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Journal of Clinical Oncology, Vol 25, No 15 (May 20), 2007: pp. 2117-2121 © 2007 American Society of Clinical Oncology. DOI: 10.1200/JCO.2006.09.3336
Aggregating and Partitioning Populations in Health Care Disparities Research: Differences in Perspective
From the Center for Health Equity Research and Promotion, Philadelphia Veterans Affairs Medical Center; Leonard Davis Institute of Health Economics, University of Pennsylvania; and the Division of General Internal Medicine, University of Pennsylvania School of Medicine, Philadelphia, PA Address reprint requests to David A. Asch, MD, Leonard Davis Institute of Health Economics, 3641 Locust Walk, Philadelphia, PA 19104-6218; e-mail: asch{at}wharton.upenn.edu
Health and health care are distributed unevenly across individuals and populations, and identifying these disparities is the first step toward remedying them. We reveal how conceptual and statistical challenges make even the identification of disparities difficult. These difficulties arise because the social, biologic, and environmental causes of disparities are intertwined, leading to statistical confounding. These difficulties arise also because the same data can be analyzed to examine care from the perspective of the patient, or from the perspective of organizations such as health systems or jurisdictions, and these alternative perspectives can yield contradictory results. The result is that health care disparities can be challenging to interpret unless the analytic and policy perspective is clear.
Considerable current research aims to identify, understand, and remediate disparities in health and health care.1,2 Disparities are common, and although they may be challenging to understand and even harder to fix, finding them does not seem to require complex techniques. In examining the delivery of health services across different racial or social groups, one often finds large differences, just as one often finds that certain groups of people are healthier or live longer than others. Given the importance of these problems in health and health care, it is not surprising that those who study population health or the delivery of health care services increasingly partition their data along racial or social lines to make comparisons relevant to this important social cause. In this article, we discuss how eagerness to identify racial disparities can rush us to partition data by race and produce misleading results. The problems that can arise do so in part because of the well-understood pitfalls of statistical confounding, and also because analytic perspectives based alternatively on current patients, future patients, or health systems or jurisdictions answer different questions that may only appear similar. We make these points using a simple set of data and analyzing it a few different ways.
A recent study of the management of localized prostate cancer in two affiliated Philadelphia hospitals revealed that 65 (50%) of 131 white patients with prostate cancer underwent prostatectomy compared with 29 (32%) of 91 black patients. These results appear to reveal a difference in the health care services received by white and black patients for the same condition. Given that the best management for prostate cancer is unclear, the results do not indicate whether white patients are advantaged or disadvantaged compared with black patients. But when the overall data are examined at the level of the two individual hospitals, what appeared at first to be a large health care disparity seems to vanish. As shown in Table 1, approximately 58% of patients at the university hospital underwent prostatectomy, and approximately 28% of patients at the affiliated Veterans Affairs (VA) hospital underwent prostatectomy. In each hospital, the rates are the same whether the patients are white or black.
These results are interesting in part because the two hospitals are adjacent and share staff urologists and urology residents. The results are also interesting because the seemingly large racial difference in prostatectomy rates seen when patients from the two hospitals are combined disappears when patients from the two hospitals are examined separately. How can such a disparity be observed when the data are viewed in aggregate, but not when the data are viewed in each of the individual hospitals that compose that aggregate?
These results reflect Simpson's Paradox, in which aggregated data yield one conclusion but the same data, when partitioned, yield another.3 A famous example of Simpson's paradox involves claims of sex discrimination in graduate admissions to the University of California at Berkeley. Men applying for graduate positions were more likely to be accepted than women (44% v 35%) and yet women were favored in the 85 departments where admissions decisions were made.4 So, for example, imagine that one of five men and two of eight women applying for a position in history are accepted and six of eight men and four of five women applying for a position in geography are accepted. Within each department, women do better than men, because 1/5 is less than 2/8 and 6/8 is less than 4/5. Yet overall, seven of 13 men receive positions and only six of 13 women.5 The reversal results because positions in history are harder to get than positions in geography. Women are more successful at both, but they seek out the harder positions more than the men do. The same phenomenon explains the paradoxical results in prostate cancer treatment in Philadelphia. White and black patients are equally likely to undergo prostatectomy in each individual hospital, but black patients are more likely to receive care in the VA hospital, where prostatectomies are harder to get. In other words, the apparent difference in prostate cancer treatment across races is confounded by site of care. We observe a much higher prostatectomy rate among white patients in aggregate because they are disproportionately represented in the university hospital, where all patients are more likely to receive prostatectomy. The narrow point that observations about care may be confounded by site is not new. For example, an enlarging literature demonstrates that observed disparities in cardiovascular care and outcomes are explained better by location than race,6,7 and the same phenomenon is observed for other conditions as well.8 What may be less appreciated is just how large these effects can be.
