5. Conduct of Limited Multivariate Logistic Regression Analyses

5.1 Introduction

Given the short project period, the small budget, and the large number of tables produced during this project, we felt it was important to attempt some initial assessment of the impact on the relationship between race/ethnicity and the use of health services of the measure of SES that we created. We believed that one way to do this efficiently was through the use of multivariate logistic regression modeling with selected utilization measures. The models were logistic because the dependent variables (measures of utilization) are all dichotomies, indicating use or no use. The models needed to be multivariate because, in addition to assessing the impact of SES on the association of racial/ethnic disparities in the use of health services covered under fee-for-service Medicare, we wanted to be able to control on beneficiary age group and gender because they are such important correlates of health services utilization and may be distributed differently across the different racial/ethnic and SES groups.

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5.2 The Approach

The approach we have chosen to take with the multivariate logistic regression modeling represents a three step-approach that is easiest explained with an example. Suppose we have established in step one that there is a relationship between being Black rather than White and having a lower rate of a particular cancer screening test in the Medicare program, even after controlling for age group and gender differences between Blacks and Whites. Let us say that the difference represents a true disparity because we know that the morbidity and mortality from this kind of cancer is higher for Blacks than Whites. In addition, as we indicated, the rate of use of the screening test, which could lead to detection of this cancer at an earlier stage when it is theoretically more possible to reduce morbidity and mortality from the disease, is lower for Blacks than Whites. Then in step two of the analysis, we want to know whether rerunning the model with the inclusion of the SES measure increases, decreases, or does not change the magnitude of the disparity between Black and White utilization.

In the third step, we add the interaction of race/ethnicity and SES to the model. With this step, we want to know whether the disparity associated with race while controlling for the effects of age and gender increases, decreases, or is not affected depending on the level of the beneficiaries' SES. Finally we want to know whether any changes that occur are statistically significant and whether they are substantively meaningful in terms of reductions in disparities.

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5.3 Modeling to Assess the Impact of SES

To understand the impact of SES on the association of race/ethnicity to disparities in the utilization of Medicare covered medical services while controlling for the effects of beneficiary age group and gender, we ran three different multivariate logistic regression models. In these models we analyzed seven selected utilization measures from three of the four substantive areas we included in the tabulation appendices.

The measures include three cancer screening measures (receipt in the past 12 months of: the combination of mammogram and Pap smear for women, the prostate specific antigen (PSA) test for men, and any of the three colorectal cancer screening tests for both sexes), three diabetes secondary preventive services for beneficiaries identified as having been diagnosed with diabetes (receipt in the past 12 months of: physiologic testing (hemoglobin A1c, lipid profile, or micro albumin) to monitor insulin needs, an eye exam, and instruction in self-care (diabetes education and self-monitoring)), and whether or not a beneficiary had a hospital or emergency department admission in the past 12 months with a diagnosis of any of the15 ambulatory care sensitive conditions (ACSCs) we included.

The first model was intended to impart an understanding of the relationship between a beneficiary's demographic characteristics (age, gender, and race/ethnicity) and the measure of utilization. It is at this stage that we made our initial assessment of whether a disparity in health care use exists between White beneficiaries and those of other races/ethnicities.

The first logistic model is represented as: logit(yij = 1 | race, x) = α + racei +ßxij + εij where racei represents the effect of the ith race, yij represents the response for the jth individual, xij represents the covariates (age and gender where appropriate) for the jth individual, εij represents the residuals for the jth individual.

The second model added the SES measure to the covariates included in the first model. This second model, compared to the first, allowed us to explore how the addition of SES changed the relationships of the other covariates included in the first model.

The second logistic model is represented as: logit(yhij = 1 | ses, race, x) = α + sesh + racei + ßxhij + εhij where racei represents the effect of the ith race, sesh represents the effect of the hth ses, yhij represents the response for the jth individual, xhij represents the covariates (age and gender where appropriate) for the jth individual, εhij represents the residuals for the jth individual.

The third model investigated the interaction of race/ethnicity and SES. We added the interaction of SES and race/ethnicity to evaluate whether the differences in utilization among the racial/ethnic groups depended on their SES level.

The third logistic model is represented as: logit(yhij = 1 | ses, race, x) = α + sesh + racei + ses*race + ßxhij + εhij where racei represents the effect of the ith race, sesh represents the effect of the hth ses, yhij represents the response for the jth individual, xhij represents the covariates (age and gender where appropriate) for the jth individual, εhij represents the residuals for the jth individual.

