A Comparison of HMO Efficiencies as a Function of Provider Autonomy
Author(s): Patrick L. Brockett, Ray E. Chang, John J. Rousseau, John H. Semple, Chuanhou Yang
Source: The Journal of Risk and Insurance, Vol. 71, No. 1 (Mar., 2004), pp. 1-19 Published by: American Risk and Insurance Association
Stable URL: http://www.jstor.org/stable/3519977 Accessed: 16/04/2009 01:01
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use.
Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
http://www.jstor.org/action/showPublisher?publisherCode=ari.
Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission.
JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org.
American Risk and Insurance Association is collaborating with JSTOR to digitize, preserve and extend access
to The Journal of Risk and Insurance.
A COMPARISON
OF HMO EFFICIENCIES
AS A
FUNCTION OF PROVIDER
AUTONOMY
Patrick L. Brockett Ray E. Chang John J. Rousseau John H. Semple Chuanhou Yang ABSTRACT
Current debates in the insurance and public policy literatures over health care financing and cost control measures continue to focus on managed care and HMOs. The lower utilization rates found in HMOs (compared to tradi- tional fee-for-service indemnity plans) have generally been attributed to the organization's incentive to eliminate all unnecessary medical services. As a consequence HMOs are often considered to be a more efficient arrangement for delivering health care. However, it is important to make a distinction between utilization and efficiency (the ratio of outcomes to resources). Few studies have investigated the effect that HMO arrangements would have on the actual efficiency of health care delivery. Because greater control over provider autonomy appears to be a recurrent theme in the literature on re- form, it is important to investigate the effects these restrictions have already had within the HMO market. In this article, the efficiencies of two major classes of HMO arrangements are compared using "game-theoretic" data envelopment analysis (DEA) models. While other studies confirm that abso- lute costs to insurance firms and sponsoring companies are lowered using HMOs, our empirical findings suggest that, within this framework, efficiency generally becomes worse when provider autonomy is restricted. This should give new fuel to the insurance companies providing fee-for-service (FFS) indemnification plans in their marketplace contentions.
Patrick L. Brockett and Chuanhou Yang are from the Department of Management Science and Information Systems, McComb School of Business, The University of Texas at Austin. Ray E. Chang is from the Department of Health Management, National Taiwan University, Taipei, Taiwan. John J. Rousseau is from the Department of Management, McComb School of Business, The University of Texas at Austin. John H. Semple is from Department of Management Information Sciences, Edwin L. Cox School of Business, Southern Methodist University, Dallas. We wish to thank J. David Cummins for his numerous insightful and useful comments on this article at various stages along the way to fruition. The article is definitely improved due to his and two anonymous referees' suggestions.
INTRODUCTION
Approximately three decades have passed since Robert Finch, then Secretary of Health, Education and Welfare, launched the U.S. Government's Health Maintenance Organization (HMO) strategy to combat what was perceived to be a financial crisis in health care. The HMO Act of 1973 gave HMOs several strategic advantages over traditional indemnity health insurance providers and was justified on the grounds that there were public policy benefits associated with the "more cost efficient" HMOs. The subsequent escalation in health care expenditures from 7.4 percent of U.S. GDP in 1970 to 12.4 percent in 1990 has only intensified public concern and turned health care financing into one of the most pressing problems facing U.S. domestic policy-makers. It has also provided impetus for the significantly increased market share of HMOs in the health insurance/health care financing marketplace.
Because the HMO is both the contractor and the medical provider, it directly bears financial risk like the traditional indemnity insurer; however, unlike the indemnity insurer, the HMO also has the opportunity and incentive to control costs by elim- inating unnecessary utilization. This arrangement has produced the desired effect. Luft's 1981 review of earlier studies showed that HMO enrollees had lower total costs (premium and out-of-pocket expenses) than enrollees in the familiar Blue Cross Blue Shield plan. Miller and Luft (1997, 2002) showed that, overall, HMOs appeared to use fewer resources. Moreover, Luft (1981) presented a variety of evidence to suggest that hospital utilization-the most cost intensive aspect of medical care-was lower in HMOs than in comparable indemnity (fee-for-service or FFS) plans. This finding has been confirmed by other studies, e.g., Hornbrook and Berki (1985), Langwell et al. (1987), and Miller and Luft (2002). As health care costs now account for approximately 26 percent of the typical firm's payroll, more corporations are turning toward HMOs and away from traditional insurance. However, there have been some rumblings of discontent.
Lower utilization and its concomitant reduction in overall expenditures are generally attributed to the HMOs incentive to eliminate all unnecessary medical services. Pre- viously, this potential for streamlining has been regarded as indicating that the HMO is a more efficient arrangement for delivering health care. It is important, however, to point out the distinction between studies of utilization and our current study of efficiency; utilization refers to the frequency with which services are used, whereas efficiency refers to the outputs produced for given levels of resources consumed. Al- though both play important roles when evaluating the performance of health care delivery systems, low utilization (or even low costs) is not synonymous with effi- ciency. Efficiency is only improved if unnecessary utilization is eliminated together with an appropriate reduction in expenditures.
To rigorously determine the health care delivery and financing system which appears to be most efficient overall, strict attention must be paid to quantifying the multi- ple inputs consumed for the multiple outputs produced. As noted by Saward and Greenlick (1981, p. 27) "counting the pieces of the [medical care] process" fails to pro- duce a coherent measure of system performance. Data Envelopment Analysis (DEA), an efficiency measurement tool introduced by Chares, Cooper, and Rhodes (1978), is one of the appropriate approaches for this situation. In the recent literature, Rosenman Siddharthan, and Aher (1997) used DEA to measure the relative technical efficiencies
of 28 HMOs licensed to practice in the state of Florida in the autumn of 1994. Bryce, Engberg, and Wholey (2000) used a nationwide sample of 585 HMOs to compare the effectiveness of DEA, stochastic production frontiers (SFR), and fixed-effects regres- sion (FER) in evaluating HMO efficiency.