Among the general lessons of Simpson's paradox is that partitions of data can at times support conclusions contradictory to those of the data as a whole. This general lesson leads to at least two questions related to this specific example. First, do these results reveal a health care disparity or not?9 The answer might seem to be not. Within each hospital, there is no difference in prostatectomy rates between blacks and whites, assuming that the black and white patients are otherwise similar in clinical characteristics and preferences for care. This finding suggests that the systems or clinicians in these hospitals do not make distinctions according to race. Nevertheless, the results suggest a disparity in patient allocation to hospital. White patients (who may, on average, have more resources) may end up in hospitals where physicians have financial incentives to increase services, and black patients may end up in hospitals where physicians do not. Given that we do not know whether prostatectomy is good or bad in this setting, it is not clear whether this disparity disadvantages the white patients or the black patients. But there is a disparity; it is not likely to be the result physicians' racial prejudices; and it might have been missed completely had we not examined the data in both their aggregated and partitioned forms. And that leads to the second question. Simpson's paradox can be observed when data are partitioned into subpopulations, such as patients seen in two different hospitals. But all data sets can be imagined as subpopulations of larger data sets that might have been collected. We examined prostatectomy rates in Philadelphia, but those data might have been part of a larger study encompassing all of Pennsylvania. If our interpretation of racial differences in prostatectomy rates of two hospitals in Philadelphia changes when we combine the data from both hospitals, might our interpretation of the prostatectomy rates in Philadelphia change when combined with data from the remainder of the state?
To approach this question, we imagined some data about prostatectomy rates in Pennsylvania—data that might have been collected from the university and VA hospitals in Pennsylvania, but outside Philadelphia. (We are ignoring the other hospitals in Pennsylvania here.) Although we fabricated the non-Philadelphia data, we did so in plausible ways. We assumed that in the remainder of the state there would be more patients, a smaller percentage of them would be black, and that overall prostatectomy rates might be half those seen in the urologist concentrated city of Philadelphia. These fabricated data are shown in Table 2, along with the real data from Philadelphia previously reported in Table 1.
The non-Philadelphia data reveal the same paradox as the Philadelphia data. Prostatectomy rates are similar across white and black patients in each of the two hospital types, but when the patients from the two hospital types are combined, whites appear to receive prostatectomy more often than blacks. More striking is that when we examine Pennsylvania as a whole, by combining the data from Philadelphia with the data from the remainder of the state, we find no difference in prostatectomy rates for white and black patients: approximately 25% of white and black patients undergo prostatectomy. In summary, we find no differences at the level of each of the individual hospitals; we find differences when we examine Philadelphia or the parts of Pennsylvania outside of Philadelphia; and then again we find no differences when we examine the entire state together. So, is there a disparity in Pennsylvania or not? Before we answer that question, it may be worth considering what might have happened had investigators begun by examining the data at the level of the state rather than working their way up from hospital to region to state. Those investigators would have quickly encountered the seemingly uninteresting result that both white and black patients have a 25% chance of prostatectomy in Pennsylvania. They might have stopped their investigation there and decided not to publish a study with negative results. But given that we know something about how those data could be partitioned and the alternative conclusions that could be reached, what is the true meaning of this seemingly uninteresting result? Is there a disparity in Pennsylvania or not? Most likely, the correct answer is that this is the wrong question. The observation that aggregated results across the state reveal no health care disparities may be politically comforting for the Governor, but meaningless to real patients who would not plausibly travel much outside their region for care. Indeed, the observed variation across regions of the state may create an agenda for the Governor to promote regional change despite seeming racial equity when the state is viewed in aggregate. Different partitions or aggregations of the same data can yield opposing conclusions, but only some of those partitions and aggregations are relevant to real clinical or policy questions.
