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# Seminars in Dental Research 151 200

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Bayesian Inference for Hospital Quality in a Selection Model John Geweke Departments of Economics and Statistics University of Iowa johngewekeuiowaedu Gautam Gowrisankaran Department of Economics Harvard University Federal Reserve Bank of San Francisco and NBER gautamigowrisankarannb er org Robert J Town School of Public Health University of Minnesota rjtownumnedu July 2002 Abstract This paper develops new econometric methods to infer hospital quality in a model with discrete dependent variables and nonrandom selection Mortality rates in patient discharge records are widely used to infer hospital quality However hospital admission is not random and some hospitals may attract patients with greater unobserved severity of illness than others In this situation the assumption of random admission leads to spurious inference about hospital quality This study controls for hospital selection using a model in which distance between the patient s residence and alternative hospitals are key exogenous variables Bayesian inference in this model is feasible using a Markov chain Monte Carlo posterior simulator and attaches posterior probabilities to quality comparisons between individual hospitals and groups of hospitals The study uses data on 74848 Medicare patients admitted to 114 hospitals in Los Angeles County from 1989 through 1992 with a diagnosis of pneumonia It finds the smallest and largest hospitals to be of the highest quality There is strong evidence of dependence between the unobserved severity of illness and the assignment of patients to hospitals whereby patients with a high unobserved severity of illness are disproportionately admitted to high quality hospitals Consequently a conventional probit model leads to inferences about quality markedly different than those in this study s selection mode We thank Pat Bajari Lanier Benkard Richard Blundell Gary Chamberlain l ke Chernew Tom Holmes Steven Stern anonymous referees and seminar participants at Duke FRB Chicago Georgetown HarvardMIT Iowa Michigan Princeton Stanford UC Davis Irvine and Riverside Virginia Yale the Econometric Society Seventh World Congress and the Society of Economic Dynamics 1999 Annual Meetings for helpful comments Any remaining errors are the sole responsibility of the authors The first author acknowledges support from NSF grant SBR 98l9444 and the second author acknowledges support from the University of Minnesota Supercomputer Institute The views expressed herein do not represent those of the Federal Reserve System the Federal Reserve Bank of San Francisco or of any other institution 1 Introduction This paper develops new econometric methods to estimate hospital quality and other models with discrete dependent variables and nonrandom selection Assessing the quality of care in hospitals is an important problem for public policy and a challenge for applied econometrics1 Policy changes in Medicare reimbursement rates and the rise of managed care as well as technological innovations have affected hospital incentives and through that hospital quality2 These quality changes have large welfare effects and hence the potential for large deadweight losses3 Hospital patient discharge databases provide several indicators plausibly associated with hospital quality Since they cover large numbers of patients and hospitals and are much less expensive to obtain and access than other sources of information they have been widely used in comparisons of hospital quality Mortality has been the most popular indicator of hospital quality in the literature it is unambiguously defined and its link with quality of care is so strong as to be tautological4 In this widely used framework the conceptual experiment that reveals hospital quality is hospitalspecific mortality rates following random assignment of a population of patients to hospitals Patients however are not randomly assigned to hospitals Patients or their physicians are likely to choose hospitals based on factors such as location convenience and their severity of illness If assignment were nonrandom but random conditional on observed characteristics then conventional dichotomous outcome models could be used to infer the outcome of the conceptual experiment from the available data However discharge data contain only crude summaries of medically pertinent information and hence many aspects of the severity of illness are unobserved Thus the assumption of random conditional assignment is not tenable and patients with the same observed characteristics are not equally likely to be admitted to all hospitals For 1 quotAs described by a leading study Quality of care is the degree to which health services for individuals and populations increase the likelihood of desired health outcomes and are consistent with current professional knowledge quot Lohr 1990 p 4 2 See Cutler 1995 Kessler and McClellan 2000 McClellan and Noguchi 1998 for studies of the effects on medical outcomes of Medicare policy the impact of managed care and the impacts of technological change respectively For instance if changes in Medicare policies cause hospitals to reduced their pneumonia mortality rates by one percentage point this would translate to over 6000 lives saved annually in the US 4 Strictly speaking mortality is an indicator of hospital mediocrity mortality is an inverse indicator of quality Subsequently we provide a precise definition of hospital quality in the context of the model developed in this study instance if patients with high unobserved severity of illness select high quality hospitals then observed mortality rates for high quality hospitals will be inconsistent and upwardly biased measures of mortality from the conceptual experiment This will be true even after controlling for observed measures of severity of illness Conventional statistical methods that ignore unobserved severity will produce misleading inferences about hospital quality This has led prominent medical experts to make a pessimistic assessment of the usefulness of discharge data in assessing hospital quality5 Recent work by Gowrisankaran and Town 1999 developed a framework to control for the nonrandom assignment of patients This work modeled mortality as a function of indicator variables for each hospital and patient discharge information The authors treat mortality as continuous and directly apply linear instrumental variables methods The identifying assumption is that a patient s mortality is not affected by how far that patient s residence is from alternative hospitals Combined with the demonstrable fact that patients are more likely to choose hospitals 39 A that are closer to home other things equal the quot for J of instrumental variables estimation in a linear model are satisfied Conceptually the estimator would predict hospital A to be of higher quality than hospital B if patients residing near hospital A have lower mortality than patients residing near hospital B after controlling for their medical and demographic characteristics The difficulty with this approach is that because the outcome variable mortality is dichotomous any internally consistent model of hospital quality and choice must be nonlinear This paper develops a logically coherent model designed to infer the outcome of the conceptual experiment that randomly assigns patients to hospitals given data that has nonrandom patient assignment6 Inference with this model is challenging because the amount of information per observation is small7 This paper develops an approach to inference in this model that is practical with the large data sets required to extract signal from noise in hospital patient discharge databases This approach is potentially applicable to a wide range of policy evaluations of 5 Leading medical researchers including lezzoni el al 1996 and government studies US GAO 1994 have both argued that discharge databases are problematic for this reason 6 Though the methods of Gowrisankaran and Town 1999 are much simpler than the ones developed in this paper there is no formal statistical