In this article, the authors contrast two arrangements within the HMO health in- surance framework: the tightly controlled, highly centralized Staff/Group HMO arrangement; and the loosely controlled, highly autonomous Independent Practice Association (IPA) arrangement. Our situation is additionally complicated by the need to compare and contrast two different systems while incorporating the above multi- plicities. The model used in the present study overcomes these difficulties by com- bining features of two well-established methodologies: Data Envelopment Analysis (DEA), and two-person zero-sum games, a theory for analyzing behavior between rational competing economic agents as introduced by von Neumann (1928) and later refined in von Neumann and Morgenstem (1944) (for a recent reference, see Fudenberg and Tirole, 2000). Because organizations in DEA are evaluated against one another to determine their relative efficiencies, it is both natural and appropriate to adopt a model that formally reflects this competitive element (see also Banker, 1980; Banker et al., 1989).
From the origins of Staff/Group HMO arrangement and the IPA arrangement, we would expect that IPAs are a more efficient delivery system than the Staff/Group arrangements. IPA physicians typically come from private practice and thus are ma- tured in an environment that encouraged patient-doctor contact. These physicians still have greater discretion over the provision of care and thus may elect to see pa- tients they might otherwise be discouraged from seeing in a more regulated, obtrusive, cost conscious system. These two systems are compared to determine which, if any, in the aggregate exhibits greater overall efficiency.
BACKGROUND
The U.S. Government initiated its Health Maintenance Organization (HMO) strategy in the early 1970s under the belief that the efficiency of health care delivery would be improved through competition. The national goal was to have 1,700 competing HMOs by 1977 and to cover 90 percent of Americans by 1980 (U.S. Department of Health, Education and Welfare, 1971). Although this goal was never reached, the emergence of HMOs as a market force has dramatically impacted the health care sector and changed the character of the health insurance marketplace. The HMO has gone from virtually no market share in 1970 to a current share of 31.7 percent in 2001 (HMO-PPO/Medicare-Medicaid Digest, 2002).
Health care plans can be classified into two broad categories: managed care and non- managed care. The managed care category includes various models of HMOs, Pre- ferred Provider Organizations (PPOs) and their variants, and managed indemnity plans (MIP). The nonmanaged category is synonymous with fee-for-service (FFS) in- demnity insurance plans. Although plans under the managed care category differ widely in organization, financial risk, accessibility, enrollment, and care provision, the common feature is that some form of utilization review is adopted to control the costs of the provider's practice (Weiner and Lissovoy, 1993).
Types of HMO Arrangements
While consensus on the definition of managed care is elusive,1 the Health Maintenance Organization Act of 1973 defines an HMO (in part) as an organization that provides basic health services for a fixed periodic payment under a community rating sys- tem.2 There are, however, several important characteristics (cf., Luft, 1981, p. 2) which differentiate HMOs from more traditional health insurance systems:
* The HMO assumes a contractual responsibility to provide or ensure the delivery of a stated range of health services. This includes at least ambulatory care and inpatient hospital services.
* The consumer makes a fixed annual or monthly payment that is independent of the use of services. (This does not exclude the possibility for some minor additional charges related to utilization.)
* The HMO assumes at least part of the financial risk or gain in the provision of services.
The most commonly referenced taxonomy for HMOs consists of the following four basic arrangements: a Staff model; a Group model; a Network model; and an Independent Practice Association (IPA) model.
The Staff and Group models are the most restrictive since physician behavior is closely monitored and health care delivery is highly centralized.3 In contrast, the IPA model affords the provider a higher degree of autonomy since physician behavior is only loosely controlled. It is thus considered a more decentralized health care delivery system because physicians remain primarily in independent practice. In 2001, over 90 million people were enrolled in 542 HMOs, with IPAs accounting for 65 percent and Staff/Group models accounting for 13 percent (HMO-PPO/Medicare-Medicaid Digest, 2002).
DEA MODEL DEVELOPMENT
To begin with, a general description of Data Envelopment Analysis (DEA) is followed by a more detailed description of the specific model that will be proposed for con- trasting Staff/Group and IPA HMOs.
Data Envelopment Analysis (DEA)
Data Envelopment Analysis (Chares, Cooper, and Rhodes, 1978) is a multi-input, multi-output efficiency measurement technique that generalizes the classical single input, single output approach used in engineering. Given are n "decision-making 1
For example, the Health Insurance Association of America (HIAA) no longer considers man- aged indemnity plans as managed care. The requirement for a plan to be considered as man- aged care is its obligation to arrange care provision.
2 The 1988 Amendments to the HMO Act changed "community rating" to "adjusted community
rating" which is a prospective experience rating.
3 Indeed, many studies combine these two groups into a single category (Group/Staff or Staff/Group).
units" (DMUs), where each unit j e { 1, 2,..., n}) has m observed inputs whose levels are denoted by the vector xT = ( jl, X j2 ..., Xjm) and s observed outputs whose levels are denoted by the vector yj = (yjl, yj2,..., yjs). DMUs are assumed to be homogenous in the sense that each consumes a similar set of inputs to produce a similar set of outputs. Each unit's observed input-output levels are then "tested" against those exhibited in the entire sample. When constant-returns-to-scale are assumed, this test is conducted by solving the fractional mathematical program
Max y(v u,V XT U xTu S.t. j <1 j=1,2, .... n X U U,v > 0.
Here, the subscript "0" is used to denote any one of the n DMUs (the "test" unit)
whose efficiency is being examined and u, v > 0 are vectors (uT = (ul, u2,..., Um) vT = (vl, v2, .... , s)) of input and output weights to be determined by the optimization in Equation (1). In practice, the condition u, v > 0 is typically relaxed to u, v > 0 for computational simplicity; where absolutely necessary, strict positivity can be achieved using algorithms based on implicit infinitesimals (Chares, Rousseau, and Semple, 1993).
