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Med Care. Author manuscript; available in PMC 2024 Jun 1.
Published in final edited form as:
Med Care. 2023 Jun 1; 61(6): 392–399.
Published online 2023 Apr 17. doi:10.1097/MLR.0000000000001849
PMCID: PMC10175195
NIHMSID: NIHMS1883702
PMID: 37068035
Michael Shwartz, PhD, Senior Investigator, Richard D. Cohen, Professor of Health Care and Operations Management Emeritus, Amy K. Rosen, PhD, Senior Research Career Scientist, Professor of Surgery, Erin Beilstein-Wedel, MA, Programming Analyst, Heather Davila, PhD, Research Health Science Specialist, Research Assistant Professor, Alex HS Harris, PhD, and Deborah Gurewich, PhD, Research Investigator, Assistant Professor of Medicine
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The publisher's final edited version of this article is available at Med Care
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Abstract
Background:
Identifying whether differences in healthcare disparities are due to within-facility or between-facility differences is key to disparity reductions. The Kitagawa decomposition divides the difference between 2 means into within-facility differences and between-facility differences that are measured on the same scale as the original disparity. It also enables identification of facilities that contribute most to within-facility differences (based on facility-level disparities and the proportion of patient population served) and between-facility differences.
Objectives:
Illustrate the value of a 2-stage Kitagawa decomposition to partition a disparity into within-facility and between-facility differences and to measure the contribution of individual facilities to each type of difference.
Subjects:
Veterans receiving a new outpatient consult for cardiology or orthopedic services during Fiscal Years 2019–2021.
Measures:
Wait time for a new patient consult
Methods:
In stage 1, we predicted wait time for each Veteran from a multivariable model; in stage 2, we aggregated individual predictions to determine mean adjusted wait times for Hispanic, Black and White Veterans and then decomposed differences in wait times between White Veterans and each of the other groups.
Results:
Noticeably longer wait times were experienced by Hispanic Veterans for cardiology (2.32 days, 6.8% longer) and Black Veterans for orthopedics (3.49 days, 10.3% longer) in both cases due entirely to within-facility differences. The results for Hispanic Veterans using orthopedics illustrate how positive within-facility differences (0.57 days) can be offset by negative between-facility differences (−0.34 days), resulting in a smaller overall disparity (0.23 days). Selecting 10 facilities for interventions in orthopedics based on the largest contributions to within-in facility differences instead of the largest disparities resulted in a higher percentage of Veterans impacted (31% and 12% of Black and White Veterans, respectively, versus 9% and 10% of Black and White Veterans, respectively) and explained 21% of the overall within-facility difference versus 11%.
Conclusion:
The Kitagawa approach allows identification of disparities that might otherwise be undetected. It also allows targeting of interventions at those facilities where improvements will have the largest impact on the overall disparity.
Keywords: Kitagawa decomposition, health care disparities, waiting time for care, quality of care
INTRODUCTION
Increased commitment to eliminating healthcare disparities1,2 has elevated the importance of identifying whether an overall difference in healthcare outcomes is due primarily to within-facility differences or between-facility differences. Within-facility differences indicate the extent to which Group A patients (e.g., people of color) have different outcomes than Group B patients at the same facility; between-facility differences indicate the extent to which facilities that treat a higher proportion of Group A patients have different outcomes for all patients than facilities that treat a lower proportion of such patients. If within-facility differences are relatively large, then interventions to reduce disparities should be targeted at those facilities contributing the most to the overall within-facility difference. Conversely, if between-facility differences are relatively large, interventions to improve overall quality should be targeted at those facilities disproportionately used by people of color. Furthermore, the partition of overall differences into within- and between-facility components may have important implications for whether or not to include variables like race and ethnicity (or social and functional risk factors) in risk adjustment models used in evaluating outcomes. For example, relatively large between-facility differences raise concerns that adjusting for race and ethnicity could “hide” poorer quality of care provided by facilities that treat a high percentage of people of color.3
Multilevel models, which are now widely used in profiling facilities,4–6 decompose the overall variance in outcomes into a within-facility component and a between-facility component. The results of this decomposition are often expressed as the intraclass correlation coefficient (ICC), a statistic which quantifies the proportion of outcome variance due to between-facility differences. However, disparities are usually measured as the difference in the mean of some outcome between 2 groups, not as a differences in the overall variance of the outcome.