model that rationalizes their approach 7 Simple measures of fit always indicate that most variation in mortality cannot be ascribed to covariates Even if all the difference in mortality rates were attributable to quality the variation in these rates is small economic interest where the outcome variable is dichotomous8 The model developed here incorporates hospital choice and mortality as endogenous variables and fixed hospital and patient characteristics as exogenous variables Hospital choice is described by a multinomial probit model and mortality by a binary probit model The mortality model includes indicator variables for each hospital to accommodate hospital speci c differences in quality as well as demographic variables and observed disease characteristics The mortality model is structural in the sense that it predicts outcomes given alternative assignments of patients to hospitals including random assignment The multinomial probit model is a reduced form relationship that provides probabilities of hospital choice conditional on observed covariates that are a function of demographic characteristics and distance of the hospital from the patient s home The random component in the binary probit model includes unobserved severity of illness and is permitted to be correlated with the random component in the multinomial choice model If after controlling for the observed covariates in the hospital choice model patients with high unobserved severity of illness are more likely to be admitted to hospital A than patients with low unobserved severity this will imply a positive correlation between the shock in the mortality equation and the shock in the hospital A choice equation We estimate this selection model using Bayesian inference from data on 74848 Medicare patients admitted to 114 hospital in Los Angeles County during 1989 to 1992 with a diagnosis of pneumonia By transforming the integration problem posed by the latent variables into a simulation problem our approach to inference computes estimates orders of magnitude faster than the method of maximum likelihood This makes inference feasible for this type of simultaneous equations model9 The basis for the simulation procedure is the fact that the model is similar to the conventional linear simultaneous equation model conditional on latent variables Using Markovchain Monte Carlo MCMC techniques we iteratively simulate latent variable values conditional on data and parameters and parameters conditional on data and latent variables The second step is computationally similar to classical instrumental variables 8 Examples include the effect of school performance based on graduation rates of prison rehabilitation programs based on recidivism rates of job training programs based on the incidence of harassment complaints and many medical outcome evaluations 9 Maximum likelihood evaluation for one parameter vector for one individual would require evaluating the joint density of the mortality and hospital choice outcome for that individual Given that we have 114 endogenous variables and that the mortality error and hospital choice error are correlated this would take several minutes on a fast supercomputer Multiplied by a data set of roughly 75000 patients necessary because of the small signal to noise ratio it would take months to evaluate the likelihood for a single parameter vector differing principally in the appearance of the discrete hospital choice in the mortality probit equation which does not pose a problem The simulation methods simultaneously recover the joint posterior distribution of parameters and latent variables10 Albert and Chib 1993 used this approach in the binary probit model and Geweke Keane and Runkle 1997 extended them to the multinomial probit model The methods developed here extend this approach to a new class of models We use these methods to address the motivating policy questions directly First to what extent is hospital quality associated with observed characteristics of hospitals such as size and ownership status Second with what degree of con dence can it be said that one hospital is of higher quality than another We model hospital quality using hierarchical priors This approach which combines some characteristics of classical xed and randomeffects models speci es the quality of each hospital as a separate parameter but assigns a more important role to the data in determining whether these parameters are similar for hospitals with similar observable characteristics relative to a normal prior Our approach provides an ef cient method for extracting the signal from the noise which is particularly important given this type of data The remainder of the paper is organized as follows Section 2 provides the speci cation of the model and methods for inference with some details relegated to an appendix The database is described in Section 3 Section 4 presents ndings on hospital quality and the role of nonrandom admission to hospitals Section 5 concludes Five appendices are available in the working paper version of this paper Appendix A1 details the construction of the prior Appendix A2 details the likelihood function and computation Appendix A3 gives evidence on the numerical accuracy of our Markov chain Monte Carlo MCMC algorithm Appendix A4 provides posterior rankings for the hospitals in our data set and Appendix A5 provides robustness results with alternative priors 2 The Model The central component of the model is a structural probit equation in which the probability of mortality is a function of the hospital to which a patient is admitted the observed 10 Surveys that discuss convergence to the posterior include Chib and Greenberg 1996 Geweke 1997 and Geweke 1999 severity of the patient s illness and the observed demographic characteristics of the patient The objective is to learn about the way the hospital to which the patient is admitted in uences the probability of mortality in this equation A multinomial probit model of hospital admission supplements the mortality model to permit nonrandom assignment of patients to hospitals This section describes in turn the speci cation of the model the prior distribution of the model parameters and methods to recover the posterior distribution of these parameters 21 Model speci cation Let 1 ln index the patients in the sample and let j lJ index hospitals in the sample There are two groups of exogenous variables in the model The kgtltl vector x1 consists of individual characteristics of patient 1 that may affect mortality including indicators for age race sex and disease stage and measures of income The qgtltl vector 21 which consists of characteristics speci c to the combination of individual 1 and hospital j includes distance between the home of patient 1 and hospital j and interactions of distance with observable patient characteristics The speci cs of these variables are given in Section 3 There are two sets of endogenous variables in the model The mortality indicator m1 is 1 if the patient dies in the hospital within ten days of admission and is 0 otherwise The J gtltl indicator vector cl has j th entry 1 if patient 1 is admitted to hospital j and 0 otherwise To present the structural mortality equation let s 1 ln be independent N0 02 random variables conditional on the exogenous variables The mortality probit m is a latent random variable 1 mi c3913x1s 1 The mortality indicator m1 1 if m1 gt 0 and m1 0 if m S 0 The structural interpretation of l is that if patient 1 were randomly assigned to hospital j then m CjSl and consequently Pml 1 j Jq39yU Note that the parameters and U are jointly unidenti ed in 1 because they can be scaled by the same arbitrary positive 11 See the NBER working paper Geweke Gowrisankaran and Town 2001 constant without changing the behavior of m In the conventional probit model this problem is avoided by setting 6 l We return to this matter in the context of the complete model below If C were in fact independent of s 7 as it would be if patients were randomly assigned to hospitals for example 7 then C would be exogenous in 1 After resolution of the above identi cation issue this model would conform with the