In other words, the DMU being tested in Equation (1) seeks to maximize its ra- tio of weighted output to weighted input, subject to the conditions that no DMU (including the test unit) attains a ratio >1 for the same set of weights (u, v > 0). As stated in Chares, Cooper, and Rhodes (1978, p. 430), this "maximization then accords the most favorable weighting that the constraints allow" to the test unit. Units that achieve an optimal ratio of 1 are termed ratio efficient; those with optimal ratios <1 are ratio inefficient. It is important to note that each unit's evaluation in- volves a separate optimization, and therefore distinct weights are computed for each unit.
Game-Theoretic DEA
When DMUs can additionally be categorized into one or more groups (e.g., IPA vs. Staff/Group), it has been customary to pool the units together for the purpose of per- forming a joint DEA analysis (see, e.g., Charnes, Cooper, and Rhodes, 1981; Grosskopf and Valdmanis, 1987). This poses significant difficulties for any study attempting to compare the performances of distinct groups. First, pooling means that each unit is compared against members of its own group in addition to members of other groups. Consequently, a characterization of "inefficient" may result from "within group" ef- fects instead of the desired "between group" effects. This situation can be repaired by comparing the test unit exclusively against members outside its own group. In the current study, this means that when the test unit is an IPA organization, it will be compared exclusively against Staff/Group organizations. Similarly, when the test unit is a Staff/Group organization, it will be tested exclusively against IPA organiza- tions. This element of competition is evident in the following mathematical program: for each DMU k E G, solve
Max yv U,V Xk U v x[ (2) s.t. < 1 j (2) XjU U, v > 0,
where G and Gc (the complement of G) are disjoint index sets describing the competing groups. This formulation can additionally be shown to solve a two-person, zero-sum "ratio" game (Rousseau and Semple, 1995), thus Equation (2) is reffered to as a game theoretic DEA model.4 Note that the input-output data for DMUk do not appear in the constraints of Equation (2). Consequently, the efficiency score for DMUk can exceed 1. Values > 1 indicate the test unit is ratio efficient with respect to the competing group, while values < 1 indicate it is ratio inefficient with respect to the competing group.
DEA EFFICIENCY PERSPECTIVES
In general, different parties to an efficiency analysis have different perspectives of what constitutes the best performance (i.e., different goals). Moreover, trying to accommo- date different perspectives in a single model can make it impossible to determine whether an item should be an input or an output. Therefore, an efficiency evaluation begins by selecting a perspective. Since the purpose of this article is to examine public policy issues in the health insurance arena, two separate perspectives are investigated, that of consumers and that of society.
Inputs and Outputs
All input and output dimensions selected for a policy level DEA analysis should satisfy the property that each output-to-input ratio is a meaningful indicator of some aspect of efficiency (see Cooper, Seiford, and Tone, 1999). The inputs and outputs selected for our perspectives meet this standard and are outlined below.
Consumers' Perspective
Consumers are the beneficiaries and purchasers of health care plans and are concerned with services received and expenses incurred. Accordingly, from the perspective of consumers, the only relevant input is out-of-pocket expense. Relevant outputs include at least outpatient and inpatient services received. The specific measures selected are detailed in the following.
Out-of-pocket expense for an HMO enrollee consists of both premiums and co- payments; however, data on co-payments are not available in most instances.5 In our analysis, we took total premiums as the sole input.
4 Cummins, Weiss, and Zi (1999) use this method to analyze the efficiency of the stock and
mutual property-liability insurers.
5
Additionally, co-payments are made directly to physicians or other health care providers, and hence most organizations keep no record of them. It is not mandatory for HMOs to re- port co-payment information to their regulators. Co-payments for outpatient visits, normally charged at US$5 or US$10 per visit, represent a minute portion of the consumers' out-of-pocket expenses. No co-payments are made for inpatient services.
Ambulatory encounters are defined as the total number of outpatient visits made by the membership of an HMO. This number is a summary measure for all outpatient services received and becomes our first output. Visits include all patient contacts with physicians, physician's assistants and other medical personnel. Inpatient services are measured using the number of hospital days (i.e., total number of patient days for which enrollees are hospitalized). This becomes our second output.
Societal Perspective
From a societal perspective, what the policy-makers care about is the total resources consumed, the aggregate cost incurred by the consumers and the HMOs considered as a whole. However, in HMOs, as in other types of insurance, premiums are signifi- cantly determined by expected expenses, which are highly correlated with the actual expenses experienced. This is verified in our samples, where the total premiums and the total expenses are almost the same. Therefore, either the total premiums or the to- tal expenses might be appropriate as an input from the societal perspective; however, as profits (a part of premiums) are dispersed back into the economy (society),6 and as companies can occasionally (intentionally or inadvertently) misprice their health care insurance products, premiums are arguably less indicative of the costs to society than are HMO expenses incurred. Accordingly, in the present analyses, the total HMO expenses are used as the sole input.7
Ambulatory and inpatient services improve the health status of the population and hence are employed as our first and second outputs respectively. In addition, expand- ing health care coverage to a larger proportion of the population is a societal benefit, thus total enrollment is taken as a third output in the societal model.8 Enrollees in HMOs include group subscribers, Medicare and Medicaid beneficiaries, and indi- vidual subscribers. Enrollment is measured here as the total member-months (TMM) during 1995.
DATA AND SAMPLE SELECTION
The data used in this study came from the 1995 Series of HCIA's HMO Database. The database includes financial, enrollment, and utilization figures as well as general company information. Items were gathered at the company level from information that HMOs supply annually to their state regulators. In 1995, the data included 538 HMOs from 46 states. For the purposes of this study, there were 36 Staff, 41 Group, and 344 IPA HMOs.9 These HMOs ranged in size from a few hundred members to over 10 million members. Some HMOs failed to report one or more of the inputs or outputs selected in the previous section and were deleted. All the remaining HMOs
6
Another potential component of total resources consumed, tax subsities, will also be redis- tributed to society and hence are not included (being a redistribution rather than a cost at the agregrate societial level).