In 1955, Kitagawa7 described several alternatives for decomposing a difference in means between 2 groups into both 2 and 3 components. The 2 components in the 2-component alternative are equivalent to what we referred to above as “within-facility differences” and “between-facility differences.” The 3-component alternative also includes an interaction between the 2 components, which is straightforward to describe but, in our context, difficult to interpret. The Kitagawa decompositions were not widely used, particularly in the health services research literature, though there was at least one early application.8 In 1973, Blinder9 and Oaxaca10 independently derived the same 2- and 3-component decomposition of the difference in 2 means as Kitagawa, although in the context of a multiple regression model. Their extension allows one to measure not only within- and between-facility differences, but also the extent to which the different distribution of covariates in the 2 groups, and each of the individual covariates, accounts for the overall difference in means. Referred to as the Blinder-Oaxaca decomposition, it has been widely used in the economics literature and increasingly in the health services literature, including in studies looking at disparities.11–14 In recognition of Kitagawa’s original work, the decomposition is increasingly referred to as “Kitagawa-Blinder-Oaxaca Decomposition”.15
In this paper, we used the Kitagawa 2-component decomposition as the second stage in a 2-stage approach for decomposing the difference in 2 means into within- and between-facility differences. In the first stage, we used a multivariable linear model to predict for each person a covariate-adjusted outcome, which was then aggregated by group and used to calculate the mean adjusted outcomes for each of the 2 groups being compared. In the second stage, we used the 2-component Kitagawa decomposition to partition the difference in mean adjusted outcomes into within-facility and between-facility differences. This approach allows complete flexibility in the type of model used to generate predictions, as well as easy identification of individual facilities that contribute the most to overall within-facility effects and between-facility effects. Thus, it provides opportunities for targeting of these facilities for further study or interventions.
We illustrate our approach using data from the Veterans Health Administration (VA) on wait times (a key measure of access) for orthopedic and cardiology consults. In response to long wait times in the VA, especially for outpatient specialty services, two major legislative acts (the 2014 Veterans Choice Act and the 2018 VA Maintaining Internal Systems and Strengthening Integrated Outside Networks Act [MISSION]) expanded Veterans’ access to care by paying for health services that Veterans receive in the community. In our earlier work, we found declines in wait times between 2015 and 2018 for 5 outpatient specialty care services. However, Black and Hispanic Veterans had, on average, longer wait times for all services.16 In a recently published paper using more current data, we found that wait time for Black and Hispanic Veterans increased more than White Veterans’ wait time during the COVID pandemic.17
Our overall goal in this study was to illustrate the use and value of the 2-stage Kitagawa decomposition to partition disparities in outcomes into within- and between-facility differences and to identify those facilities which contribute the most to each component. This study received a non-human subjects research determination from the VA Boston Institutional Review Board.
METHODS
We used data on the wait time for a “new” outpatient cardiology or orthopedic consult during fiscal year (FY) 2019-FY2021 (October 1, 2018 – September 30, 2021). The dataset included consults in the VA’s Corporate Data Warehouse from 140 VA Medical Centers, referred to as “facilities.” We included both consults internal to the VA and those made to community care (CC) under the Choice and MISSION Acts. CC consults were associated with the VA facility that initiated the consult. Details of the dataset, variable definitions and source files for variables are described in previous work.16 In our analytic file, we eliminated one facility, Manilla (239 consults), which had extremely long wait times.