conventional textbook speci cation of the binary probit model However it is likely that in observed data q depends in part on s the admission of patient 139 to hospital j takes into account information that is correlated with s The conventional probit model is then misspeci ed To develop a more plausible model of hospital choice we assume that patients become infected with one of the many bacterial or viral agents that can cause pneumonia and it has been determined that they are sufficiently ill to bene t from inpatient treatment At that point the patient or the patient s agent selects from the set of J hospitals the hospital to which the patient will be admitted The actual choice decision will be a complex function of many factors such as severity of illness characteristics of the hospital the patient s primary care physician etc One important observable in uence on choice is distance previous research has shown that the farther a patient is from a hospital the less likely is the patient to be admitted to that hospital other observables constant12 To present the reduced form model of hospital choice define the J gtltq matrix Z Z zllz zml Let the Jgtltl vectors x N0i iln be mutually independent 1 conditional on the exogenous variables and let 3 j lJ denote the correlation between 1 I and x Define the J gtltl hospital choice latent vector multinomial probit E as 2 6i Zam The choice indicator vector q cl1cm39 has entry CU 1 if Z k lJ and CU 0 otherwise As above with l the parameters a and i are jointly unidenti ed since scaling a by any positive constant and i by the square of that constant leaves the distribution of 12 See Luft el al 1990 and Burns and Wholey 1992 q conditional on Z unaffected We return to this matter in the context of the prior distribution in Section 22 As is customary in models with J choices it is easier to work with J l latent utilities and normalize the Jth utility to 0 Accordingly we de ne the J l X q matrix Z 211 Zuafxz EmaquotZNA 2U a the J 1X1 veCtorS n1 11 1Jquotquot xJ71 1J39 and 0 EIEJ71 E I and the J lgtltJ 1 matrix 2 varrl Note that 3 of Zloc 171 If the unobserved severity of illness affects hospital choice the mortality and choice error terms will be correlated Let 3 denote the correlation between 1 and 111 j lJ l The larger is p j the more likely is a patient with a high unobserved severity of illness 81 to be admitted to hospital j Thus we shall refer to p j as the hospital j severity correlation The hospital severity correlations are a useful way to characterize severity of illness by hospital since they are independent of the scale of s which we know from 1 is unidenti ed Now we can write the variance of the joint error terms as 4 varslnl39 where 71 is a J lgtltl vector with 71 13672152 To permit unobserved severity of illness to affect hospital choice in any way consistent with the model the only restriction we place on 71 is that varslnl39 be positive definite Since this implies complicated restrictions on 71 a more graceful treatment is to work with the population regression of the shock 81 in l on the shock vector 1 in 3 5 8 n 5 00Vn 0 In this regression 5 is a J lgtltl parameter vector and the scale of s is normalized by var 1l This specification simultaneously resolves the identification problem due to the scaling in l and incorporates all permissible values of 71 25 in 4 With this reparametrization the variance of the shock in the mortality probit equation is 02 525 1 and the correlation between 1 and n1 is J71 12 6 p Zk15k2kj2 525 1 In the hypothetical experiment in which patient 139 is admitted to hospital j by means of a random assignment cl Pml llyq Rcl39 Xfy5Z 1 2 We shall refer to 7 q j5 25 11 2 as the hospital j quality probit Differences in these probits across hospitals may be used to address quality comparisons for individual hospitals In the conventional probit model with normalization cr l the hospital j quality probit is q j To compare groups of hospitals define qG Z 0qu where G is the group of interest and the weight co is proportional to the jEG number of patients admitted to hospital j define p6 and q analogously 22 Prior distributions The number of free parameters in Z is JJ l2 l that is 6441 in our sample with Jll4 hospitals We make one major simplification that i1 J so that after differencing Z 1H eHe1 where en denotes an 71 X1 vector of units We introduce some evidence on the plausibility of this assumption in Section 44 Estimating these parameters would increase the computation time by orders of magnitude and also complicate our MCMC simulation algorithm13 We choose independent prior distributions for the parameter vectors a 5 y and so as to include all reasonable parameter values well within their support We discuss specific aspects of these priors here14 First we utilize a variance component structure and a hierarchical prior to specify that hospital qualities are similar ex ante while allowing the data to determine the degree of similarity ex post Each hospital 139 is in one of four ownership categories j and one of for size categories 13 Keane 1992 shows that E is the source of irregularity in the multinomial probit likelihood function 14 Appendix A1 of the Working Paper version of this paper Geweke Gowrisankaran and Town 2001 contains detailed descriptions of all the priors k detailed in Section 32 If hospital 139 is of ownership category j and size category k then decompose A p j sk ul The prior distributions of the components 31 p1p4 31quot34 and ulu114 are jointly Gaussian mean zero and mutually independent The common term A has standard deviation 3 essentially a at prior The other Z Z 2 components have variances 1p 1 and 1 s u 9 respectively grouped together in the vector 1quot 1 1 Given 1 the prior specifies that hospital quality is more strongly correlated between hospitals that share the same size or ownership speci cation However we employ a hierarchical prior distribution with the variance terms having independent prior distributions 1251 N 952 5 j p su in the standard probit model15 Second since 111 U u an iid prior on 5 implies a prior on 5 that is not exchangeable with respect to the Jm hospital which is undesirable since the numbering of hospitals is arbitrary We use the prior 5 NN 0 05224 with 05 0196 which implies an exchangeable and diffuse prior for 3 16 Third the priors for the selection model need to be carefully scaled relative to the conventional probit model to account for the different values of 0 across the models From 5 02 525 1 in the selection model but 6 1 in the probit model Since 5 NN0U Z391 it follows that 525 l N 652952 J 1 1 and E 5 25 1 a J ll Thus in the hierarchical hospital quality prior in the selection model 125 652 J ll Ej2 N 952 Similarly we scale the selection model prior standard deviations for A and y by 052 J l 1112 relative to the probit model The choice of the prior distributions of a and y is relatively straightforward As with B and 5 the governing principle is that reasonable values be well within the support of the prior distribution and care must be taken to maintain the same scale in the probit and selection models With respect to the last consideration note in particular that the impact of covariates in 15 The centered 99 prior credible interval for each I is 22 17 Robustness of our results with respect to variation in these and other priors is summarized in Section 44 and detailed in Appendix A5 V2 in the selection the selection model corresponding to y in the probit model is y Z 1 model by means of the same reasoning leading to 7 23 Inference The observed data are ClZlclmliln which can be abbreviated as y The model contains latent variables mic 139 ln which can be abbreviated y The parameter vectors area y and 5 which can be collected in the vector 0 The model speci ed in Section 21 provides pyy 0 and the prior distributions in Section 22 provide p0 Explicit expressions for these densities are given in Appendix A2 From Bayes rule the distribution of the unobservables y and 9 conditional on the data and model speci cation is 8 py9yp9pyy 9py0C p9pyy 9 The objective is to obtain the posterior distribution of functions such as the hospital