7 We have also run the model with both premiums and expenses included as inputs (co-linearity is not a problem with DEA) and the same three outputs described. The results are essentially the same and are not reported.
8 In fact universal coverage was the main objective of President Clinton's nationalized health
care plan and was the rallying point for proponents. 9 The 117 remaining organizations were Network HMOs.
TABLE 1
Sample Statistics (Noncost-Adjusted)
Member Ambulatory Hospital Total Total
Months Encounters Days Premium Expenses
IPA HMOs Sample mean (x) 1748500 5.89 0.33 $1628.64 $1555.09 Sample SD (s) 1922743 8.99 0.15 $309.18 $299.68 Staff/Group HMOs Sample mean (x) 1700656 6.23 0.34 $1937.62 $1884.92 Sample SD (s) 1562806 3.83 0.17 $915.83 $883.05
were then studied to ensure that the HMOs in our sample were financially viable and HMOs whose total premiums do not meet or exceed (to the nearest 1 percent) their expenditures were deleted.
For the population outlined above, the database provided observations on 19 Staff/Group HMO and 85 IPA plans. Although the Staff/Group sample, as well as the IPA subsamples which include 19 IPAs randomly selected from the 85 IPAs, would be too small for most statistical tests based on normality, it is quite adequate for the nonparametric methodsl0 employed in this article.
We adjusted all payments (premium dollars, total expenses) for regional cost differ- ences among HMOs by a "cost differential" index. This index is constructed as a population weighted combination of city and county level hospice11 wage indices used by Medicare for Hospice care.12 This care represents a basket of like services- including ambulatory care and hospital care-adjusted to reflect different regional costs. The counties in which each HMO operates are reported in our database so we are able to construct a unique regional cost index for each HMO. The cost differential indices for all the HMOs in our sample and the raw data are given in the Appendix. The summary statistics for the sample are given in Table 1 (noncost-adjusted) and Table 2 (cost-adjusted) below. Premiums, ambulatory visits, hospital days, total expenses were all calculated on a per member per year basis.
RESULTS AND IMPLICATIONS
The 85 IPA observations are temporarily pooled with the 19 Staff/Group HMOs for the purpose of scaling. Each input and output is divided by its average in the
10
Indeed, small sample sizes and departures from normality are the primary reasons for using nonparametric techniques (see, e.g., p. 35 of Sigel and Castellan, 1988).
1 Hospice is a special way of caring for people who are terminally ill, and for their family. This care includes physical care and counseling. Hospice care is covered under Medicare Part A (Hospital Insurance).
12 The hospice wage indices are from HCFA Medicare payment systems: http://www.hcfa.
gov/medicare/hospiceps.htm (based on 1996 hospital cost report data). And the popula- tion data are from U.S. Census Bureau county population estimates http://eire.census.gov/ popest/archives/county/co-99_8.php (1996).
TABLE 2
Sample Statistics (Cost-Adjusted)
Member Ambulatory Hospital Total Total Months Encounters Days Premium Expenses IPA HMOs Sample mean (x) 1748500 5.89 0.33 $1471.17 $1404.36 Sample SD (s) 1922743 8.99 0.15 $306.85 $292.60 Staff/Group HMOs Sample mean (x) 1700656 6.23 0.34 $1830.61 $1780.17 Sample SD (s) 1562806 3.83 0.17 $792.41 $762.36
108 unit pooled sample. This scaling is necessary to ensure that the results are units invariant.
Equal sample sizes for the IPA vs. G/S DEA comparison in this article were used. Smaller samples intensify the upward bias on DEA scores, and when using grouped data, equal sample sizes should be used to ensure equal bias. Because the IPA sample is much larger, it was randomly sampled with replacement 19 IPAs to run against the 19 G/S units. The process was repeated a total of 20 times to check the robustness of results to different IPA samples, so 20 different IPA samples (each of size 19) were run against the 19 (fixed) G/S HMOs.
Both the regular "collective frontier" DEA model, where all units (IPA and G/S units) are included in the reference set, and the cross-frontier DEA model, where the units of one group are run exclusively against the efficient frontier of the alternative group, were run. The results are presented below. Analysis to detect efficiency differences between two groups was performed by the rank statistical method outlined in Brockett and Golany (1996).13
For both the consumers' and societal perspectives, the null hypothesis is: IPA HMOs and G/S HMOs are equally efficient. For each run, we rank the efficiency scores of the 38 HMOs, compute the rank sum for the IPAs and G/Ss, respectively, and the corresponding p-values of Mann-Whitney tests. We reject the null hypothesis if the p-value is <1 percent.
Societal Perspective
Recall that the input is total expenses, and the three outputs are total member months, ambulatory encounters, and hospital days. As before, the input and outputs are scaled by their respective (pooled sample) averages prior to implementing Equation (2). The results are given in Tables 3 and 4 below.
13
Cummins, Rubio-Misas, and Zi (2002) measured the difference between the stock and mutual frontiers for each operating point to determine which technology is dominant. Our measure combines both technical dominance and efficiency, and uses a rank statistical test to enhance robustness and because of the intrinsically nonmetric nature of efficiency scores.
TABLE 3
Tests of the Null Hypothesis of Equal Efficiency Between HMOs: Societal Perspective, Collective Frontier Method
IPA and G/S
Run No. IPA Rank Sum G/S Rank Sum p-Value
1 329 412 0.11284 2 324 417 0.08730 3 307 434 0.03188 4 308 433 0.03403 5 298 443 0.01715 6 315 426 0.05258 7 342 399 0.20269 8 295 446 0.01375 9 283 458 0.00532 10 304 437 0.02610 11 301 440 0.02123 12 293 448 0.01183 13 318 423 0.06267 14 295 446 0.01375 15 290 451 0.00938 16 303 438 0.02438 17 323 418 0.08276 18 310 431 0.03867 19 301 440 0.02123 20 293 448 0.01183
Note: Mann-Whitney test is used to test the hypotheses. The alternative hypothesis is: the IPA (Independent Practice Association) HMOs are more efficient than the G/S (Group/Staff) HMOs. The significance level is 1 percent.
