journal of the Royal Statistical Society , 159 : 385 – 444 . Ser. A
   Google Scholar
• Jacquier , E. , Poison , N. and Rossi , P. 1994 . “Bayesian Analysis of Stochastic Volatility Models,” . Journal of Business and Economic Statistics , 12 : 371 – 389 .
   Web of Science ®Google Scholar
• Kahn , M. J. and Raftery , A. E. 1996 . “Discharge Rates of Medicare Stroke Patients to Skilled Nursing Facilities: Bayesian Logistic Regression With Unobserved Heterogeneity,” . Journal of the American Statistical Association , 91 : 29 – 41 .
   Web of Science ®Google Scholar
• Kass , R. E. and Raftery , A. E. 1995 . “Bayes Factors,” . Journal of the American Statistical Association , 90 : 773 – 795 .
   Web of Science ®Google Scholar
• Kass , R. E. and Steffey , D. 1989 . “Approximate Bayesian Inference in Conditionally Independent Hierarchical Models (Parametric Empirical Bayes Models),” . Journal of the American Statistical Association , 84 : 717 – 726 .
   Web of Science ®Google Scholar
• Kass , R. E. and Wasserman , L. 1995 . “A Reference Bayesian Test for Nested Hypotheses and Its Relationship to the Schwarz Criterion,” . Journal of the American Statistical Association , 90 : 928 – 934 .
   Web of Science ®Google Scholar
• Keeler , E. , Rubestein , L. , Kahn , K. , Draper , D. , Harrison , E. , McGinty , M. , Rogers , W. and Brook , R. 1992 . “Hospital Characteristics and Quality of Care,” . Journal of the American Medical Association , 268 : 1709 – 1714 .
   PubMed Web of Science ®Google Scholar
• Khattree , R. and Naik , D. N. 1995 . Applied Multivariate Statistics With SAS Software , Cary , NC : SAS Institute, Inc .
   Google Scholar
• Laird , N. M. and Ware , J. H. 1982 . “Random Effects Models for Longitudinal Data,” . Biometrics , 38 : 963 – 974 .
   PubMed Web of Science ®Google Scholar
• Laud , P. W. and Ibrahim , J. G. 1995 . “Predictive Model Selection,” . Journal of the Royal Statistical Society , 57 : 247 – 262 . Ser. B
   Google Scholar
• Lee , Y. and Nelder , J. A. 1996 . “Hierarchical Generalized Linear Models” . Journal of the Royal Statistical Society , 58 : 619 – 678 . (with discussion), Ser. B
   Google Scholar
• Lin , X. and Breslow , N. E. 1996 . “Bias Correction in Generalized Linear Mixed Models With Multiple Components of Dispersion,” . Journal of the American Statistical Association , 91 : 1007 – 1016 .
   Web of Science ®Google Scholar
• Lindstrom , M. J. and Bates , D. M. 1988 . “Newton–Raphson and EM Algorithms for Linear Mixed Effect Models for Repeated Measures Data,” . Journal of the American Statistical Association , 83 : 1014 – 1022 .
   Web of Science ®Google Scholar
• Liu , C. 1996 . “Bayesian Robust Multivariate Linear Regression With Incomplete Data,” . Journal of the American Statistical Association , 91 : 1219 – 1227 .
   Web of Science ®Google Scholar
• Longford , N. T. 1987 . “A Fast Scoring Algorithm for Maximum Likelihood Estimation in Unbalanced Mixed Models With Nested Random Effects,” . Biometrika , 74 : 817 – 827 .
   Web of Science ®Google Scholar
• Malec , D. , Sedransk , J. , Moriarity , C. L. and LeClere , F. B. 1997 . “Small Area Inference for Binary Variables in the National Health Interview Survey,” . Journal of the American Statistical Association , 92 : 815 – 826 .
   Web of Science ®Google Scholar
• McClellan , M. , McNeil , B. J. and Newhouse , J. P. 1994 . “Does More Intensive Treatment of Acute Myocardial Infarction in the Elderly Reduce Mortality? Analysis Using Instrumental Variables,” . Journal of the American Medical Association , 272 : 859 – 866 .
   PubMed Web of Science ®Google Scholar
• McCullagh , P. and Nelder , J. 1989 . Generalized Linear Models , London : Chapman and Hall .
   Google Scholar
• McNeil , B. , Pedersen , S. and Gatsonis , C. 1992 . “Current Issues in Profiling Quality of Care,” . Inquiry , 29 : 298 – 307 .
   PubMed Web of Science ®Google Scholar
• Natarajan , K. , Ghosh , M. and Maiti , T. 1998 . “Hierarchical Bayes Quality Measurement Plan,” unpublished manuscript submitted to Communications in Statistics: Simulation and Computation.