For both cardiology and orthopedics, we report descriptive statistics on new patient consults (the unit of analysis) and the characteristics of individual Veterans receiving these services, and compare characteristics of Black non-Hispanic Veterans (referred to as “Black” Veterans) and Hispanic Veterans to White non-Hispanic Veterans (referred to as “White” Veterans). Because of large sample sizes, all p-values were < 0.001. Therefore, we reported standardized mean differences (SMDs, the difference between 2 means divided by a pooled estimate of the standard deviation – this is also called the “effect size”) and interpreted SMDs as small (0.20), medium (0.50), or large (0.80).18
Calculating Adjusted Wait Times from Predictions of a Multiple Regression Model (Stage 1):
We were interested in analyzing wait time disparities by race and ethnicity group after adjusting for other sociodemographic characteristics and several other variables (see below) that might confound the relationship between race and ethnicity group and wait time. We calculated adjusted wait times from the predictions of a multivariable linear model (i.e., using marginal estimates). The dependent variable was the new-patient wait time for a completed cardiology or orthopedic consult. Following recommended methodology,19 a new patient was defined as a Veteran who had not had an encounter within the same stop code (i.e., an identifier that indicates the type of clinical encounter the Veteran received) in the prior 24 months at the same VA Medical Center. New-patient wait time was defined as the number of days from when a Veteran’s primary care or specialty care provider requested a consultation for a cardiology or orthopedic service to when the first medical appointment for that service occurred. The independent variables of substantive interest in the model were the race and ethnicity category variables White, Black and Hispanic. Other independent variables included were age (mean centered), sex (male/female), marital status (married, divorced/separated, widowed, single, unknown), housing instability (yes/no), food insecurity (yes/no), rurality (urban or rural, based on where the patient lived), concurrent Nosos score (calculated using data from the year in which the consult occurred) and Veterans’ priority level (grouped into 3 categories: 1–4, 5–6, and 7–8). The concurrent Nosos risk score, developed to predict expected total VA costs for each Veteran during the current year, includes measures of both clinical disease burden and various social risk factors. A risk score is calculated for each Veteran for each year and then recalibrated so that the mean score for all Veterans in the year equals 1.20 Priority level ranges from 1–8 indicating priority for VA enrollment, which is based on service-connected disabilities and income level, with lower scores representing higher VA enrollment priority.21
For White, Black and Hispanic Veterans, and for cardiology and orthopedics, we calculated both overall and facility-level means of the predicted wait times from the multivariable model. These are marginal means, which we refer to as “mean adjusted wait times.” Disparities calculated from the difference in marginal means, which are estimates for groups, are lower than disparities estimated from the coefficients associated with indicator variables for race or ethnicity group in the regression model. The model coefficients are conditional estimates made for individuals under the assumption that all other variables in the model are held constant. To highlight the value of adjusting for confounders (i.e., adjusting for risk), we also calculated “mean unadjusted wait times” directly from the data for each race and ethnicity group, both overall- and at the facility-level.
Decomposing a difference in mean adjusted wait times between 2 race/ethnicity groups into a within-facility difference and a between-facility difference (Stage 2):
The derivation of the Kitagawa decomposition that follows is similar to that in Shwartz et al.8 We illustrate the decomposition by considering the mean adjusted wait time of Black Veterans minus the mean adjusted wait time of White Veterans.
Let Pi(B) = of all Black Veterans nationally who received an orthopedic consult, the proportion that received it at facility i; and Ti(B) = the mean wait time of Black Veterans seen at facility i. Then, ∑i Ti(B)* Pi(B) = the mean wait time for Black Veterans. Similarly, ∑i Ti(W)* Pi(W) = the mean wait time for White Veterans. [Note: If you know the mean wait times of each of 3 facilities (e.g., 3, 5, and 6 days) and you know the proportion of individuals in the population seen at each facility (e.g., .2, .5, and .3), then the mean wait time for the population is 3(.2)+5(.5)+6(.3).]
Let ai = [Ti(B) + Ti(W)] / 2. The larger the value of ai, the longer the average wait time at facility i for all Veterans. Let bi = Ti(B) – ai = ai – Ti(W). These equations follow since ai is the mid-point between Ti(B) and Ti(W). When bi is larger, there is a larger difference in wait times at facility i between Black and White Veterans.
The difference in average wait times for Black Veterans and White Veterans =
(eq. 1)
(eq. 2)
(eq. 3)
In eq. 3, [Pi(B) – Pi(W)] is a measure of the extent to which Black and White Veterans differ in their use of facility i. If Black and White Veterans used facilities similarly, then Pi(B)= Pi(W) for all i and there would be no between-facility differences. As ai (i.e., a measure of the wait time for all Veterans) becomes smaller, a given difference in the proportion of Black and White Veteran contributes less to between-facility differences. The largest contribution to between-facility differences comes from facilities that have large differences in the proportion of Black Veterans and White Veterans that use the facility and have long wait times for all Veterans. Also, facilities disproportionately used by White Veterans (i.e., Pi(W)> Pi(B)) reduce the overall between-facility difference. If facilities disproportionately used by White Veterans also have long wait times for all Veterans, the overall between-facility effect could be negative.