For the collective frontier DEA model, the Mann-Whitney Rank test (nlpA = 19, ncs =
19) for "equally efficient" versus the one-sided alternative "the IPA HMOs are more efficient than the G/S HMOs" supported the alternative hypothesis for 18 of the 20 runs at the 10 percent or less significance levels. Only two of the runs did not support the alternative hypothesis at these significance levels. The p-values of these two runs are 0.20269 and 0.11284, respectively. These empirical findings suggest that from a societal perspective the decentralized IPAs are relatively more efficient, in an overall sense, than the more regulated Staff/Group arrangements.
More dramatic results were obtained using the cross-frontier DEA model. The Mann-
Whitney Rank Test (nIpA = 19, nG/s = 19) for "equally efficient" versus the one-sided
alternative "the IPA HMOs are more efficient than the G/S HMOs" supported the alternative hypothesis for all the 20 runs at the 5 percent or less significance levels. And 19 of them had p-values <1 percent.
Consumers' Perspective
In the consumer model, the input is the total premium, and the outputs are am- bulatory encounters and hospital days. In the societal model, it is found that IPAs
TABLE 4
Tests of the Null Hypothesis of Equal Efficiency Between IPA and G/S HMOs: Societal Perspective, Cross-Frontier Method
IPA Rank Sum
252 286 259 263 214 252 311 242 236 241 220 217 238 224 202 222 250 259 244 222 G/S Rank Sum 489 455 482 478 527 489 430 499 505 500 521 524 503 517 539 519 491 482 497 519
Note: Mann-Whitney test is used to test the hypotheses. The alternative hypothesis is: the IPA (Independent Practice Association) HMOs are more efficient than the G/S (Group/Staff) HMOs. The significance level is 1 percent.
are more efficient than G/Ss. In this section, it is first checked to see if this conclu- sion remains true for the consumer model. The alternative hypothesis of the test is that IPAs are more efficient than G/Ss, and test results of the consumer model us- ing both the collective frontier and cross-frontier methods are presented in Tables 5 and 6.
For the collective frontier DEA model, the Mann-Whitney Rank Test (nlPA = 19, nG/S = 19) for "equally efficient" versus the one-sided alternative "the IPA HMOs are more efficient than the G/S HMOs" did not support the alternative hypoth- esis for 16 of the 20 runs at the 10 percent or less significance levels. But four of the runs supported this alternative hypothesis at 10 percent significance levels. The p-values of these four runs were 0.074209, 0.078396, 0.082759, and 0.092030, respectively.
For the cross-frontier DEA model, the Mann-Whitney Rank Test (nIpA = 19, nc/s =
19) for "equally efficient" versus the one-sided alternative "the IPA HMOs are more efficient than the G/S HMOs" did not support the alternative hypothesis for 18 of the 20 runs at the 10 percent or less significance levels. Only two runs supported the
Run No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 p-Value 0.000271 0.006813 0.000567 0.000849 0.000002 0.000271 0.041186 0.000088 0.000043 0.000078 0.000006 0.000004 0.000055 0.000009 0.000000 0.000007 0.000217 0.000567 0.000111 0.000007
TABLE 5
Tests of the Null Hypothesis of Equal Efficiency Between IPA and Consumers' Perspective, Collective Frontier Method
IPA Rank Sum 325 338 340 346 364 331 341 349 352 323 370 348 358 331 321 369 351 322 346 334 G/S Rank Sum 416 403 401 395 377 410 400 392 389 418 371 393 383 410 420 372 390 419 395 407
Note: Mann-Whitney test is used to test the hypotheses. p-value (1) corresponds to the alternative hypothesis: IPA (Independent Practice Association) HMOs are more efficient than the G/S (Group/Staff) HMOs, while p-value (2) corresponds to the alternative hypothesis: the G/S HMOs are more efficient than the IPA HMOs. The significance level is 1 percent.
alternative hypothesis. And the p-values for these two runs are 0.001141 and 0.082759, respectively (note that one would expect two significant results at the 10 percent level of significance in twenty repetitions).
These results alone cannot tell us whether the converse is true, i.e., whether the IPAs are significantly more efficient than the G/Ss or not. We need to conduct another test with the alternative hypothesis that G/Ss are more efficient than IPAs to do this. However, due to the symmetry of the Mann-Whitney test statistic, the p-values for this alternative hypothesis can be derived from the p-values for the previous alternative hypothesis by taking 1 minus the previous p-value. The final column in Tables 5 and 6 show this result.