For all three multivariate logistic models we used SUDAAN®, a statistical analysis software package developed by RTI that is specifically designed to provide accurate analyses of weighted, cluster-correlated survey data (http://www.rti.org/sudaan/). We used the logistic regression procedure to model the probability of receiving a given treatment and we elected to use a with-replacement design because the percentage of people sampled within a given stratum was small. While we have presented the odd ratios, we have chosen to interpret the models on the basis of differences in the predicted marginals (Korn and Graubard, 1999). In logistic regression, the predicted marginal estimates the percentage or probability of beneficiaries receiving a service for a given racial/ethnic group controlling for all of the other variables in the model. The predicted marginals are equivalent to least squares means when analyzing multiple linear regression model results from a simple random sample survey.

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5.4 Modeling to Establish Racial/Ethnic Health Care Disparities

From the lines in Table 5-1 for each of the services analyzed without SES in the model, we are able to establish in a preliminary way the extent to which there are racial/ethnic disparities with respect to the use of these services. The same can be done from Table 5-2 which contains the odd-ratios from the same analysis. Table 5-3 is a summary of the percentage point differences in service utilization between Whites and minorities with and without the SES measure in the model.

Looking at the age and gender adjusted predicted percentages for the first six service use measures, minorities almost always had lower utilization than Whites, suggesting disparities exist. The only exception was for receipt of instruction in diabetes self-care for which the percentage of Black diabetics getting the service equaled White diabetics. For the seventh measure, hospitalization for any ACSC, the difference in utilization indicating a disparity is reversed because a higher level of hospitalization for ACSC diagnoses is interpreted as a disparity representing poorer quality ambulatory care, i.e., hospitalization for these conditions should be avoidable with appropriate and timely ambulatory care. With this ACSC measure, there were statistically significant disparities between the rates of hospitalization for Whites and minorities. However, there was one reversal in the direction of the differences. While minorities in general had significantly higher rates of hospitalization than Whites for ACSCs, Asian/Pacific Islander beneficiaries had a lower rate that was statistically significant as well. Furthermore, the magnitude of disparities between minority beneficiaries and Whites represented by these seven utilization measures ranged from very small (e.g., Asians/Pacific Islanders) to substantial (e.g., American Indians/Alaska Natives and Hispanics).

Table 5.1 Estimated Percent of Utilization With and Without SES Included in the Multivariate Logistic Models for Beneficiaries by Race/Ethnicity Adjusted for Gender and Age

Type of Service	SES	Race/Ethnicity
		White15	Black	Hispanic	Asian/Pacific Islander	American Indian/ Alaska Native
Mammogram and PAP Smear	Without SES	35%	26%*	22%*	22%*	19%*
	With SES	35	28*	24*	23*	25*
PSA	Without SES	39	30*	30*	33*	17*
	With SES	40	32*	31*	34*	25*
Any Colorectal Cancer Screening	Without SES	16	11*	10*	13*	7*
	With SES	16	12*	11*	14*	10*
Eye Exam	Without SES	62	54*	54*	58*	48*
	With SES	62	56*	58*	58*	53*
Physiologic Measures	Without SES	88	81*	82*	86*	48*
	With SES	88	82*	84*	86*	64*
Instruction in Self-Care	Without SES	54	54	47*	44*	25*
	With SES	54	52*	48*	45*	35*
Any ACSC	Without SES	7	11*	8*	5*	11*
	With SES	7	10*	8*	5*	10*

¹⁵White is the reference level, so all statistical tests are comparing the other race/ethnicity groups to Whites.
*Indicates p-value < 0.001

Table 5.2 Odds Ratios for Utilization With and Without SES Included in the Multivariate Logistic Models for Beneficiaries by Race/Ethnicity

Type of Service	SES	Race/Ethnicity
		White16	Black	Hispanic	Asian/Pacific Islander	American Indian/ Alaska Native
Mammogram and PAP Smear	Without SES	1.00	0.65	0.50	0.52	0.43
	With SES	1.00	0.71	0.58	0.53	0.59
PSA	Without SES	1.00	0.67	0.65	0.75	0.31
	With SES	1.00	0.71	0.68	0.76	0.48
Any Colorectal Cancer Screening	Without SES	1.00	0.67	0.56	0.82	0.40
	With SES	1.00	0.73	0.62	0.82	0.58
Eye Exam	Without SES	1.00	0.74	0.71	0.85	0.56
	With SES	1.00	0.79	0.86	0.84	0.70
Physiologic Measures	Without SES	1.00	0.56	0.59	0.82	0.12
	With SES	1.00	0.60	0.70	0.84	0.24
Instruction in Self-Care	Without SES	1.00	0.98	0.75	0.66	0.27
	With SES	1.00	0.92	0.77	0.67	0.44
Any ACSC	Without SES	1.00	1.60	1.12	0.66	1.55
	With SES	1.00	1.46	1.07	0.67	1.48

¹⁶White is the reference category and odds ratios are adjusted for gender and age.

