# Measuring differences and similarities in hospital caseloads: a conceptual and empirical analysis.

In 1983, Medicare began implementing a new payment system for hospitals. Reimbursement was no longer based on the actual costs the hospital incurred to treat a patient; instead, rates were determined per case from historical national average costs within the patient's diagnosis-related group (DRG). Because Medicare was paying them on a fixed rate per patient, hospitals could no longer be financially indifferent to interhospital rivalry. While hospitals receiving cost-based reimbursement had not needed to worry about maintaining a high occupancy rate to cover their sizable fixed costs, under prospective payment they had to compete for patients or see payments fall accordingly.Thus, the introduction of prospective payment engendered unprecedented competition among hospitals for patients. This has placed a premium on projecting a positive community image and establishing a good reputation to attract patients. The technologies and services a hospital offers are highly visible within the community and, given the difficulties of assessing hospital care, are likely to be viewed as indicators of quality. Hence, competition may lead hospitals to diversify into new services to enhance their reputations.

This diversification of hospitals into new services can have two negative effects. First, outcomes research reveals that larger hospital volumes are associated with superior outcomes for some procedures and illnesses (Luft et al. 1990). This makes the concentration of a procedure within one hospital desirable, as volumes can be expected to decrease as more hospitals offer a service, fragmenting the market. Thus, from this viewpoint, having hospitals with very different caseloads, each concentrating on particular illnesses or procedures, would be desirable. Second, to the extent that there are economies of scale in hospital production, costs could be reduced by having each hospital produce a small number of products in large quantity. This would reduce underutilized capacity and the associated costs of having equipment, units, or personnel sitting idle. Again, this would lead to hospitals with very different case mixes. Recent evidence (Woods, Saywell, Nyhuis, et al. 1992) also indicates that costs may decrease when very sophisticated cases are concentrated in one hospital, fully exploiting the learning curve.

Supporters of market competition among hospitals would argue that such regionalization will eventually result from their policies. While in the short run competition may lead to hospitals diversifying into new services, economic theory would predict that competition and price incentives eventually will lead hospitals to reduce the services they offer. Hospitals will concentrate on services for which they have a comparative advantage, and will reduce or eliminate other services that their competitors can provide more efficiently. Thus, the argument goes, the competitive environment will lead to this type of regionalization.

From a policy viewpoint it seems critical to develop measures that can document the extent to which hospitals are diversifying and markets are becoming regionalized. If the competitive market strategy is, in fact, leading to increased diversification rather than regionalization, then this policy should be reassessed. Other policies such as regulatory planning (certificate of need) or selective contracting could be reconsidered.

Unfortunately, developing measures of diversification and regionalization is difficult because of the vast number of different outputs that a hospital can produce and the vast number of combinations in which these outputs can be produced. A review of the literature reveals that even deciding on a terminology for discussing differences and similarities in hospital caseloads is difficult. Authors customarily refer to hospitals as being "specialized," although hospital "differentiation" or "diversification" are occasionally discussed. Unfortunately, there seems to be no standardized usage of these terms.

This article evaluates several measures that have been used to distinguish among hospital caseloads and introduces two alternative measures. The sensitivity of these measures to differences in hospital characteristics is analyzed using multivariate regression analysis. We also examine one market in greater detail to show how caseload differences are reflected in the index measures.

To determine the extent of duplication of services, or the extent to which hospitals have become more "specialized" over time, it is necessary to develop some measures with which to compare caseloads. The second section of this article is a critique of four measures that have been used in the literature. We then describe the measures used in this article and present a case study employing these measures for one market area. Next, national descriptive analysis is presented. We then utilize five alternative measures of hospital differentiation as the dependent variables in regression analysis to determine the sensitivity of these measures to hospital characteristics, and to examine the extent to which these measures may lead to different conclusions. Our final section presents a brief conclusion to the article.

DEFINING DIFFERENTIATION

MEASURES OF HOSPITAL CASELOADS

Measures of hospital caseloads can be divided into two basic categories: (1) those based on the services offered by the hospital and (2) those based on the case mix of patients treated. Methods utilizing the presence of facilities or equipment may be more consistent with the manner in which hospitals consider expanding. Rather than deciding to treat a certain type of illness, the hospital decides whether to buy the equipment, hire the personnel, or open the facility needed to offer a particular service.