For the collective frontier DEA model, the Mann-Whitney Rank Test (nIpA = 19, nG/S = 19) for "equally efficient" versus the one-sided alternative "the G/S HMOs are more efficient than the IPA HMOs" did not support the alternative hypothesis for all the 20 runs at the 10 percent or less significance levels. Actually, the p-values are all over 0.5. These empirical findings suggest that the G/Ss are not more efficient than the
G/S HMOs: Run No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 p-Value (1) 0.092030 0.171354 0.186615 0.237221 0.424746 0.124416 0.194552 0.265104 0.294563 0.082759 0.494177 0.255628 0.357580 0.124416 0.074209 0.482535 0.284577 0.078396 0.237221 0.143300 p-Value (2) 0.907970 0.828646 0.813385 0.762779 0.575254 0.875584 0.805448 0.734896 0.705437 0.917241 0.505823 0.744372 0.642420 0.875584 0.925791 0.517465 0.715423 0.921604 0.762779 0.856700
I
I
TABLE 6
Tests of the Null Hypothesis of Equal Efficiency Between IPA and G/S HMOs: Consumers' Perspective, Cross-Frontier Method
Run No. IPA Rank Sum G/S Rank Sum p-Value (1) p-Value (2)
1 452 289 0.991329 0.008671 2 464 277 0.996830 0.003170 3 437 304 0.973898 0.026102 4 453 288 0.991992 0.008008 5 350 391 0.274756 0.725244 6 353 388 0.304708 0.695292 7 476 265 0.998965 0.001035 8 463 278 0.996538 0.003462 9 389 352 0.705437 0.294563 10 361 380 0.390756 0.609244 11 388 353 0.695292 0.304708 12 331 410 0.124416 0.875584 13 399 342 0.797310 0.202690 14 394 347 0.753668 0.246332 15 266 475 0.001141 0.998859 16 323 418 0.082759 0.917241 17 410 331 0.875584 0.124416 18 394 347 0.753668 0.246332 19 430 311 0.958814 0.041186 20 405 336 0.843085 0.156915
Note: Mann-Whitney test is used to test the hypotheses. p-value (1) corresponds to the alternative hypothesis: IPA (Independent Practice Association) HMOs are more efficient than the G/S (Group/Staff) HMOs, while p-value (2) corresponds to the alternative hypothesis: the G/S HMOs are more efficient than the IPA HMOs. The significance level is 1 percent.
IPAs. Combined with the corresponding results from the previous test that IPAs are more efficient than G/Ss, we can say that the IPAs are still a little more efficient than G/Ss using the collective frontier DEA model from the consumers' perspective, even though it had only two significant runs.
For the cross-frontier DEA model, the Mann-Whitney Rank Test (nIPA = 19, ncG/ = 19) for "equally efficient" versus the one-sided alternative "the G/S HMOs are more efficient than the IPA HMOs" supported the alternative hypothesis for 7 of the 20 runs at the 10 percent or less significance levels. The p-values of these seven runs were 0.001035, 0.003170, 0.003462, 0.008008, 0.008671, 0.026102, and 0.041186. Compared with the corresponding results (only 2 runs were significant) from the test that IPAs are more efficient than G/Ss, this result suggests that the G/Ss are more efficient than the IPAs.
These results for the cross-frontier model different from the results found for the societal models, where the IPAs are shown to be more efficient than G/Ss. The reason for this disparity seems to be because of the inclusion of a single G/S unit from Iowa
that is truly "superefficient."14 No other G/S unit comes close, but this single unit can dominate any sample of IPAs and dictates the results in cross-frontier analysis. Moreover, while a few IPAs are most likely overachievers, the fact that we subsampled the IPAs mitigates the effects of a few IPA overachievers (not in all of our random samples); however, we do not subsample the G/S units so the one dominant G/S unit prevails. Rerunning the analysis with this unit removed yields the result that the IPAs dominate the G/Ss from both the consumer and the societal perspectives. In addition, the entire analysis was also run using 1992 data, and the results with the 1992 data also are also consistent with the IPA units being more efficient than the G/S units.
CONCLUDING REMARKS
The current study applied a new game-theoretic DEA model to evaluate the rela- tive overall efficiencies of two principle HMO categories, viz., the less autonomous Staff/Group arrangement and the more autonomous IPA arrangement. The mod- els used here focus on intergroup comparisons of efficiency. Since one's view of what constitutes best performance is conditioned on one's perspective, it is neces- sary to address the question from two perspectives: that of consumers and that of society.
From a societal perspective, the results from both the collective and cross-frontier models suggest that the IPAs are more efficient than the G/Ss. This does not seem surprising given the origins of these plans. IPA physicians typically come from private practice and thus matured in an environment that encouraged patient-doctor contact. These physicians still have greater discretion over the provision of care and thus may elect to see patients they might otherwise be discouraged from seeing in a more regulated, obtrusive, cost-conscious system.
From the consumers' perspective, the results from the collective frontier model also suggest that the IPAs are a more efficient delivery system than Group/Staff arrange- ments. But the results from the cross-frontier model suggest the opposite. However, closer examination of the data indicates that the result of a single G/S unit from Iowa whose data indicates that it is "superefficient." No other G/S unit comes close to per- formance of this unit, and in cross-frontier analysis this unit outperforms all the IPAs. Reanalyzing using the 1992 data, and analysis with this single G/S unit removed does not show this anomaly.
The results of the study should be viewed as a preamble to the debate concern- ing the actual efficiency of HMOs versus traditional insurers since it distinguishes between "efficiency" and "utilization," and focuses the analysis on efficiency. Our initial findings suggest that provider autonomy played a significant role in se- curing greater efficiency within the HMO sector in 1995. This conclusion is es- pecially evident from a societal public-policy perspective and therefore should be of immediate interest to those designing new health care delivery systems in the future.
