Discharge Rates of Medicare Stroke Patients to Skilled Nursing Facilities: Bayesian Logistic Regression with Unobserved Heterogeneity

Abstract We determine factors, both hospital-specific and market area-specific, associated with hospitals' propensities for discharging Medicare stroke patients to skilled nursing facilities (SNF's) in California and Florida. Logistic regression is generalized to the case of a betabinomial, hierarchical model, in which covariate information is included in the hyperparameters of the second-stage beta distribution. It is found that the posterior mean of the proportion discharged to SNF is approximately a weighted average (i.e., shrinkage estimator) of the logistic regression estimator and the observed rate. We develop fully Bayesian inference that takes into account uncertainty about the hyperparameters, and we find that this also allows us to test for overdispersion in a natural way. The number of observed zeros (i.e., hospitals that sent no stroke patients to a SNF) is excessive compared to the number expected from a standard logistic regression model and is fit better by the hierarchical betabinomial mod...

[1]  J. G. Skellam.  A Probability Distribution Derived from the Binomial Distribution by Regarding the Probability of Success as Variable between the Sets of Trials , 1948 .

[2]  N. D. Bruijn.  Asymptotic methods in analysis , 1958 .

[3]  G. J. Goodhardt,et al.  The Beta‐Binomial Model for Consumer Purchasing Behaviour , 1970 .

[4]  David R. Cox.  The analysis of binary data , 1970 .

[5]  P. R. Fisk,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1971 .

[6]  M. J. R. Healy,et al.  Animal Litters as Experimental Units , 1972 .

[7]  Joel C. Kleinman,et al.  Proportions with Extraneous Variance: Single and Independent Samples , 1973 .

[8]  Griffiths Da.  Maximum likelihood estimation for the beta-binomial distribution and an application to the household distribution of the total number of cases of a disease. , 1973 .

[9]  D. A. Williams,et al.  The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity. , 1975, Biometrics.

[10]  Williams Da,et al.  The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity. , 1975 .

[11]  Martin Crowder,et al.  Beta-binomial Anova for Proportions , 1978 .

[12]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[13]  Haseman Jk,et al.  Analysis of dichotomous response data from certain toxicological experiments. , 1979 .

[14]  W. Cleveland.  Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[15]  L. Kupper,et al.  Analysis of dichotomous response data from certain toxicological experiments. , 1979, Biometrics.

[16]  J. Atchison,et al.  Logistic-normal distributions:Some properties and uses , 1980 .

[17]  D. A. Williams,et al.  Extra‐Binomial Variation in Logistic Linear Models , 1982 .

[18]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[19]  J. Ware,et al.  Random-effects models for serial observations with binary response. , 1984, Biometrics.

[20]  G. Y. Wong,et al.  The Hierarchical Logistic Regression Model for Multilevel Analysis , 1985 .

[21]  Murray Aitkin,et al.  Variance Component Models with Binary Response: Interviewer Variability , 1985 .

[22]  Ross L. Prentice,et al.  Binary Regression Using an Extended Beta-Binomial Distribution, with Discussion of Correlation Induced by Covariate Measurement Errors , 1986 .

[23]  L. Tierney,et al.  Accurate Approximations for Posterior Moments and Marginal Densities , 1986 .

[24]  Prospective Payment for Medicare Posthospital Services , 1986 .

[25]  A. Palmer,et al.  Extending the Medicare Prospective Payment System to Posthospital Care , 1986 .

[26]  R. Tamura,et al.  The incorporation of historical control information in tests of proportions: simulation study of Tarone's procedure. , 1986, Biometrics.

[27]  J. Berger,et al.  Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence , 1987 .

[28]  R. Tamura,et al.  A stabilized moment estimator for the beta-binomial distribution. , 1987, Biometrics.

[29]  Peter J. Danaher,et al.  PARAMETER ESTIMATION AND APPLICATIONS FOR A GENERALISATION OF THE BETA‐BINOMIAL DISTRIBUTION , 1988 .

[30]  C. Neu,et al.  Posthospital Care Before and After the Medicare Prospective Payment System , 1988 .

[31]  D. Gianola,et al.  Mixed models for binomial data with an application to lamb mortality , 1988 .

[32]  J. Albert.  Computational methods using a Bayesian hierarchical generalized linear model , 1988 .

[33]  Adrian E. Raftery,et al.  Approximate Bayes factors for generalized linear models , 1988 .

[34]  堀篭 教夫,et al.  Bayes Empirical Bayesの概念と信頼性への応用 , 1989 .

[35]  Variation in the Utilization of the Medicare Skilled Nursing Facility Benefit. , 1989 .

[36]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[37]  L. Tierney,et al.  Fully Exponential Laplace Approximations to Expectations and Variances of Nonpositive Functions , 1989 .

[38]  Diane Lambert,et al.  Generalizing Logistic Regression by Nonparametric Mixing , 1989 .

[39]  Stephen M. Stigler,et al.  The 1988 Neyman Memorial Lecture: A Galtonian Perspective on Shrinkage Estimators , 1990 .

[40]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[41]  P. McCullagh,et al.  Generalized Linear Models, 2nd Edn. , 1990 .

[42]  M. Karim.  Generalized Linear Models With Random Effects , 1991 .

[43]  G. Casella,et al.  Explaining the Gibbs Sampler , 1992 .

[44]  Bruce W. Char,et al.  First Leaves: A Tutorial Introduction to Maple V , 1992 .

[45]  John A. Nelder,et al.  Generalized linear models. 2nd ed. , 1993 .