It might also be relevant to ask what kind of care is delivered in the state's university hospitals compared with its VA hospitals. That question might be interesting because even though patients might not plausibly travel around the state for their care, we might want to observe how the various organizational or financial circumstances that define university and VA hospitals are associated with different care patterns. The bottom two rows of Table 2 report the same data as the rows above, but now rearranged to answer the question about differences between Pennsylvania university and VA hospitals. These two rows reveal that, at both university and VA hospitals, white patients receive less surgery than black patients. We find these results even though the same data appear to tell us that across the state prostatectomy rates are the same for white and black patients and even though within Philadelphia, and also within the parts of Pennsylvania outside of Philadelphia, prostatectomy rates are higher for white patients than for black patients. Given a look at this different partition of the same data, what is the right disparity question and what is the correct answer to that question? Figure 1 provides a graphical analysis standardized for the percentage of patients treated in Philadelphia along the horizontal axis and partitioned according to university or VA setting by the two different lines. The graph yields three observations we already knew: First, within each of the hospitals, white and black patients are treated the same. This finding is evident because the lines for white and black patients treated in university settings are effectively superimposed, and the same is true for white and black patients treated in VA settings. There are no observable racial health care disparities at the level of the hospital once the data are standardized for geographic distribution along the horizontal axis. Second, prostatectomy rates are higher in university hospitals than in VA hospitals. This finding is evident because at all points, the line reflecting university prostatectomy rates is higher than the line for VA prostatectomy rates. Third, prostatectomy rates are higher in Philadelphia than they are in the remainder of the state. This is evident because both lines slope up to the right.
It is easy to be distracted by the four points, which reflect observed prostatectomy rates for white and black patients treated in VA and university hospitals in the last two rows of Table 2. Because they are so vividly portrayed, they prompt a series of pair-wise comparisons with sometimes paradoxical results. Surprising reversals arise because black patients are more likely to get their care in VA hospitals (which have lower prostatectomy rates) but are also more likely to get their care in Philadelphia (which has higher prostatectomy rates). The four points are misleading because they are the unadjusted effects of nonrandom allocation of subjects into the sample. The true story is in the lines. The lines tell a story of important disparities in care, but disparities that are determined by hospital type and geographic location. If these data are to be believed (and they should not be, because the non-Philadelphia data are fabricated) then if a patient wants to get his prostate removed, he should go to a university hospital in Philadelphia, and if he doesn't, he should go to a VA hospital elsewhere. The health care disparity is real because real patients often have no choice of where to get their care, but instead choices are made for them out of social circumstances and often out of historical and ongoing prejudices.
We produced seemingly contradictory results using only simple sums and quotients, not complex statistical manipulations. And in each case we made comparisons that seem reasonable. Conflicting interpretations of the same data provide a cautionary tale. Some people might throw up their hands and decide that no stable conclusions about health care disparities can ever be drawn, and so none should be trusted. Others might argue that these results merely reveal the importance of multivariable modeling. We reach a more general conclusion, which is that data like these can indeed yield conflicting interpretations, but they can also yield tremendous insights when the analytic and policy perspective is clear. For example, an analysis could assume the perspective of patients. In the case of the Berkeley sex discrimination case, an analysis at the level of the university differed from an analysis at the level of the department, but because students apply to departments and not the university as a whole, the latter better reflects how decisions are made. An analysis of the prostatectomy rates in white and black patients across the Commonwealth of Pennsylvania is unlikely to represent the reality prostate cancer patients face, because most would never travel across the Commonwealth for care. For analyses to reflect the experiences of patients and communities, the analyses have to respect the boundaries that patients face. Pooling of patients across regions may increase the seeming scope of the results, but may erase the clinical meaning of those aggregated results if, in real settings, patients do not cross those regions. Although much recent research addresses the role of geography in creating and sustaining health care disparities, patients may be captive not just by geographic distance, but also by insurance systems, entrenched referral patterns, or sociocultural factors that determine patterns of care. Each of these structures creates boundaries that patients do not cross and that analyses designed to reflect patient perspectives