14 We wonder if the data for this one unit is actually correct (we have serious doubts). This
APPENDIX
Regional Cost Indices and Raw Data
Total Type Premiums GRP 542224342 GRP 80997607 GRP 564582438 GRP 295386651 GRP 166461910 GRP 43047386 GRP 45517996 GRP 69806175 GRP 73031279 GRP 831198526 GRP 325881667 GRP 362887460 GRP 36890270 GRP 721268445 GRP 216185913 STA 550172960 STA 37208483 STA 272502581 STA 58955058 IPA 82419459 IPA 36285155 IPA 820248609 IPA 138496629 IPA 786976380 IPA 172874136 IPA 85290738 IPA 159115910 IPA 520310979 IPA 66407813 IPA 205168499 IPA 279892583 IPA 149690254 IPA 809520412 IPA 209132099 IPA 62805423 IPA 33459506 IPA 204674721 IPA 41174759 IPA 97053991 IPA 52640437 IPA 48396594 IPA 381591362 IPA 329105938 IPA 522873542 Total Expenses 520493660 80878189 546503171 266538066 161068028 40393487 44171589 69423166 71952106 818563205 325439868 363668832 36342439 717922749 217258608 511079208 35159501 266917542 58591315 76876777 36083289 782298708 138596252 760630155 156635118 85649238 158901307 490260935 64635672 201847187 259254837 147665617 780750982 191104397 59161702 30543590 189172150 37838203 87141923 52339358 43967557 353472233 297215235 515264758 Member Months 3695207 543591 1220684 2170309 1185929 315960 304932 551341 495513 5715505 2065932 2248381 302184 4618276 1851643 2644351 351540 1562497 468706 646967 332378 6975097 1024274 3657970 1560666 850173 1523343 3645014 450215 1641589 2211590 1096168 5721186 799287 527304 265425 1476886 276013 735801 489797 387995 3463483 2628712 4387837 Ambulatory Hospital Encounters Days 1698474 81386 227473 12918 585501 22824 932380 34847 519418 22410 197766 15706 509048 21943 218736 9885 148497 11314 4269267 180466 882942 82723 924167 59320 51169 10756 1969138 98866 990175 50427 961780 109055 114058 5497 600729 29859 405540 11037 267934 10826 145261 3983 2590169 161056 494028 30536 1250529 342386 561845 26363 108506 12062 469859 28482 1362633 107614 202736 19281 771229 37678 432169 72335 446198 22903 2451984 157925 361033 54849 96035 15076 55899 4979 628954 36354 111933 7179 395756 17292 225184 9517 177102 7654 306789 69172 1248639 64683 2084223 121226 (continued) Regional Cost Index 1.0753 1.2825 1.1360 1.0326 1.0676 0.9264 0.8770 0.9932 1.1456 1.1176 1.2196 1.0281 1.0323 1.1565 0.9131 1.0744 1.0799 0.9348 0.9974 0.9921 1.0084 1.3325 1.3598 1.3266 1.2877 1.3245 1.0996 1.0547 1.0193 1.2905 1.3109 1.2905 1.0300 1.0797 0.9824 1.1434 1.0376 0.9762 0.8861 0.9100 0.9685 1.0334 1.0490 1.1091
APPENDIX (Continued) Regional
Cost Total Total Member Ambulatory Hospital
Index Type Premiums Expenses Months Encounters Days
1.2042 IPA 704244651 694649303 4581339 1799209 117196 1.2044 IPA 609242386 605831383 3777521 1426271 89131 1.1178 IPA 291819219 277656373 2354885 917980 66811 1.1166 IPA 94434978 87032442 658514 96468 22318 1.1040 IPA 238111707 236726746 1802707 528264 43983 0.9476 IPA 269602153 268657030 2187704 640703 40886 1.1103 IPA 166749980 163510877 1135159 846804 42858 0.9591 IPA 54563360 45982060 375027 132647 9891 0.9841 IPA 37108648 32649703 258666 111550 5409 0.9645 IPA 62754189 62137057 560336 3974822 12853 1.0246 IPA 30579543 30182727 289583 147527 5458 1.0660 IPA 46415874 46314213 316301 121963 3719 1.2013 IPA 171768565 150773557 1228105 654136 24208 1.2164 IPA 234525886 224023226 1251510 1300878 72657 1.2164 IPA 867034277 741948450 6134615 2779471 208217 1.2640 IPA 283115543 273370484 1914824 812371 56306 1.2668 IPA 233341677 234512561 1469007 593710 42623 1.2265 IPA 34448153 29975168 271777 78844 5156 1.2355 IPA 124572182 121783692 816057 210704 20839 0.9350 IPA 38357040 35603717 323257 251535 12149 1.5198 IPA 137075894 135114436 967204 1073847 26100 1.4437 IPA 139313348 135095894 1171843 602428 23592 0.9533 IPA 335025601 334955788 2831232 943365 87558 1.5357 IPA 1081232555 1060166883 7257103 2350076 222057 1.1244 IPA 37797371 34724144 278066 93510 7547 1.5254 IPA 841994204 687551699 6076018 2229833 178441 1.5082 IPA 75426103 70209576 604261 191967 14342 1.4887 IPA 48032972 45209143 334665 131991 7472 1.4667 IPA 59090089 58995348 410880 89255 9561 1.5469 IPA 82122908 74305616 479506 86932 22061 0.9552 IPA 198214069 183731197 1507870 545541 30265 0.9725 IPA 34733607 34214678 284386 121936 7701 1.0184 IPA 75602951 74717610 550701 247144 10745 1.0446 IPA 50433473 49494368 425759 60916 11034 0.9851 IPA 38396792 36791082 290637 89036 10301 1.0236 IPA 87591934 84794530 690411 428080 18360 1.1386 IPA 634315760 630567917 5640548 5623967 176902 1.1252 IPA 73419527 73053093 661898 364101 28057 1.1536 IPA 50792809 50904640 466847 125207 7092 0.8955 IPA 142615992 138953101 1222093 485752 28067 1.0984 IPA 1312067811 1282695758 8904087 4637545 378304 1.1891 IPA 1045082645 1010702012 6825434 2155896 320656 1.1241 IPA 114363354 111610565 848336 378617 26996 (continued)
I
I
APPENDIX
(Continued)
Regional
Cost Total Total Member Ambulatory Hospital
Index Type Premiums Expenses Months Encounters Days
1.0140 IPA 173171138 153411241 1464384 607888 32339 1.1891 IPA 207422231 208040780 1037876 252797 64216 1.1959 IPA 337437604 334428972 2615698 698614 85482 0.9410 IPA 122245729 114847179 1096512 423777 27642 0.8977 IPA 49698304 44539525 407803 213653 7378 0.9870 IPA 46941749 46819683 406787 27652 8915 0.9336 IPA 70771934 68785867 617510 601321 11257 0.9758 IPA 509443995 479990805 3506553 1145084 97127 0.9736 IPA 298641016 294558071 1423248 442367 54715 1.0226 IPA 259761776 247006540 1761341 598855 49490 1.0105 IPA 58718058 55678252 471598 152181 7933 0.9496 IPA 339937843 330304960 2582494 1559055 62591 1.0002 IPA 41340075 37807347 308445 98056 5336 0.9857 IPA 74644403 73107758 636859 276524 11211 1.1352 IPA 162607731 157896873 1490136 469637 24998 1.1900 IPA 72118272 71878276 440580 147829 14851 1.0222 IPA 160367923 160118263 1142840 847381 29784 REFERENCES
Banker, R. D., 1980, A Game Theoretic Approach to Measuring Efficiency, European Journal of Operational Research, 5: 1261-1264.