Table 5.3 Summary of Adjusted Marginal Percentage Point Differences in Selected Health Services Utilization between Whites and Minority Groups With and Without SES in the Logistic Model

Type of Service	SES	Race/Ethnicity
		Black - White	Hispanic - White	Asian/Pacific Islander - White	American Indian/ Alaska Native - White
Mammogram and PAP Smear	Without SES	-9%	-13%	-13%	-16%
	With SES	-7	-11	-12	-10
PSA	Without SES	-9	-9	-6	-22
	With SES	-8	-9	-6	-15
Any Colorectal Cancer Screening	Without SES	-5	-6	-3	-9
	With SES	-4	-5	-2	-6
Eye Exam	Without SES	-8	-8	-4	-14
	With SES	-6	-4	-4	-9
Physiologic Measures	Without SES	-7	-6	-2	-40
	With SES	-6	-4	-2	-24
Instruction in Self-Care	Without SES	0	-7	-10	-29
	With SES	-2	-6	-9	-19
Any ACSC	Without SES	4	1	-2	4
	With SES	3	1	-2	3

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5.5 Impact of SES on Differences in Estimated Percent Utilization

In all of the models we used to predict the utilization measures, the SES measure was statistically significant, accounting for added variance in the utilization measures. (The output of the SUDAAN® multivariate logistic regression analyses with significance test results is presented in Appendix I.) However, the increase in the amount of variance explained with the addition of the SES measure varied across the different measures of utilization. The model investigating the percentage of female beneficiaries receiving both a Pap smear and a mammogram was the least affected by the addition of SES to the model, and the model of having experienced a hospitalization for any ambulatory care sensitive condition (ACSC) was the most affected, with 1.1 percent and 22.2 percent increases in the amount of variance explained by the regression models, respectively.

The addition of SES to the models had the greatest impact on the estimated percentage of utilization for the different health care measures across race/ethnicity. The estimated percentage utilization by racial/ethnic group with SES in the logistic models controlling for age and gender (where appropriate) is also presented in Table 5.1, and the odds-ratios for the same analysis is presented in Table 5.2. Generally, when SES was added to the logistic model, the percentage of utilization for minorities increased, moving it closer to the percentage of utilization for Whites. This suggests that the racial/ethnic basis of the disparity is not as large when the effect of SES is taken into account. The results for gender and age, however, were hardly affected by the addition of SES to the model. For most measures, the percentage of utilization by gender or by age was not changed by the addition of SES to the models.

Impact of SES on Cancer Screening Use Differences. The three cancer screening measures investigated from Appendix B included the receipt during 2002 of both a mammogram and a Pap smear, a PSA test, and any of three types of colorectal cancer screening test. Across all three cancer screenings, the percentage of minority beneficiaries as compared to White beneficiaries receiving these screenings was considerably less, with American Indian/Alaska Natives almost always having the lowest utilization rates of all the minorities. For White female beneficiaries, after controlling for age, the estimated percentage receiving a mammogram and a Pap smear was 35 (Table 5.1) compared to only 19 percent for American Indian/Alaska Natives, 26 percent for Blacks, 22 percent for Asians/Pacific Islanders, and 22 percent for Hispanics. When SES was added to the model, the estimated percentage of White female beneficiaries receiving a mammogram and a Pap smear remained at 35 percent, however, the estimated percentage of minorities receiving a mammogram and a Pap smear increased. It increased to 25 percent for American Indian/Alaska Natives, 28 percent for Blacks, 23 percent for Asian/Pacific Islanders, and 24 percent for Hispanics. This represents a six percentage point reduction in the original disparity between Whites and American Indians/Alaska Natives, a two percentage point reduction for Hispanics and Blacks, and a one percentage point reduction for Asians/Pacific Islanders. The increases in their utilization after controlling for SES moved the utilization rate of mammograms and Pap smears for minorities closer to the rate of Whites. Although not completely erasing the difference in the percent of Whites and other minorities receiving both a mammogram and a Pap smear, the addition of the SES did reduce the original health care disparity.