should not cross either. In addition, analyses situated from patient perspectives may better reflect community interests than do analyses structured around physicians or health systems. Second, analyses might focus beyond the current perspectives of patients and instead focus on what might be. This perspective can inform policy decisions that cross patient boundaries, or help illuminate and strike down those boundaries. For example, no obvious racial disparities are found in Philadelphia among patients who seek care at the VA hospital or among patients who seek care at the university hospital, but prostatectomy rates are substantially different at those two sites, regardless of race. Even if the patients who receive care at the VA hospital would never receive care at the university hospital, and vice versa—separate "regions" of care that are clearly not geographic because these two hospitals are across the street from each other—the pooled and the comparative analyses tell us much about the potential origins of disparities, and perhaps something about how to remediate them. Earlier, we suggested that an explanation might be that urologists at the university hospital earn more money when they operate on prostate cancer but the same urologists (or at least a subset of them) do not earn more money when they operate on prostate cancer next door at the VA hospital. The same physicians may also practice differently in private hospital and public hospital settings for other reasons, altering their practice patterns not based on race, but on socioeconomic status, veteran status, or other patient characteristics that may distinguish a hospital. Different analyses of these data might tell additional stories. For example, perhaps patients at the VA hospital are riskier surgical candidates or perhaps patients at the university hospital are more likely to seek aggressive care. Third, analyses of disparities might be situated within jurisdictions or organizations whose borders are defined for some other purpose. A report about racial differences in care among patients in Pennsylvania or within the Veterans Health System can have political value if it reveals an embarrassing disparity that prompts a call for change or, alternatively, if it demonstrates equity and a standard for others to reach. Analyses at the level of jurisdictions or organizations also have practical value in the sense that states or health systems may have the resources or authority to effect change.
Each of these perspectives has merit, but each has a different goal. In the end, disparities in health and health care are a product of location, wealth, education, status, culture, prejudice or any of a large number of social, biologic, and environmental phenomena that are themselves intertwined. The lack of statistical independence among these underlying phenomena reflects this complexity, but also limits the value of any single analysis. In this case, a fully-interacted multivariable analysis would have uncovered each of the phenomena observed here, but one would have had to think about each of the variables to interact in the first place, and other variables not reported here might be even more important. Multivariable analysis can sometimes protect us from statistical confounding, but careful thought about the problem is always necessary to ensure that we answer all the right questions.
The authors indicated no potential conflicts of interest.
Conception and design: David A. Asch, Katrina Armstrong Data analysis and interpretation: David A. Asch, Katrina Armstrong Manuscript writing: David A. Asch, Katrina Armstrong Final approval of manuscript: David A. Asch, Katrina Armstrong
We thank Virginia Chang, MD, PhD, and Judith Long, MD, for helpful comments on earlier drafts of this article.
Supported in part by a Department of the Army Prostate Cancer Research Program Young Investigator Award (K.A.). Authors' disclosures of potential conflicts of interest and author contributions are found at the end of this article.
1. Institute of Medicine. Unequal Treatment: Confronting Racial and Ethnic Disparities in Health Care. Washington, DC, National Academies Press, 2002 2. Long JA, Chang VW, Ibrahim SA, et al: Update on the health disparities literature. Ann Intern Med 141: 805-812, 2004 3. Simpson EH: The interpretation of interaction in contingency tables. J Royal Statistical Soc Series B 13: 238-241, 1951 4. Rickel PH, Hjammel EA, O'Connell JW: Sex bias in graduate admissions: Data from Berkeley. Science 187: 398-404, 1975 5. Malinas G, Bigelow J: Simpson's Paradox, in Zalta EN (ed): The Stanford Encyclopedia of Philosophy (Spring 2004 Edition). http://plato.stanford.edu/archives/spr2004/entries/paradox-simpson/ 6. Skinner J, Chandra A, Staiger D, et al: Mortality after acute myocardial infarction in hospitals that disproportionately treat black patients. Circulation 112: 2634-2641, 2005 7. Barnato AE, Lucas FL, Staiger D, et al: Hospital-level racial disparities in acute myocardial infarction treatment and outcomes. Med Care 43: 303-307, 2005[CrossRef][Medline] 8. Zaslavsky AM, Ayanian JZ: Integrating research on racial and ethnic disparities in health care over place and time. Med Care 43: 303-307, 2005[CrossRef][Medline] 9. Rathore SS, Krumholz HM: Differences, disparities, and biases: Clarifying racial variations in health care use. Ann Intern Med 141: 635-638, 2004 Submitted September 25, 2006; accepted February 28, 2007.
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Copyright © 2007 by the American Society of Clinical Oncology, Online ISSN: 1527-7755. Print ISSN: 0732-183X
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ABSTRACT
INTRODUCTION