In the second term in eq. 3, bi is a measure of the difference in mean wait time between Black and White Veterans who used facility i (i.e., the within-facility difference). The difference for facility i is weighted by the extent to which Veterans use facility i (i.e., [Pi(B) + Pi(W)]). Thus, the same difference in wait times between Black and White Veterans contributes more to disparities if that difference occurs at a facility that is heavily used by both Black and White Veterans. The within-facility difference is positive in facilities where Black Veterans wait longer than White Veterans (i.e., where bi is positive) and negative in facilities where White Veterans wait longer than Black Veterans. Similar to the between-facility difference, the overall within-facility difference could be either positive or negative.
Analyses:
We created 2 datasets, one consisting of cardiology consults and the other orthopedic consults. We compared characteristics of Black and Hispanic Veterans to White Veterans within each dataset using SMDs.
Using eq. 3, for each specialty, for Black compared to White Veterans and Hispanic compared to White Veterans, we decomposed Non-White minus White Veteran adjusted mean wait times into a within-facility difference [∑i bi*[Pi(B) + Pi(W)] and a between-facility difference [∑i ai*[Pi(B) – Pi(W)]. Then, for each specialty and each comparison, we ranked facilities based on their individual-level contribution to the overall within-facility difference (i.e., [bi*[Pi(B) + Pi(W)]) and graphed the relationship between rank and percentage of the cumulative within-facility difference accounted for.
Finally, to help guide researchers and managers in selecting a small subset of facilities (we assume 10) for further investigation or implementation of interventions designed to reduce within-facility disparities, we compared 2 different selection criteria: 1) facilities with the largest contribution to the overall within-facility differences; and 2) facilities with the largest difference in wait times. The second approach ignores the proportion of Veterans using the facility.
RESULTS
Table 1 compares characteristics of White to Black and Hispanic Veterans in the cardiology dataset. SDC 1 shows the same comparison in the orthopedics dataset. Noticeable differences across the services were that compared to White Veterans, both Black and Hispanic Veterans were on average 4 to 7 years younger; Black Veterans were somewhat more likely to be female (13% and 18% in cardiology and orthopedics, respectively) than White Veterans (6% and 9%); and White Veterans were much more likely to live in rural areas (44%) than Black Veterans (17% to 18% across the 2 services) and Hispanic Veterans (17% to 18%).
Table 1:
Cardiology: Veteran-level variables by race/ethnicity group and standardized mean differences
| White | Black | Hispanic | P_BW | SMD_BW* | P_HW | SMD_HW* | |
|---|---|---|---|---|---|---|---|
| Number of consults (N) | 488566 | 112652 | 41806 | ||||
| Age (mean (SD)) | 68.38 (12.35) | 63.23 (12.26) | 63.41 (15.20) | <0.001 | 0.418 | <0.001 | 0.358 |
| Male (N (%)) | 459978 (94.1) | 97975 (87.0) | 38682 (92.5) | <0.001 | 0.247 | <0.001 | 0.065 |
| Nosos score (mean (SD)) | 1.84 (2.35) | 2.33 (2.81) | 1.89 (2.43) | <0.001 | 0.189 | <0.001 | 0.021 |
| Priority Group (N (%)) | |||||||
| 1_4 | 294111 (60.2) | 76361 (67.8) | 29014 (69.4) | <0.001 | 0.159 | <0.001 | 0.194 |
| 5_6 | 124312 (25.4) | 24415 (21.7) | 9171 (21.9) | <0.001 | 0.089 | <0.001 | 0.083 |