However, these types of service measures have two drawbacks. First, they indicate only whether the service is present or not; the measures give no idea of intensity of usage or volume. Second, these measures either fail to provide an index measure, or they provide an index that is not reliable. For example, Luft, Robinson, Garnick, et al. (1986) use the presence (or absence) of 29 services to study differences among hospitals. Luft provides no index measure; instead he examines each service individually. Ranking methods such as the Guttman Scale Index (Edwards, Miller, and Schumacher 1972) and Berry Groupings (Berry 1973) yield index values based on the most complex service(s) a hospital offers. For example, a Guttman Index of 18 indicates that a hospital offers open heart surgery (service 18) but does not have an organ bank (service 19). It is assumed that services are always added in identical order, and that the hospital offers all "simpler" services with index values 1 through 17. However, Edwards finds that this assumption is violated for 13 percent of the general and acute care hospitals in her sample. This limits the analytic uses of the measure since hospitals with the same index value may offer drastically different combinations of services.

Examining the illnesses treated is an alternative method of comparing hospital caseloads. Measures based on cases treated, rather than services provided, can capture more of the differentiation among hospital caseloads since a given service, such as radiology or open heart surgery, (1) may be used to treat many different types of patients and (2) may be used with differing levels of frequency. This type of measure has been found in previous literature; we now discuss six measures of hospital caseloads based on illness treated, as measured by DRGs.

INFORMATION THEORY INDEX

Farley (1989) and Farley and Hogan (1990) calculate an information theory index (ITI) as discussed by Theil (1967) that measures hospital "specialization":

IT|I.sub.h~ = |Sigma~/1 = 1 (|N.sub.ih~/|N.sub.h~) * ln|(|N.sub.ih~/|N.sub.h~)/||Theta~.sub.i~~

where

|N.sub.ih~ = cases of DR|G.sub.i~ treated in |hospital.sub.h~;

|N.sub.h~ = number of discharges in |hospital.sub.h~;

||Theta~.sub.i~ = cases of DR|G.sub.i~ in the United States/total cases in the United States;

and

ln||center dot~~ = natural log of relative hospital caseloads.

Thus, the index is a weighted log of hospital DRG proportions compared to national DRG proportions. DRGs more commonly treated in the hospital are weighted more heavily than less common DRGs. The resulting index number is equal to zero if no specialization occurs (if the hospital proportions equal the national proportions for all DRGs), and increases as the level of specialization becomes greater (as the hospital proportions diverge more from the national proportions).

Thus, the ITI measures a hospital as more "specialized" as its caseload deviates more from that of the typical hospital. Therefore, hospitals that treat either a very narrow or a very broad range of cases will tend to have relatively high index values: an unsophisticated hospital treating only the simplest cases and offering few services could have the same index value as a tertiary care hospital. A serious drawback of the ITI is its inability to distinguish between these two types of "specialization."

Further, the integer nature of admissions means that the index is biased upward, and this bias can be especially significant for small hospitals. For example, if the national proportion of cases in DR|G.sub.i~ is 3.5 percent, the ITI for a hospital treating 100 patients will always indicate some specialization. The integer nature of admissions makes it impossible for the hospital proportions to equal the national proportions. Other measures that rely on caseload proportions will suffer from a similar bias. Farley and Hogan (1990) discuss the nature of this bias at length and describe several procedures for evaluating the expected value of the ITI. For regression analysis, they suggest including the inverse of the number of discharges as an additional independent variable to correct for this bias.

STATISTICAL MEASURE OF DISTANCE

Zwanziger, Melnick, and Rahman (1990) calculate a distance measure:

|Mathematical Expression Omitted~

where |P.sub.ih~ is the proportion of total discharges from the hospital in a DRG cluster, and |Mathematical Expression Omitted~ is the average proportion of discharges from a cluster across all hospitals competing with the given hospital. Zwanziger, Melnick, and Rahman base their measure on 48 DRG clusters that they define by the complexity of treatment and physician specialty; however, interpretation of the measure is similar if it is constructed at the DRG level.

The distance measure is conceptually very similar to Farley's measure of "specialization" in that it compares a hospital's DRG proportions to those of an "average" hospital. Like the ITI, the distance measure has a lower bound of zero. This measure differs from the ITI in that it weights all clusters equally. It would seem desirable to weight the clusters by some measure of relative frequency. Otherwise, relatively rare diagnoses that may account for only a few cases count as heavily in the index as diagnoses that comprise hundreds of cases.