   Google Scholar
• Normand , S. L. , Glickman , M. and Gatsonis , C. 1997a . “Statistical Methods for Profiling Providers: Issues and Applications,” . Journal of the American Statistical Association , 92 : 803 – 814 .
   Web of Science ®Google Scholar
• Normand , S. L. , Glickman , M. E. and Ryan , T. 1997b . “Modeling Mortality Rates for Elderly Heart Attack Patients: Profiling Hospitals in the Cooperative Cardiovascular Project,” . In Case Studies in Bayesian Statistics , Edited by: Gatsonis , C. , Hodges , J. , Kass , R. and Singpurwalla , N. 155 – 236 . New York : Springer-Verlag .
   Google Scholar
• O'Hagan , A. 1994 . Kendall's Advanced Theory of Statistics, Vol. 2B: Bayesian Inference , New York : Wiley .
   Google Scholar
• Pashos , C. L. , Newhouse , J. P. and McNeil , B. J. 1993 . “Temporal Changes in the Care and Outcomes of Elderly Patients With Acute Myocardial Infarction, 1987 Through 1990,” . Journal of the American Medical Association , 270 : 1832 – 1837 .
   Web of Science ®Google Scholar
• Paul-Shaheen , P. , Clark , J. D. and Williams , D. 1987 . “Small Area Analysis: A Review and Analysis of the North American Literature,” . Journal of Health Politics, Policy and Law , 14 : 741 – 809 .
   Web of Science ®Google Scholar
• Rubin , D. B. 1988 . “Using the SIR Algorithm to Simulate Posterior Distributions,” . In Bayesian Statistics 3 , Edited by: Bernardo , J. M. , DeGroot , M. H. , Lindley , D. V. and Smith , A. F. M. 395 – 402 . Oxford , , U.K. : Clarendon Press .
   Google Scholar
• Smith , A. F. M. and Roberts , G. O. 1993 . “Bayesian Computation via the Gibbs Sampler and Related Markov Chain Monte Carlo Methods,” . Journal of the Royal Statistical Society , 55 : 3 – 23 . Ser. B
   Google Scholar
• Spiegelhalter , D. J. , Best , N. G. , Gilks , W. R. and Inskip , H. 1996 . “Hepatitis B: A Case Study in MCMC Methods,” . In Markov Chain Monte Carlo in Practice , Edited by: Gilks , W. R. , Richardson , S. and Spiegelhalter , D. J. 21 – 44 . London : Chapman and Hall .
   Google Scholar
• Tierney , L. 1994 . “Markov Chains for Exploring Posterior Distributions,” . The Annals of Statistics , 22 : 1701 – 1762 .
   Web of Science ®Google Scholar
• Udvarhelyi , I. S. , Gatsonis , C. , Epstein , A. , Pashos , C. , Newhouse , J. P. and McNeil , B. J. 1992 . “Acute Myocardial Infarction in the Medicare Population: Process of Care and Clinical Outcomes,” . Journal of the American Medical Association , 18 : 2530 – 2536 .
   Google Scholar
• Verdinelli , I. and Wasserman , L. 1995 . “Computing Bayes Factors Using the Savage-Dickey Density Ratio,” . Journal of the American Statistical Association , 90 : 614 – 618 .
   Web of Science ®Google Scholar
• Weiss , R. E. 1996 . “Bayesian Model Checking with Applications to Hierarchical Models,” , UCLA School of Public Health, Dept. of Biostatistics . technical report
   Google Scholar
• Wennberg , J. and Gittelsohn , A. 1982 . “Variations in Medical Care Among Small Areas,” . Scientific American , 246 : 120 – 134 .
   PubMed Web of Science ®Google Scholar
• Wolfe , R. and Becker , M. 1994 . “Modeling Utilization Rates,” , University of Michigan, Dept. of Biostatistics . technical report
   Google Scholar
• Wong , G. and Mason , W. 1985 . “The Hierarchical Logistic Regression Model for Multilevel Analysis,” . Journal of the American Statistical Association , 80 : 513 – 524 .
   Web of Science ®Google Scholar
• Wong , G. and Mason , W. 1991 . “Contextually Specific Effects and Other Generalizations of the Hierarchical Linear Model for Comparative Analysis,” . Journal of the American Statistical Association , 86 : 487 – 503 .
   Web of Science ®Google Scholar
• Zeger , S. and Karim , M. 1991 . “Generalized Linear Models With Random Effects: A Gibbs Sampling Approach,” . Journal of the American Statistical Association , 86 : 79 – 86 .
   Web of Science ®Google Scholar
• Zeger , S. , Liang , K. and Albert , P. 1988 . “Models for Longitudinal Data: A Generalized Estimating Equations Approach,” . Biometrics , 44 : 1049 – 1066 .
   PubMed Web of Science ®Google Scholar