The results of adding SES to the model were similar for the other two cancer screening measures we examined – having a PSA test, and having any of three types of colorectal cancer test. Most notable was the change in the estimated percent of male American Indians/Alaska Natives receiving a PSA test. Without SES in the model, an estimated 17 percent of male American Indians/Alaska Natives had a PSA test; 22 percentage points less than Whites. With the addition of SES to the model, the estimated percentage of American Indians/Alaska Natives receiving a PSA test increased to 25 percent while the percentage of Whites remained unchanged. This narrowed the disparity between American Indians/Alaska Natives and Whites by eight percentage points, from 22 to 14 percentage points. Similar patterns in the percentage of male beneficiaries receiving a PSA test existed for the other minority groups, but the addition of the SES variable to the model reduced the disparity between them and Whites less; two percentage points for Blacks and only one percentage point for Asians/Pacific Islanders and Hispanics.

For receipt of any of the three types of colorectal screening, the disparity between the predicted marginals of White and American Indian/Alaskan Native beneficiaries was nine percentage points, the largest in the model without SES, followed by a six percentage point disparity for Hispanics, five percentage points for Blacks, and three percentage points for Asians/Pacific Islanders. As resulted when SES was added to the model of receiving both a mammogram and a Pap smear, as well as for having a PSA test, adding SES to the model for colorectal cancer testing reduced the disparity between Whites and American Indians/Alaskan Natives to six percentage points, to five percentage points between Whites and Hispanics, to only two percentage points for Asian/Pacific Islanders, and to four percentage points between Whites and Blacks.

Impact of SES on Secondary Diabetes Prevention Services Use Differences. The diabetes utilization rates were calculated among beneficiaries with diagnosed diabetes; approximately 13 percent of Medicare beneficiaries were identified as having diabetes. Among Medicare beneficiaries diagnosed with diabetes, those receiving physiologic measures (hemoglobin A1c, lipid profile, or micro albumin) had the highest percentage of utilization among the three measures modeled; eye exam and instruction in self-care were the other two measures modeled. An estimated 88 percent of White beneficiaries diagnosed with diabetes received physiologic measurement services compared to 81 percent of Blacks, 86 percent of Asians/Pacific Islanders, 82 percent of Hispanics, and only 48 percent of American Indians/Alaska Natives. When controlling for SES, the estimated percentage of American Indian/Alaska Native beneficiaries with diabetes receiving physiologic measures increased by 16 percentage points, thereby narrowing the difference between Whites and American Indians/Alaska Natives from 40 percentage points to 24 percentage points. The estimated adjusted marginal percentage of the other minority groups receiving physiologic measures also increased, thus drawing them closer to the estimated White rate (which did not change), although not as dramatically as for American Indians/Alaska Natives. Without controlling for SES, the percent of Blacks and Hispanics receiving physiologic measures is seven and six percentage points less than Whites, respectively. However, when we controlled for SES in the model, the difference from Whites was reduced to six and four percentage points for Blacks and Hispanics, respectively.

The difference between Whites and minority groups receiving instructions in self-care was sizeable in the first model not controlling on SES. For Asians/Pacific Islanders, this difference was ten percentage points, for Hispanics seven percentage points, and for American Indians/Alaskan Natives 29 percentage points. Controlling for SES did not change the disparity much for Asians/Pacific Islanders or Hispanics (brought them one percentage point closer to Whites), but for American Indians/Alaska Natives, the difference was reduced by ten percentage points. The results for Blacks were puzzling because without SES in the model there was no disparity with Whites, but adding SES produced a two percentage point disparity.

The final diabetes measure included in the multivariate modeling was whether or not an eye exam was received. As with all the other measures, Whites had the largest percentage receiving this service and this percentage did not change with the addition of SES to the model. Results for Hispanics and American Indians/Alaska Natives changed the most when controlling for SES. Without controlling for SES, 48 percent of American Indians/Alaska Natives and 54 percent of Hispanics compared to 62 percent of Whites received an eye exam. With SES in the model, an estimated 53 percent of American Indians/Alaska Natives and 58 percent of Hispanics received an eye exam; a four and five percentage point increase respectively for both of these minorities groups with the addition of SES to the model. The percentage of Blacks receiving this service also increased when controlling for SES, but only by two percentage points. The percentage of Asians/Pacific Islanders receiving this service did not change by having SES in the model.

Impact of SES on Differences in Hospitalization for Any Ambulatory Care Sensitive Condition. This measure behaved differently than the cancer screening and diabetes preventive services utilization measures. Asian/Pacific Islanders had the lowest percentage of ACSC hospitalizations, with Whites next, and with Blacks, Hispanics, and American Indian/Alaskan Natives having the most. The changes resulting from the addition of the SES measure were very small for this measure. Blacks and American Indians/Alaskan Natives were the only groups with any change and the percentage of both of them having a hospitalization for an ACSC dropped by one percentage point, moving them closer to the rate of Whites.

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