INTERNAL HERFINDAHL INDEX

Zwanziger, Melnick, and Rahman (1990) also construct an internal Herfindahl index as the sum of the squares of the discharges from a DRG cluster viewed as a proportion of all discharges from the hospital. This measure is analogous to the Herfindahl index used to measure market concentration; however, in this application it measures the concentration of cases within a hospital. A hospital with all of its discharges in one DRG cluster would have a value of one. The lower bound is determined by the number of DRG clusters used in the analysis. For example, 52 clusters would mean the smallest value of the internal Herfindahl index would be (1/52). As the number of clusters increases, this lower bound approaches zero.

This measure is conceptually much different than the indexes discussed earlier. While both the ITI and the distance measure compare a hospital's caseload to that of an "average" hospital, the internal Herfindahl is based solely on the hospital's own caseload. While an average hospital would have the minimum possible ITI or distance value (zero), its Herfindahl would be neither at the minimum nor the maximum.

DYNAMIC MARKET SHARE

Dranove and White (1989) designate a hospital as specializing in a DRG "if there is a persistent increase |emphasis added~ in its market share for this DRG above its initial average market share for all DRGs". Thus, this is a dynamic concept of specialization.

This definition allows a hospital to specialize in all DRGs at once if its overall market share rises. Thus, it seems to confound "specialization" with growth. It would seem desirable in a dynamic model to deflate DRG growth by growth or shrinkage of the hospital's total market share to relative growth in the DRG caseload.

ALTERNATIVE MEASURES

This article also uses two measures of hospital caseloads that have not been utilized elsewhere. Unlike the complex measures just discussed, both of these measures have the advantage of being easily understood and interpreted. Thus, if our measures are highly correlated with the more complicated indexes, they will serve as readily interpreted proxies capturing the same distinctions among caseloads. Alternatively, our measures may be preferable if they are more sensitive indicators of distinctions among hospitals' caseloads. For example, a measure that differentiates the caseloads of major teaching hospitals from those of nonteaching hospitals will have applications beyond those of a measure that makes no such distinction.

Our first new measure is the number of distinct DRGs in which the hospital treats any cases. Unlike the internal Herfindahl, it is a linear measure. Thus, one case in a rare DRG has a large effect relative to the effect it would have on the internal Herfindahl. The weight on this DRG in the count of DRGs is 1/N where N is the number of DRGs treated; the weight in the internal Herfindahl would be 1/C, the number of cases treated. This lack of weighting may be an undesirable property. It can lead to two hospitals with similar caseloads having very different DRG counts if one hospital treats a single case in many DRGs. This simple measure is particularly successful, however, at distinguishing tertiary care hospitals (which treat many DRGs) from less sophisticated hospitals (which treat fewer). By comparison, the more sophisticated ITI is limited in its ability to make this type distinction.

A second easily calculated measure is the percentage of a hospital's cases in the five most common Medicare DRGs. For 1987 these DRGs were DRG 14 -- Specific Cerebrovascular Disorders except TIA (306,929 discharges nationally); DRG 89 -- Simple Pneumonia & Pleurisy, Age |is greater than~ 17, with CC (321,844 cases); DRG 127 -- Heart Failure and Shock (490,539 cases); DRG 140 -- Angina Pectoris (350,340 cases); and DRG 182 -- Esophagitis, Gastroenteritis, & Miscellaneous Digestive Disorders, Age |is greater than~ 17, with CC (263,743 cases). Hospitals treating a higher percentage of patients in the common DRGs, by definition, treat a lower percentage of cases in other DRGs. While this measure incorporates no data on the remainder of the case mix, a low percentage of patients in other DRGs would be indicative of fewer services being offered (or utilized) at the hospital.

PROPOSED TERMINOLOGY

As shown, researchers have used many measures to compare similarities and differences among hospital caseloads. This profusion of measures is not surprising since the concept of differentiation is poorly defined among multiproduct firms, and since researchers have addressed different questions, making the use of different indexes appropriate in many instances. One could refer to the degree to which a hospital's products are differentiated from each other. For example, how many DRGs does a hospital treat? Are they similar or do they require very different types of inputs for treatment? Alternatively, differentiation could look for similarities between each hospital's output mix and that produced in the market. For example, is any other hospital treating the same DRG? A third type of differentiation would examine the extent to which different hospitals treat the same illnesses in the same proportions. For example, does any other hospital treat this same caseload?