quality probits q and qjxl39y the probability of mortality under random hospital admission of a patient with observed characteristics q to hospital j This objective requires integrating a highly nonlinear function over millions of dimensions most of which correspond to latent variables This cannot be accomplished analytically The parameter vector and latent variables can be partitioned into groups such that the posterior distribution of any one group conditional on all the others is of a single easily recognized form that is easy to simulate Details of the partition are given in Appendix A2 The problem is then well suited to attack by execution of a Gibbs sampling algorithm Gelfand and Smith 1990 Geweke 1999 In this approach each group of parameters and latent variables is simulated conditional on all the others Following each pass through the entire vector of latent variables and parameters all parameter values are recorded in a le As detailed in Appendix A2 the Gibbs sampling algorithm is ergodic and its unique limiting distribution is the posterior distribution Therefore dependent draws from the posterior distribution of any function of the parameters g9 can be made by computing the value of g 16 Appendix Al documents further details of this prior distribution including the reasoning leading to the choice lt75 0196 corresponding to the recorded parameter values after discarding initial iterations of the Gibbs sampling algorithm to allow for convergence We used parallel computing methods and a supercomputer exploiting the fact that in each iteration of the Gibbs sampling algorithm the latent variables cz391n are conditionally independent across individuals The iterations themselves are executed serially The results reported in Section 4 are based on every 10111 draw from 19000 successive iterations a total of 1900 draws after discarding 1000 bum in iterations based on convergence diagnostics For comparison purposes we apply the same procedures to a conventional probit model for mortality using the Gibbs sampling algorithm described in Albert and Chib 1993 Appendix A3 provides details on the numerical accuracy of our Gibbs sampling algorithm 3 The Data The primary source of data for this study is the Version B Discharge Data from the State of California Office of Statewide Health Planning and Development These data provide records for all patients discharged from any California acutecare hospital during the years 1989 through 1992 We confine our attention to patients who were over 65 at the time of admission During this time period the vast majority of patients over 65 were covered by traditional Medicare fee forservice insurance which has standardized hospitalization benefits We confine our attention to Los Angeles County A large metropolitan area is best suited to our purposes because it has a large base of patients and contains multiple hospitals in every size and ownership class We limit our study to a single disease because there is evidence that the relation between mortality and covariates is disease specific17 We choose pneumonia in particular for three reasons First it is a common disease18 that provides the large sample needed to draw inferences about hospital quality Second inhospital death is a relatively frequent outcome for pneumonia patients which makes it a relevant disease to examine through the medium of hospital discharge records Third 17 See Wray el al 1997 18 Pneumonia and in uenza alone constitute the sixth leading cause of death in the US and the fourth leading cause of death for those over 65 National Center for Health Statistics 1996 Pneumonia is also the leading cause of death among patients with nosocomial hospital acquired infections Pennington 1994 11 there is independent evidence that an appropriately adjusted inhospital mortality rate for pneumonia is correlated with the quality of inhospital care The secondary source of data is the Annual Survey of Hospitals Database published by the American Hospital Association AHA Among other information the AHA data contain the addresses ownership status and size of each hospital in our sample 31 Sample construction The sample was selected through a process of eliminating patients from the 19891992 Version B Discharge Data The rst quali cation for selection is that the patient live in a Los Angeles County zip code be admitted to a Los Angeles County hospital and be over 65 at the time of admission The second quali cation is that one of the ve ICD9CM disease codes speci ed in the discharge data be 481 482 485 486 or 4838 as suggested by Iezzoni et al 1996 to de ne pneumonia The third quali cation is that the source of admission must be either routine or from the emergency room This eliminates patients transferred into the hospital from another medical facility or admitted from an intermediate care or skilled nursing facility To the extent that placement in these facilities is correlated with unobserved disease severity and to the extent that such facilities may be systematically located near higher quality hospitals the key assumption that distance from the hospital is exogenous in our model would be violated This step eliminates approximately 23 percent of the patients from the sample The fourth quali cation is that the patient be admitted to a hospital with at least 80 admissions for pneumonia in our data set This screen reduces J and thereby computation time Its potential to introduce sample selection bias is limited by the fact that it eliminates fewer than one per cent of the patients 32 Variable construction The covariate vector q in the mortality probit equations contains an indicator for each year demographic variables and indicators of disease severity Most of the demographic variables are constructed from the discharge records These are four age indicators 7074 7579 19 See Keeler et al 1990 and McGarvey and Harper 1993 12 8084 and 85 or older an indicator for female and indicators for black Hispanic Native American and Asian respectively The discharge records contain no information on socioeconomic status As a proxy for the patient s household income we use the mean 1990 census household income for households with the same zip code race and age class as the patient20 Indicators of disease severity in q are constructed from the admission disease staging information contained in the discharge records Disease staging has been shown to be as good as some risk adjustment data based on chart review of medical records21 Since some of the 13 stages have very few patients we aggregated stages into five groups stage 11 stages 13 through 23 stages 31 through 36 stage 37 and stage 38 Indicator variables for all but stage 11 are included in q The indicator for mortality m x is set to 1 if the patient died in the hospital within ten days of admission otherwise m1 0 The horizon for mortality is limited to ten days because beyond this point hospitals sometimes transfer terminally ill patients to other facilities and this decision appears to vary considerably by hospital To control for differential patient transfer Gowrisankaran and Town 1999 used a hazard model as an alternative to the 10day inpatient mortality but found little difference between the two specifications In two separate studies of heart disease patients McClellan McNeil and Newhouse 1994 and McClellan and Staiger 1999b find that there is a very strong correlation between 7day mortality and 30day mortality rates across hospitals22 Table 1 provides a summary of the distribution of demographic characteristics and disease severity in the sample together with mortality rates Within each age group the composition of the sample by race and sex closely re ects the demographics of Los Angeles County Older individuals enter the sample in greater proportion to their numbers in the population than do younger ones Within each age group threequarters of the sample is 20 The census provides only two relevant age categories 65 74 and 75 instead of four Thus we aggregated the discharge data age categories to this level Additionally the census provides income only within cells To find the mean income we took the mean value for each cell