Banker, R. D., A. Chares, W. W. Cooper, et al., 1989, Constrained Game Formulations and Interpretations for Data Envelopment Analysis, European Journal of Operational Research, 40: 299-308.
Brockett, P. L., and B. Golany, 1996, Using Rank Statistics for Determining Program- matic Efficiency Differences in Data Envelopment Analysis, Management Science, 42(3): 466-472.
Bryce, C., J. Engberg, and D. Wholey, 2000, Comparing the Agreement Among Al- ternative Models in Evaluating HMO Efficiency, Health Services Research, 35(2): 509- 528.
Chang, R. E., 1994, A Constrained Game Theoretic Approach for Evaluating the Perfor- mance of Health Maintenance Organizations, Unpublished Doctoral Dissertation, The University of Texas at Arlington.
Chares, A., W. W. Cooper, and E. Rhodes, 1978, Measuring the Efficiency of Decision- Making Units, European Journal of Operational Research, 2: 429-444.
Chares, A., W. W. Cooper, and E. Rhodes, 1981, Evaluating Program and Manage- rial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through, Management Science, 27(6): 668-697.
Chames, A., W. W. Cooper, Q. L. Wei, et al. 1989, Cone-Ratio Data Envelopment Analysis and Multi-Objective Programming, International Journal of Systems Science, 20: 1099-1118.
Charnes, A., J. J. Rousseau, and J. H. Semple, 1993, An Effective Non-Archimedean Anti-Degeneracy/Cycling Linear Programming Method Especially for Data En- velopment Analysis and Like Models, Annals of Operations Research, 47: 271- 278.
Cooper, W. W., L. M. Seiford, and K. Tone, 1999, Data Envelopment Analysis (Norwell, MA: Kluwer Academic Publishers).
Fudenberg, D., and J. Tirole, 2000, Game Theory (Cambridge, MA: MIT Press). Grosskopf, S., and V. Valdmanis, 1987, Measuring Hospital Performance: A Non-
Parametric Approach, Journal of Health Economics, 6(2): 89-107.
HCIA, 1993, The Guide to the Managed Care Industry (Baltimore, MD: HCIA Inc.). HMO-PPO/Medicare-Medicaid Digest, 2002.
Hombrook, M. C., and S. E. Berki, 1985, Practice Mode and Payment Method: Effects on Use, Costs, Quality, and Access, Medical Care, 23(5): 484-511.
Langwell, K. M., L. Rossiter, R. Brown, et al. 1987, Early Experience of Health Main- tenance Organizations Under Medicare Competition Demonstrations, Health Care Financing Review, 8(3): 37-55.
Luft, H. S., 1981, Health Maintenance Organizations: Dimensions of Performance (New York: Wiley).
Miller, R., and H. Luft, 1997, Does Managed Care Lead to Better or Worse Quality of Care?, Health Affairs, 16(5): 7-25.
Miller, R., and H. Luft, 2002, HMO Plan Performance Update: An Analysis of the Literature, 1997-2001, Health Affairs, 21(4): 63-86.
Roll, Y., W. D. Cook, and B. Golany, 1991, Controlling factor weights in data envelop- ment analysis, HE Transactions, 23: 2-9.
Rosenman, R., K. Siddharthan, and M. Ahem, 1997, Output Efficiency of Health Main- tenance Organizations in Florida, Health Economics, 6: 295-302.
Rousseau, J. J., and J. Semple, 1995, Two-Person Ratio Efficiency Games, Management Science, 41, 3:435-441.
Rousseau, J. J., and J. Semple, 1997, Dominant Competitive Factors for Evaluat- ing Program Efficiency in Grouped Data, Annals of Operations Research, 73: 253- 276.
Saward, E. W., and M. R. Greenlick, 1981, Health Policy and the HMO, in: J. B. McKinlay, ed., Health Maintenance Organizations (Cambridge, MA: The MIT Press, pp. 1-30).
Siegel, S., and N. J. Castellan, Jr., 1988, Nonparametric Statisticsfor the Behavioral Sciences, 2nd edition (New York: McGraw-Hill).
Semple, J., 1997, Constrained Games for Evaluating Organizational Performance, European Journal of Operational Research, 96, 103-112.
Thompson, R. G., F. D. Singleton, R. M. Thrall, et al., 1986, Comparative Site Eval- uations for Locating a High Energy Physics Laboratory in Texas, Interfaces, 16: 35-49.
U.S. Department of Health, Education and Welfare, 1971, Toward a Comprehensive Health Policyfor the 1970s: A White Paper (Washington, D.C.: U.S. Government Print- ing Office).
von Neumann, J., 1928, Zur Theorie der Gesellschaftsspiele, Mathematische Annalen, 100: 295-320.
von Neumann, J., and 0. Morgenstern, 1944, Theory of Games and Economic Behavior, 1st edition (Princeton, NJ: Princeton University Press).
Weiner, J. P., and G. de Lissovoy, 1993, A Taxonomy for Managed Care and Health Insurance Plans, Journal of Health Politics, Policy and Law, 18(1): 75-103.