Different researchers have used terms such as "specialized" to refer to many different types of hospitals. For example, one will argue that a teaching hospital is specialized because it treats an unusual case mix including many complicated and uncommon cases. Another will argue that a teaching hospital is not specialized because it treats so many types of cases -- that an eye and ear hospital is specialized because it treats a very narrow range of cases. To simplify our discussion, we propose the following terminology to be used through the remainder of this article.

Diversification is used in economic industrial organization theory to describe the number of types of outputs a firm produces. Use of the term diversification to describe the number of different DRGs treated in a hospital (or services offered) is consistent with the usual usage in describing a multiproduct firm.

Specialization is used to compare the similarity between a hospital's caseload and a "typical" caseload. Thus, our use of the term is narrower than the use often employed. As a hospital's caseload deviates more from that of the typical hospital, it is considered to be more specialized.

Differentiation will be used broadly to describe any measure of specialization or diversification.

Given these definitions, small hospitals treating only the most routine cases will not be very diverse; those offering more complex services will be more diverse. A specialized hospital could be (a) a small hospital treating only the most routine cases, (b) a tertiary care hospital treating many of the most difficult and unusual cases, or (c) a hospital treating primarily one type of illness, such as a psychiatric or rehabilitation hospital.

MEASURES USED IN THIS ARTICLE

Different researchers, using different data sets for their hospital caseload statistics, have constructed and analyzed differentiation measures such as those discussed in the previous sections. It is difficult to compare the conclusions of these studies since differing results may be caused by either geographic or temporal differences in caseloads or by the unique features of the differentiation measures employed. To allow direct comparisons of the differentiation measures, we construct five measures using the same data. Our five measures of hospital caseloads are

* An information theory index in which hospital proportions of DRG cases are compared to national proportions;

* An information theory index in which the market proportions of DRG cases are used as the denominator: the properties of this index are analogous to those of the index based on national proportions. The market ITI may be of interest since it is comparing hospitals not to a national average caseload but to other hospitals in the particular area. Thus, area-specific differences in discharges caused by differences in epidemiology or treatment patterns will not be counted as specialization using the market ITI, while they are counted as such by the national ITI;

* An internal Herfindahl index, calculated at the DRG level: thus, this measure differs from that used by Zwanziger, Melnick, and Rahman (1990) in that it is calculated over 470 DRGs rather than across DRG clusters. We use the less aggregated components to make the index measure consistent with our other measures, which are all defined at the DRG level;

* The number of different DRGs in which the hospital treats any cases; and

* The percentage of the hospital's Medicare cases accounted for by the five most frequent DRGs nationally.

Descriptive and regression analysis then compares the ability of these different measures to distinguish hospital caseloads.

DATA

The primary source of data for this study is the Medpar Medicare claims data for 1987, which provide a 100 percent sample of Part A Medicare discharges during calendar year 1987. Claims paid under prospective payment were aggregated into a matrix showing the number of cases in each DRG treated by each provider. Cases in DRGs 471-475 were apportioned to their corresponding original DRGs. We then identified the market in which each hospital was located. Markets were defined as all metropolitan statistical areas (MSAs) or, in New England, New England County Metropolitan Areas (NECMAs), and all remaining rural areas within each state. American Hospital Association (AHA) data were used to provide descriptive information on hospitals. The Area Resource File (ARF) was used to provide demographic information on hospital markets. The resulting file containing 5,403 hospitals constitutes 95 percent of the hospitals in the Medpar sample. The hospitals missing from our data because they could not be merged to AHA data were dispersed across states and tended to have very low numbers of Medicare discharges.

CASE STUDY

To illustrate the extent to which the five index measures reflect similarities and differences in caseloads, we present DRG level data and index measures for one market, the San Francisco metropolitan area, in Table 1. San Francisco offers an interesting case study since it is a geographically compact MSA, with a high degree of competition among neighboring hospitals (Luft, Garnick, Mark, et al. 1990). To simplify comparisons, we present statistics for 13 representative hospitals out of the 27 in the MSA (which includes San Francisco and neighboring San Mateo and Marin counties). Hospitals are arrayed by number of Medicare discharges (ranging from 75 for hospital 1 to 4,668 for hospital 13). Thus, if the proportion of cases treated in each hospital is constant, the number of cases in any row will always increase as the table is read from left to right.