as the income for each household in that cell For the highest cell 100000 or more we assumed a mean income of 140000 Income is measured in units of 100000 and income squared in units of billions of dollars squared 21 See Thomas and Ashcroft 1991 Iezzoni el al 1996 showed excellent agreement of disease stage with the ratings of other systems 22 As caveats note that heart disease is very different from pneumonia and that these studies examine mortality not inpatient mortality classi ed in the least severe disease stage Mortality rates increase gradually with age increase sharply with disease stage are a little higher for men than for women and are lower for Asians and Hispanics than for whites or blacks The covariate matrix Z1 contains variables speci c to the combination of patient 139 and each hospital The additional information in Z not contained in q is the distance of the patient s home from each hospital The discharge data include patient zip codes and the AHA data include hospital zip codes The Census TIGER database provides the latitude and longitude of the centroid of each zip code Given these standard great circle trigonometric formulas provide the distance between each patient home and hospital23 The ve variables in Z are distance in hundreds of kilometers distancesquared the product of distance and an age indicator 1 for 65 69 2 for 7074 3 for 7579 4 for 8084 5 for 85 the product of distance and disease stage 11 38 and the product of distance and income in units of 100000 The prior distribution and subsequent analyses require the size and ownership status of each hospital This information was obtained from the AHA survey and is summarized in Table 2 We speci ed private teaching public operated by Los Angeles county other notforpro t and forpro t hospitals as four mutually exclusive ownership categories While mortality rates differ slightly by ownership category none of the differences are signi cant at conventional levels The same is true by size category Contrasts in mortality rates are stronger between crossclassi ed cells in Table 2 For example the mean of the cells private notforpro t with 151200 beds 1111 and private forpro t with 201300 beds 1054 are signi cantly greater than the overall mean at the 5 level 4 Findings The model set forth in Section 2 applied to the data described in Section 3 yields evidence on systematic differences in quality across hospitals provides insight into the interaction between hospital choice and hospital quality and suggests quality orderings among hospitals This section summarizes these ndings 41 Patient mortality and hospital choice Table 3 presents the posterior means and standard deviations of some parameters and functions of parameters in the selection and standard probit models Table 3 details qG pG j525112 and 125251 for the selection model and y q and 12 for the probit model24 The mortality equation has three groups of covariates demographics disease severity and hospital indicators In the case of the demographic and disease severity covariates coefficient posterior means in the selection and probit models are similar to each other and closely re ect the mortality rates presented in Table 1 Posterior standard deviations indicate substantial information about differences in mortality probabilities across demographic group In the case of the hospital quality probits there are greater and more interesting differences between the selection model the probit model and the raw data Both the probit model and the raw data Table 2 do not draw any sharp distinctions in hospital quality by size or ownership class However the selection model finds sharp distinctions by size This suggests that controls for both observed and unobserved severity of illness are important The posterior means of the hyperparameters I carry forward the substantial uncertainty about hospital qualities in the prior distribution combined with the information in the data The prior mean of each If is 041 In the case of the four ownership components p and size components sk the data combine with the prior to lower the posterior mean to 021 In the case of the 114 individual hospital components u the data provide more information about the common variance and lower the posterior mean to 0037 25 Posterior means and standard deviations of the choice covariate coefficient vector 05 show that as expected distance is an important factor in describing the hospital of admission 23 For zip codes that contain more than one hospital we used addresslevel latitude and longitude data from the Census TIGER database which stores the geographic location of every block corner and will interpolate from that to find the latitude and longitude of any address 24 The normalization of y and 12 facilitates comparison between the two models 25 The mean of an inverted gamma distribution for 12 ofthe form 3212 N 12 v is E12 szv 7 2 Ifthe prior were conjugate then the posterior mean of each If would be 125 d2 3 where d2 is the sum of squares due to p sk or ux and n 4 in the first two cases and n 114 in the last The lower bound on the posterior mean would then be 125n 3 or 018 in the first two cases and 0011 in the last case 15 The posterior mean of 71365 implies that a hospital that is 20 kilometers farther from a patient s home than another has a normalized probit that is 1365 X 02JE m 2 units lower The quadratic term in the equation is highly signi cant but since distances are at most 100 kilometers within Los Angeles County its substantive effect is not great Interactions of distance with age and severity both have negative coefficients with posterior standard deviations small relative to their posterior means Given that age class varies between 1 and 5 and observed severity varies between 11 and 38 the posterior mean of the distance coefficient varies between 71444 and 7 1708 with distance decreasing in age and observed severity of illness The reason for this is likely due to the increased cost and difficulty of transport for severely ill patients Patients in zip codes with higher average income are more likely to be admitted to nearby hospitals Table 4 provides explicit posterior probabilities for hospital group quality comparisons using the selection model and also lists the mean and standard deviation of the posterior probability of mortality at each type of hospital given a 10 mortality roughly the sample mean at other types There are sharp differences based on hospital size Panel A The posterior probability that the group hospital quality probit for the largesthospital group exceeds that of the smallesthospital group is 071 and the posterior probability that it is greater than that of the other two size groups exceeds 095 The posterior probability that the smallesthospital group quality probit exceeds that of the secondsmallest group similarly exceeds 095 This is re ected in a mortality rate of 117 for the 150200 bed category given a mortality rate of 10 for the smallest size of hospital These findings are in rough agreement with the literature A study by Keeler et al 1992 which examined the relationship between hospital quality and size using a very detailed and expensive data set that included pneumonia patients along with patients with other more complex diagnoses found that hospital quality increases with bed size However in their study they did not allow for a nonlinear relationship between hospital size and morality rates thus they could not uncover the Ushaped relationship between hospital quality and size that we do Successful pneumonia treatments are linked to identifying the pathogen responsible for the infection and administering the appropriate antibacterial agent early in the progression of the disease and subsequently monitoring and adjusting the dosage of the drug Rello and Valles 1998 Pennington 1994 McGarvey and Harper 1993 There is evidence that smaller hospitals may be better at the timely administration of antibiotics Fine et al 1998 which may explain why we observe that they have better outcomes Furthermore since small hospitals are likely to treat a disproportionate number of pneumonia patients relative to more technically challenging