The nine DRG clusters presented serve as indicators of whether or not a hospital offered a service, and the extent to which it emphasized the service. The first two clusters are two of the five most common DRGs, heart failure and shock (DRG 127) and simple pneumonia (DRG 89), and can be treated in virtually all hospitals. The next group of four clusters (major orthopedics, transurethral procedures, psychoses, TABULAR DATA OMITTED and vascular surgery) are cases treated in all but the smallest hospitals, and represent four different services found in the hospitals. The final three clusters (craniotomy, cardiac surgery, and kidney transplant) are generally found only in relatively large, sophisticated hospitals. The hospitals' values for each of five differentiation measures used are presented below the Medicare volumes data.

The total number of discharges is a very strong determinant for four of the index measures. The national and market ITI, as well as the internal Herfindahl index, are inversely related to size, while the number of different DRGs is positively related to size. In this sample of hospitals, the relationship between the five most common DRGs and size is not nearly as obvious.

To examine how well the indexes distinguish caseload differences beyond differences in total discharges, we focus on four hospitals with unusual patterns of DRG clusters. Hospital 1 treats no patients in any of our categories, including the most common DRGs. Twenty-five percent of the patients in hospital 3 are being treated for psychoses, far more than in any other hospital. Hospital 7 is a midsized hospital where an unusually large number of craniotomies are performed. Hospital 7 is one of the four Kaiser hospitals in San Francisco (along with hospitals 6, 8, and 10); Kaiser appears to have concentrated some services rather than having all hospitals fully diversified. Hospital 13 is the University of California at San Francisco Hospital, a major teaching hospital. It treats relatively low numbers of the very common cases, but very large numbers of cases in two of the most concentrated clusters, craniotomy (164 cases) and kidney transplant (144 cases).

In each instance, the ITI for our "atypical" hospitals is substantially higher than for other hospitals of similar sizes. For example, the national ITI for hospital 3 is 1.24 while the ITI for hospital 4, having a much more typical caseload, is only 0.39. Although the distinctions are generally somewhat smaller, the market ITIs for the atypical hospitals are also larger than for similar-size counterparts.

The internal Herfindahl index is also able to differentiate hospitals with very atypical caseloads. For instance, the internal Herfindahl for hospital 3 is .073, while for hospital 4 it is only .024. The weakness of this index may be its inability to distinguish among hospitals with more typical caseloads. The amount of variation in the internal Herfindahl for, say, hospitals 8, 9, and 10, is much less than in the other indexes.

The number of different DRGs treated is very strongly related to the number of discharges. For this sample, it does not appear to be sensitive to differences in caseloads; values for hospitals with similar numbers of discharges indicate that they are treating similar numbers of DRGs.

The percentage of cases in the five most common DRGs strongly reflects the specialization of hospitals 1 (0 percent) and 13 (5.8 percent). Our other atypical hospitals, and the larger hospitals, also tend to have lower values for this index, indicating less reliance on these common cases.

It is also interesting to note that some of the most complex, high-technology procedures are not concentrated in a single hospital. For example, rather than having one hospital that specializes in kidney transplants, the San Francisco market contains two hospitals performing these operations. Similarly, one might expect cardiac surgery to be heavily concentrated in a few hospitals that specialize in these procedures. Instead, eight hospitals in San Francisco perform these procedures with Medicare volumes ranging from 23 to 265 (not shown). This competition for complex cases is not unique to San Francisco. For example, in 1987, 28 MSAs contained six or more hospitals performing CABG (coronary artery bypass graft) surgery on Medicare patients (Dayhoff and Cromwell 1992).

NATIONAL DESCRIPTIVE ANALYSIS

Table 2 presents mean values for each differentiation measure using the following breakdowns: census regions, urban/rural status, and bed-size categories. Comparison of the nationally based ITI and the market-based ITI values reveal that for every breakdown the market-based mean is lower than the nationally based mean. This reflects the fact that part of the differences observed in the patients treated stems from differences across markets, not across hospitals within a market. For example, the mean rural value is .66 for the national ITI but .52 for the market ITI, indicating less "specialization" or deviation from the average. This implies that hospitals resemble their local competitors more closely than they resemble a national "average" hospital. This result is not surprising given market level differences in the demand for services and characteristics in treatment patterns.