illnesses26 they may also develop expertise in this disease That in turn may overcome advantages that mediumsized hospitals may have in other dimensions such as laboratory facilities There are less sharp differences in the selection model based on ownership Panel B Overall private teaching hospitals have the highest quality public hospital have the lowest quality and other hospitals are in the middle However from the posterior standard deviations of the mortality rates it is evident that there are no definitive comparisons among ownership categories There is debate in health policy circles regarding the role that forprofit hospitals should play in the Us health system Gray 1991 Sloan 2000 Some have argued that private not forprofit hospitals may better serve the public interest because they are more likely to provide better care Our results indicate that for the treatment of pneumonia in older patients and the hospitals in our sample there is no evidence of this Keeler et al 1992 also found public hospitals in large cities to be of lower quality while the difference in quality between forprofit and notforprofit hospitals is less pronounced McClellan and Staiger 1999a conclude that the quality difference in forprofit and notforprofit hospitals is small and if anything forprofits likely provide better care in the treatment of heart attacks Private teaching hospitals which are generally viewed as providing superior care Keeler et al 1992 do appear to offer significantly higher quality according to the selection model 42 Selection and selection bias We present some statistics on the relationship between the posterior means of q q and 3 across the 114 hospitals in Table 5 These statistics allow us to uncover the importance of selection and the relationship between selection and quality 26 Performing a simple multinomial logit regression of Southern California patients we found that pneumonia patients were more likely to be admitted to smaller hospitals than were hospital patients generally In contrast acute myocardial infarction heart attack patients were more likely to be admitted to larger hospitals than the average hospital patient Unlike pneumonia treatments acute myocardial infarction treatments often include hightechnology surgery such as cardiac catheterization angioplasty or bypass 17 We start by analyzing the quantitative importance of selection in in uencing patient mortality In the simple probit model the variance in unobserved disease severity s is normalized to be 1 From the posterior means of the coefficients on observed disease severity in the model Table 3 and the distribution of observed patient characteristics in the population Table 1 one may approximate the variance in the contribution of observed demographics and disease severity to the mortality probit it is about 045 The variance in the mortality probit due to variation in hospital quality is about 0013 Table 5 Panel A much smaller than the variance due to unobserved severity of illness which is normalized to 1 This decomposition of variance is about the same in the selection model 7 variation in hospital quality is slightly higher Table 5 but it is still quite small relative to disease severity In the selection model the variation in unobserved disease severity is decomposed into a component that is independent of the hospital assignment process Q from 5 with variance 1 and a component that is a function of the hospital assignment probits 1115 also from 5 The variance of the latter term 5 25 has a posterior mean of 87 which is much larger than the independent component This constitutes strong evidence against random assignment of patients and suggests that the simple probit model provides misleading inferences about hospital quality Since patient selection is important we are interested in understanding the relationship between selection and quality Table 5 Panel A reveals a positive relationship between the posterior means of q and pf the correlation between posterior means is 0517 Panel A and a simple least squares regression of the posterior means of the pf on the posterior means of the q shows a slope coefficient of 0183 that is signi cantly positive I of over 627 Thus hospitals with higher quality higher qj have a greater propensity to be selected by patients with greater unobserved disease severity higher 8 This is also re ected in Table 3 which shows similar patterns of qG and p6 across types of hospitals In any selection model conditional on observed characteristics including observed severity the observed mortality rate for each hospital will be decomposed into a hospital quality 27 Since results in Table 5 are based on posterior means they do not take into account dispersion in the posterior To account for this dispersion one can examine the sample relation between q q and p as a function of the parameters and consider the posterior uncertainty associated with this relationship This would yield values of Table 5 for each draw from the posterior simulator One can then compute the mean value across the draws This method yields similar results component and an unobserved severity component Panel C of Table 5 shows that in this relationship hospital quality q in the probit model is well described as a linear function of hospital quality q and severity correlation p in the selection model From the regression relation reported in panel C of Table 5 it is clear that variation in hospital severity correlation substantially drives variation in inferred hospital quality q in the probit model From the regressions in panels B and C one can infer the slope coefficient of 712 905 l553gtlt124 in panel D Thus variation in hospital severity correlation accounts for a substantial portion of the variation in hospital mortality rates in the selection model whereas in the simple probit model this variation must be attributed to quality differences 43 Orderng by quality The model and approach to inference described in Section 2 provide the complete posterior distribution of all the parameters in the model and any functions of these parameters In particular corresponding to the parameter values in any iteration of the Gibbs sampling algorithm it is a simple matter to compute the corresponding hospital quality probits q The 1900 draws used to obtain the posterior moments reported in this section therefore also provide 1900 draws from the joint distribution of the hospital quality probits q Pairwise comparisons between hospitals are then straightforward For example for two hospitals j and k the numerical approximation to the posterior probability that q gt qk is the fraction of iterations in which q gt qk and the joint distribution of q and qk could easily be plotted Comparing all 114 hospitals simultaneously is more challenging A formal approach to ordering hospitals by quality would begin with a loss function for orderings Suppose the 114 element vector of quality ranks is 1 and the estimated quality rank vector is f If the loss function is f 1 Ar i where A is a positive definite matrix then f should be the posterior mean of 128 This estimate may in turn be approximated numerically by sorting hospital qualities q in each iteration of the Gibbs sampler finding the corresponding rank for each hospital and then averaging the ranks across all iterations The resulting estimated ranks 19 are 28 See for example Bernardo and Smith 1994 Section 515 for this standard result as well as the one on medians used in the next paragraph generally not integers Ifthe loss function were 2 a II rjl where all a gt 0 then I should be the median of the posterior distribution of V which in turn is an integer with probability one Appendix A4 provides rankings based on both loss functions The choice of loss function turns out not to have a large effect on the orderings of relative quality The rankings produced by these alternative loss functions are similar The posterior distributions of 1 and of the hospital qualities convey the uncertainty associated with the rankings For most pairwise combinations of hospitals in the top and bottom quartiles the posterior that the quality of the former exceeds the latter is rarely less