Since the information theory index is greater for hospitals that deviate more from the average, the very large or very small hospitals should have higher values than those of average bed size -- and presumably average case mix. This pattern is observed, both for the rural and the urban bed-size categories. Both the national and market ITI initially TABULAR DATA OMITTED fall as bed-size increases; then for the largest size category they rise again.

The mean value for the proportion of a hospital's patients treated for the five most common DRGs is 21.8 percent, meaning that over one-fifth of the average hospital's patients receive treatment for one of these five DRGs. The lower mean values in the Northeast and West regions are statistically different than those in the Midwest and South. This could be caused by the higher proportion of small, rural hospitals in the Midwest and the South. Urban hospitals have a lower percentage of cases in the five DRGs than do rural hospitals. This distinction is maintained when comparing urban and rural hospitals of roughly the same bed size, although the differential is diminished. For both the urban and rural bed-size categories, the prevalence of the five DRGs is inversely related to bed size. For example, these five DRGs constitute 22.1 percent of the Medicare cases in the smallest urban hospitals, 18.3 percent of the Medicare cases in urban hospitals with 200-299 beds, and 13.5 percent of the Medicare cases in urban hospitals with more than 504 beds. This monotonic relationship is consistent with the theory that as bed size increases, more services are offered by a hospital, and the "common" DRGs therefore become a smaller share of total cases treated.

The number of different DRGs treated in each hospital has a mean value of 184, while 10 percent of all hospitals treat fewer than 67 DRGs and 10 percent of all hospitals treat more than 312 DRGs (not shown). The mean value for the Northeast is substantially higher than for other regions, probably as a result of its higher proportion of large urban hospitals. Urban hospitals clearly tend to be more diversified than rural hospitals; on average an urban hospital treats 70 percent more DRGs than does a rural hospital. However, this difference is apparently a function of the difference in mean bed size for urban and rural areas. Comparing rural and urban hospitals with similar bed sizes reveals similar mean values. For example, 100-169-bed rural hospitals treat an average of 214 DRGs, while 100-199-bed urban hospitals treat an average of 208 DRGs.

The internal Herfindahl has a mean value of .033 -- this would be the equivalent of a hospital treating an equal number of cases in 30 DRGs. Unlike the other measures, the mean values of the internal Herfindahl are virtually identical for urban and rural hospitals, with values of .033 and .032, respectively. Also, unlike the other measures, the mean values by bed size show no apparent pattern. These surprising results are probably due to the fact that the index is good at discriminating differences in proportions among the top several DRG categories but not differences among the distribution across many small categories. This arises from the use of squared percentages, which tends to ignore all but the largest values.

Table 3 presents correlations for the five index measures. The correlation between the national ITI and market ITI is quite high at .93, as expected. The relatively high correlations between the internal Herfindahl and the ITI measures (.75 and .60) are somewhat surprising, given the differences in the patterns of mean values seen earlier. The ITI values are negatively correlated with the number of DRGs treated. The exceptionally high ITI values for very small hospitals no doubt weigh heavily in this relationship. The index measure with the overall weakest correlation to other indexes is the percent of cases in the five most common DRGs. This index seems to be measuring some attribute of hospital caseloads that differs from the attributes measured by the other indexes.

TABULAR DATA OMITTED

REGRESSION RESULTS

Regression analysis was performed using each of these five alternative measures of differentiation as the dependent variable. The independent variables include both hospital and market characteristics. One variable, the inverse of the number of Medicare discharges, comes from the Medpar file. This variable was included to correct for the bias present in the information theory index (Farley and Hogan 1990). We include the variable in all regressions to facilitate comparisons of results using the multiple differentiation measures.

Regression analysis is customarily used to determine the effect of each of the independent variables on the dependent variable. Thus, our regressions indicate the effect of hospital and market characteristics on our differentiation measures -- indicating, for example, whether teaching hospitals are differentiated from nonteaching hospitals. However, since our focus is on evaluating alternative measures of hospital caseloads, a different interpretation may be more useful. Given the known differences between teaching and nonteaching hospitals, the coefficient on this variable can be interpreted as indicating the sensitivity of the dependent variable to differences associated with this independent variable. Thus, a regression with no significant coefficients would be interpreted as indicating that the differentiation measure was insensitive to caseload differences associated with our hospital and market characteristics, not as indicating that no caseload differences existed.

Comparisons of the effects of the independent variables in the different regressions can be made using standardized (i.e., normalized) regression coefficients, which can be compared directly. The regressions are based on a sample of 2,861 urban hospitals.