than 08 and exceeds 09 more often than not An approximate rule of thumb for the accuracy of rankings is that if a hospital is ranked at quantile x then the posterior probability that its true rank is above the median is also x Appendix A4 provides all the rankings and several aspects of their joint posterior distribution 44 Speci cation and robustness A key assumption in the selection model is that the distances between the patients homes and the 114 hospitals in the sample constitute variables that may be used to control for the non random assignment patients to hospitals Because of the nonlinear relationship between the endogenous variables hospital choice in the mortality equation and the instruments this relationship was modeled explicitly Table 3 reveals an indisputably strong link between the measures in Z and the choice of hospital For instance distance and its square explain about 30 of the variance of the probits The findings are in accord with the literature The further assumption that distances from hospitals to patients are uncorrelated with unobserved disease severity cannot be examined so directly One plausible alternative is that there remain geographic variations in unobserved disease severity after accounting for the observed covariates listed in the first two panels of Table 3 We examined this possibility from three angles First in a conventional probit model for mortality using the observed covariates hospital choice dummies and patient zip code dummies the zip code dummies are insignificant Second the same is true if dummies for nearest hospital replace zip code dummies In both equations the coefficients on the hospital choice dummies are jointly significant in the presence of the zip code dummies Finally we conducted a more direct examination by retrieving the 20 unobserved disease severity component from the mortality probit equation in each iteration of the MCMC algorithm In the regression of this component on zip code dummies and the other regressors the dummies were jointly insigni cant in every iteration All these ndings are consistent with the absence of any unobserved geographic component of disease severity Given the large number of endogenous variables in the selection model quite a few assumptions about functional form were required The dimensionality of the problem is perhaps most evident in the 6440 potentially independent free parameters in Z the prior variance matrix in the multinomial hospital assignment model The selection model takes the extreme step of assuming that shocks to the probits in this model are iid normal before differencing Section 22 If this assumption is reasonable then the ll3gtltl vectors of posterior shocks 1 139 ln which may be retrieved in each iteration of the MCMC algorithm should be consistent with the specification 2 1J71 eHe39J1 If it is not 7 for example if patients with certain characteristics all choose from one small group of hospitals 7 then this will be evidenced by a constructed covariance matrix S n l71 21111 17nl 1T39 being substantially different from Z A conventional goodness of fit test carried out at the 5 level rejects the null hypothesis in slightly over half the iterations of the MCMC algorithm We conclude that there may well be misspecification of the covariance structure in the multinomial hospital assignment covariance matrix but it is probably not severe Due to the large number of parameters in Z information about the covariance structure beyond the data would be required to deal constructively with this potential misspecification The sensitivity of findings to the specification of the prior distribution can be examined in a number of ways To convey the nature of the sensitivity we set up three further variants of the selection model Variant A effectively eliminates the instruments from the entire model by scaling the prior standard deviations of the coefficient vector 05 in the multinomial hospital assignment model by the factor 10396 This variant leaves only the functional form to identify the hospitalspecific parameters in the mortality equation Variant B scales the prior standard deviations of a in the original selection model downward by a factor of 5 and 12 downward by a factor of 25 Variant C is like Variant B except that prior standard deviations are increased by a 29 See Luft et al 1990 and Gowrisankaran and Town 1999 21 factor of 5 relative to the base model Thus variants B and C provide alternative priors that are plausible from the perspective of the subjective prior in the base selection model Appendix A5 provides a detailed set of results for each of these prior distributions As one might expect coef cients on covariates in the mortality probit equation show very little sensitivity to the choice from among the four prior distributions The same is true in the hospital choice multinomial probit model with the obvious exception of prior A The ndings about hospital mortality Section 41 are the same in variants B and C as in the base selection model quality is a U shaped function of size private teaching hospitals have the highest and public hospitals the lowest quality with differences in this dimension remaining small By contrast variant A shows little effect of size or ownership and the point estimates display neither the U shape for size nor the ownership ranking of the base model The correlations between hospital quality posterior means in the base selection model and variants B and C are both 080 By contrast the correlation between hospital quality posterior means in the base selection model and variant A is only 034 We conclude that reasonable variants on the prior produce distinct but insubstantial differences whereas elimination of the instruments from the model has strong and substantial effects 5 Conclusion This study has extended existing econometric methods in order to measure hospital quality using the experience of patients admitted to hospitals in nonrandom fashion Using discharge records for almost 75000 older pneumonia patients from 114 hospitals in Los Angeles County we nd evidence of differences in quality between hospitals of different size and ownership classi cations The smallest and largest hospitals exhibit higher quality than other hospitals We also detect substantial differences in quality for a sizable minority of individual hospitals As an important byproduct our methods produce information about the hospital admissions process Patients with greater unobserved severity of illness tend overall to be admitted to hospitals of higher quality Consequently more conventional methods that ignore nonrandom admission when applied to this data set tend to lower the inferred quality of good hospitals and raise that of poor ones relative to our ndings We nd that variation across 22 individual hospitals in the unobserved severity of illness is at least as great as variation in quality and that this variation accounts for most of the large discrepancy between inference about hospital quality in our model and with more conventional methods The procedures used here are at the current frontier of intensive computational methods in econometrics A supercomputer and several days of computing were required to obtain the results reported here Recent and imminent innovations in numerical methods and computing technology should sharply reduce the real costs of these procedures in the near term Given the policy importance of assessing quality of care in hospitals we believe there is a signi cant return to further investment in these methods and their application to similar questions in health policy and related elds 23 Table 1 Frequency and mortality rates by age disease stage racial and sex categories Severity and A e Categories Demographic 6569 70 74 7579 8084 Over 84 T111 Categories years years years years years Disease 8409 10254 11524 11168 14864 56217 Stage 11 501 509 583 582 1018 694 o 31316615 846 1021 1017 912 1069 4865 g9 2 3 39 591 597 688 1009 1020 785 a m Disease 3 Sta 6 3 1 670 769 1018 973 1478 4908 g3639 1269 1287 1483 1607 2199 1670 D Disease 1350 1598 1707 1381 1664 7700 Stage 37 1533 1477 1681 2213 2818 1956 Disease 156 228 218 239 317 1158 