Table 4 reports standardized regression coefficients. Reading down a column indicates which variables have the greatest relative effect in each regression. For example, in the national ITI column the inverse discharges variable has a coefficient of .537. This means that a change of one standard deviation in the inverse of discharges would correspond to slightly over a one-half standard-deviation change in the ITI.

The most striking result of this analysis seems to be that size is a very important factor affecting differentiation among hospitals, even holding the number of Medicare discharges constant.(1) The five independent variables that have the largest coefficients in each equation are underlined in Table 4. The bed-size dummy variables have four of the five largest coefficients in four of these regressions. The exception is the regression with the percentage of common DRGs as the dependent variable: here bed-size variables have two of the four largest coefficients.

TABULAR DATA OMITTED

Table 4 also allows comparisons along rows that indicate the relative importance of a given independent variable in each of the regressions. Opposite coefficient signs across a row do not necessarily indicate a conflict. For example, the coefficient for a major teaching hospital is .043 in the national ITI regression and -.175 in the regression for percent of the five most common DRGs. The first coefficient indicates that teaching hospitals have caseloads that are atypical, ceteris paribus. The second indicates that teaching hospitals also treat a relatively small percentage of cases in the most common DRGs. These relationships are consistent, not contradictory. In fact, none of the significant coefficients indicates contradictory relationships.

A second important result is that the sensitivity of the dependent variable to hospital characteristics (other than bed size) and area characteristics varies greatly depending on the measure of differentiation. For example, the internal Herfindahl index has the largest R-squared value of the five regressions, and is very sensitive to variations in discharges and bed size. However, characteristics such as major teaching status and ownership are not significantly related to variations in this measure.

Row comparisons reveal that ownership is more important for determining the percentage of common DRGs and the number of DRGs treated than for determining the other differentiation measures, although the effects of ownership are much smaller than the effects of size. Government hospitals, for example, treat more cases in the common DRGs and also treat a relatively small number of different DRGs, holding bed size, and so forth, constant.

The percentage of cases in the five most common DRGs seems to be the most sensitive indicator of a teaching hospital. The coefficients on major teaching (-.175) and minor teaching (-.151) are the largest in their respective rows, indicating that teaching hospitals treat a much lower proportion of cases in the five most common DRGs. Teaching hospitals treat a diverse, difficult case mix, which implies that the simpler, common DRGs are less predominant there than for other hospitals.

CONCLUSION

Prior to the 1980s, regulation, such as certificate of need, was relied on to prevent wasteful duplication of hospital services. During and since the 1980s, with prospective payment in place, much greater reliance has been put on market forces to produce a desirable, efficient allocation of cases. Economic theory predicts that competition and price incentives eventually should lead hospitals to reduce the services they offer. Hospitals would offer services they could provide efficiently and would eliminate services for which their competition had a comparative advantage. The extent to which prospective payment has encouraged desirable specialization is an important issue for policymakers. If specialization is not occurring, policymakers may want to reconsider regulation, or encourage selective contracting with hospitals to force specialization in the market.

Using an information theory index Farley and Hogan (1990) found that hospitals became more specialized from 1980 to 1985. This case-mix specialization corresponded to an estimated savings of more than $1 billion per year across the industry. Our work indicates that this measure of specialization is generally positively correlated with other caseload indexes. However, the other indexes may be more sensitive to some aspects of a hospital's case mix or to differences associated with hospital characteristics, such as teaching status. Thus, replication of this work using other indexes could verify the increase in specialization, and might provide a clearer picture of market or hospital characteristics associated with changing caseloads.

NOTE

1. The inverse of the number of Medicare discharges was included in the information theory index regressions to correct for bias. It was included in the other regressions for comparability; to the extent that these measures incur bias from the use of proportions, it may correct there also. Regressions run without this variable yield similar coefficients on the remaining variables. The table presented here shows coefficients on the bed-size variables for two caseload measures to illustrate the effects of excluding the inverse of discharges variable from the regression. The bed-size coefficients are significant at the 1 percent level in all cases, and exclusion of the discharge variable has small effects on the magnitude of the coefficients.

TABULAR DATA OMITTED

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Author: | Dayhoff, Debra A.; Cromwell, Jerry |
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Publication: | Health Services Research |

Date: | Aug 1, 1993 |

Words: | 6379 |

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