Stage 38 4551 4210 4403 5649 5394 4914 7100 9301 10796 10542 14256 51995 Wh te 720 768 875 1044 1389 1010 Black 1498 1405 1295 1207 1433 6919 974 861 780 1060 1332 1004 8 H 2013 2032 1941 1978 2709 10830 g lspamc 631 541 685 779 1104 770 Asian 794 1106 1129 930 971 4990 617 606 638 827 1133 759 Native 24 26 25 16 23 114 American 417 769 800 3750 2609 1491 Female 5335 7010 8116 7955 12092 40899 5 661 622 734 925 1324 914 to Male 5703 6860 7368 6718 7300 33949 812 842 923 1087 1351 1012 11429 13387 15484 14673 19392 74848 Column Totals 730 731 824 999 1334 959 The rst number in each cell is the cell frequency and the second number is the mortality rate in that cell 24 Table 2 Hospital frequency patients treated and mortality by hospital classi cation 150 Beds or 151 200 201 300 Over 300 ROW Totals Less Beds Beds Beds 9 4 18 19 50 5355 4741 2369 15526 21545 44181 917 1111 942 971 962 Private For 32 15 7 1 55 9792 6627 4412 973 21804 pm t 924 957 1054 1048 966 5 5 Tigcvli itgg 0 0 0 6802 6802 917 917 1 3 4 Public 0 0 232 1829 2061 862 957 946 Column 41 19 26 28 114 Totals 14533 8996 20170 31149 74848 922 997 965 961 959 The rst number in each cell is the number of hospitals in that category the second number is the total number of pneumonia patients discharged from hospitals in that cell and the third number is the mortality rate patient weighted for patients who were discharged from hospitals in that cell 25 Table 3 Posterior means and standard deviations Coefficient Selection model Probit model y SZSH Demographic covariates y SZSH Disease severity covariates gtx Eb 35w gt3 gag 2E3 00mg 3320 H DU 0 OH 1 m Varlance of quality Distance l365 2 1243 Distance gtlt Age 045 0025 Distance X 031 X X Dlstance 0974 0258 Hospital choice covariates Speci cations also include indicators for each year 26 Table 4 Posterior probability comparisons of group hospital quality probits selection model A Hospitals grouped by size 0116 0019 S 150 beds 151200 beds 201300 beds gt 300 beds 1 16 71 S 150 beds 010 0086 0007 0089 0007 0104 0006 99 82 100 151200 beds 0117 0009 010 0109 0009 0121 0007 84 18 98 201300 beds 0108 0007 0093 0008 010 0112 0006 29 0 2 gt 300 beds 0097 0006 0083 0006 0090 0005 010 B Hospitals grouped by ownership classi cation Private Private Private Public notforpro t forpro t teaching Private 54 60 23 notforpro t 010 0101 0005 0103 0008 0088 0015 Private 46 56 20 forpro t 010 0005 010 0103 0009 0088 0014 Private 40 44 22 teaching 0098 0008 0099 0009 010 0087 0017 Public 77 80 78 0116 0018 0118 0022 010 The rst number in each cell is the posterior probability that the group quality probit qG in the column category exceeds qG in the row category and the second number is the posterior mean probability of mortality in the row category given a 10 probability of mortality in the column category with the posterior standard deviation of this statistic in parentheses 27 Table 5 Relations between hospital quality probits and severity correlations in the sample A Variances and correlations ofposterior means of q q and p 41 0148 766 324 1 0105 0128 325 P1 0018 0017 0022 Covariances shown below main diagonal correlations shown above the main diagonal B OLS regression of p j posterior means on q posterior means p 124 q R2 105 s044 034 C OLS regression of q posterior means on q and p j posterior means q 905 q 1553 p R2 954s022 020 052 D OLS regression of q posterior means on q posterior means q 712 q R2 587 s 073 056 28 References Albert and Chib 1993 Bayesian Analysis of Binary and Polychotomous Response Data Journal of the American StatisticalAssociation 422 66979 Bernardo and Smith 1994 Bayesian Theory Chichester John Wiley and Sons Burns L Wholey D 1992 The Impact of Physician Characteristics in Conditional Choice Models for Hospital Care Journal ofHealth Economics 11 4362 Chib S and Greenberg 1996 Markov Chain Monte Carlo Simulation Methods in Econometrics Econometric Theory 12 40931 Cutler D M 1995 The Incidence of Adverse Medical Outcomes Under Prospective Payment Econometrica 631 2950 Fine JM JD Scinto DH Galusha MK Petrillo TP Meehan 1998 Patient and Hospital Characteristics Associated with Timely Care of Elderly Patients Hospitalized with Pneumonia Results from the Medicare Quality Indication System Pneumonia Module AbstractBook Association of Health Services Research 15 Gelfand AE and AFM Smith 1990 Sampling Based Approaches to Calculating Marginal Densities Journal ofthe American StatisticalAssociation 85 398409 Geweke J 1997 Posterior Simulators in Econometrics in D Kreps and KF Wallis eds Advances in Economics anal Econometrics Theory anal Applications vol III Cambridge Cambridge University Press 128 165 Geweke J 1999 Using Simulation Methods for Bayesian Econometric Models Inference Development and Communication with discussion and rejoinder Econometric Reviews 18 1126 Geweke J G Gowrisankaran and R Town 2001 Bayesian Inference for Hospital Quality in a Selection Model Cambridge MA NBER Working Paper 8497 Geweke J M Keane and D Runkle 1997 Statistical Inference in the Multinomial Multiperiod Probit Model Journal ofEconometrics 80 12565 Gowrisankaran G and R Town 1999 Estimating the Quality of Care in Hospitals Using Instrumental Variables Journal of Health Economics 18 74767 Gray B 1991 The Pro t Motive anal Patient Care Cambridge MA Harvard University Press Iezzoni LL 1997 Risk Adjustment for Measuring Health Care Outcomes Ann Arbor MI Health Administration Press 2quotd Edition 29 Iezzoni LI et al 1996 quotSeverity Measurement Methods and Judging Hospital Death Rates for Pneumoniaquot Medical Care 341 1128 Keane MP 1992 A Note on Identi cation in the Multinomial Probit Model Journal of Business and Economic Statistics 10 193200 Keeler E B KL Kahn D Draper MJ Sherwood LV Rubenstein EJ Reinisch J Kosecoff and RH Brook 1990 Changes in Sickness at Admission Following the Introduction of the Prospective Payment System Journal of the American Medical Association 264 196268 Keeler E B et al 1992 Hospital Characteristics and Quality of Care Journal of the American Medical Association 268 13 170914 Kessler D and McClellan 2000 Is Hospital Competition Socially Wasteful Quarterly Journal ofEconomics 115 2 577615 Lohr KN ed 1990 Medicare A Strategy for Quality Assurance Volume I Washington DC National Academy Press Luft H et al 1990 Does Quality In uence Choice of Hospital Journal of the American Medical Association 263 28992906 McClellan M B McNeil and J Newhouse 1994 Does More Intensive Treatment of Acute Myocardial Infarction in the Elderly Reduce Mortality Journal of the American MedicalAssociation 272 859866 McClellan M and H Noguchi 1998 Technological Change in HeartDisease Treatment Does High Tech Mean Low Value American Economic Review Papers and Proceedings 88 2 9096 McClellan M and D Staiger 1999a Comparing Hospital Quality at ForPro t and NotFor Pro t Hospitals NBER Working Paper 7324 McClellan M and D Staiger 1999b The Quality of Health Care Providers NBER Working Paper 7327 McGarvey R and J Harper 1993 Pneumonia Mortality Reduction and Quality Improvement in a Community Hospital Quality Review Bulletin 19 12430 National Center for Health Statistics 1996 Available on the Internet at httpwwwcdcgovnchswwwnchshomehtm Pennington J 1994 Respiratory Infections Diagnosis and Management New York Raven Press 3r edition 30 Rello J and J Valles 1998 Mortality as an Outcome in HospitalAcquired Pneumonia Infection Control and Hospital Epidemiology 1910 7957 Sloan F 2000 Notforpro t Ownership and Hospital Behavior in A J Culyer and JP Newhouse ed The Handbook of Health Economics Volume 1 Amsterdam ElseVier Science Thomas JW and MLF Ashcroft 1991 Measuring Severity of Illness SiX Severity Systems and their Ability to Explain Costvariations Inquiry 28 3955 United States General Accounting Of ce 1994 quotReport Cardsquot Are Useful But Signi cant Issues Need to be Addressed GAOHEHS94219 Washington DC United States General Accounting Of ce Wray N J Hollingsworth N Petersen and C Ashton 1997 CaseMix Adjustment Using Administrative Databases A Paradigm to Guide Future Research Medical Care Research andReview 54 326356 31

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