| 7_8 | 70143 (14.4) | 11876 (10.5) | 3621 (8.7) | <0.001 | 0.116 | <0.001 | 0.179 |
| Rurality (N (%)) | |||||||
| Urban | 270804 (55.4) | 92056 (81.7) | 34874 (83.4) | <0.001 | 0.590 | <0.001 | 0.638 |
| Rural | 216972 (44.4) | 20310 (18.0) | 6847 (16.4) | <0.001 | 0.594 | <0.001 | 0.640 |
| Unknown | 790 (0.2) | 286 (0.3) | 85 (0.2) | <0.001 | 0.020 | 0.044 | 0.010 |
| Marital Status (N (%)) | |||||||
| Married | 277536 (56.8) | 48306 (42.9) | 23744 (56.8) | <0.001 | 0.281 | 0.967 | <0.001 |
| Divorced | 120523 (24.7) | 30964 (27.5) | 9468 (22.6) | <0.001 | 0.064 | <0.001 | 0.048 |
| Widowed | 28171 (5.8) | 4899 (4.3) | 1645 (3.9) | <0.001 | 0.065 | <0.001 | 0.085 |
| Single | 53596 (11.0) | 26407 (23.4) | 6126 (14.7) | <0.001 | 0.335 | <0.001 | 0.110 |
| Unknown | 8740 (1.8) | 2076 (1.8) | 823 (2.0) | 0.22 | 0.004 | 0.008 | 0.013 |
| Homeless group (N (%)) | |||||||
| Not Homeless | 418162 (85.6) | 90779 (80.6) | 35205 (84.2) | <0.001 | 0.134 | <0.001 | 0.039 |
| Homeless or At Risk | 14585 (3.0) | 10053 (8.9) | 1744 (4.2) | <0.001 | 0.253 | <0.001 | 0.064 |
| Unknown | 55819 (11.4) | 11820 (10.5) | 4857 (11.6) | <0.001 | 0.030 | 0.234 | 0.006 |
| Food Insecurity (N (%)) | |||||||
| Not food insecure | 406879 (83.3) | 93614 (83.1) | 34533 (82.6) | 0.145 | 0.005 | <0.001 | 0.018 |
| Yes, food insecure | 2389 (0.5) | 1416 (1.3) | 410 (1.0) | <0.001 | 0.083 | <0.001 | 0.058 |
| Unknown | 79298 (16.2) | 17622 (15.6) | 6863 (16.4) | <0.001 | 0.016 | 0.324 | 0.005 |
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*:SMD_BW-standardized mean difference: Black Veterans compared to White Veterans; SMD_HW-standarized mean difference: Hispanic Veterans compared to White Veterans
Table 2 shows the coefficients of the multivariable model used in the cardiology sample to predict wait times for Hispanic compared to White Veterans; SD2 shows coefficients in the orthopedics sample. As expected with the large sample sizes, most coefficients were statistically significant at the p<0.001 level. After adjusting for other variables in the model, the coefficient associated with cardiology services for Hispanic Veterans compared to White Veterans was 3.50. This individual-level estimate indicated that a Hispanic Veteran with the same covariate values as a White Veteran waited on average 3.50 days longer for an appointment. The comparable wait time for Black Veterans compared to White Veterans in orthopedic services was 4.21 days longer (for all estimates, p<0.001).
Table 2:
Regression coefficients and p-values from the model used for Hispanic/White Veteran cardiology analysis and Black/White Veteran orthopedic analysis
| Variables | Cardiology Hispanic/White Veteran Model N=527312 | Orthopedics Black/White Veteran Model N=608834 |
|---|---|---|
| (Intercept) | 24.849 (p< 0.001) | 33.179 (p< 0.001) |
| Age (mean centered) | 0.141 (p< 0.001) | 0.020 (p< 0.001) |
| Sex (ref= Male) | −0.477 (p= 0.017) | 0.610 (p< 0.001) |
| Patient Race/Ethnicity (Ref = White) | 3.504 (p< 0.001) | 4.208 (p< 0.001) |
| Nosos Concurrent | −0.541 (p< 0.001) | −0.623 (p< 0.001) |
| Priority Group (ref=1–4) | ||
| 5–6 | −0.142 (p= 0.208) | −1.299 (p< 0.001) |
| 7–8 | −1.488 (p< 0.001) | −2.813 (p< 0.001) |
| Rurality (ref=Urban) | ||
| Rural | 1.953 (p< 0.001) | 2.381 (p< 0.001) |
| Unknown | 4.922 (p< 0.001) | −4.021 (p< 0.001) |
| Marital Status (ref=Married) | ||
| Divorced | 0.281 (p= 0.014) | −0.320 (p= 0.001) |
| Widowed | −0.022 (p= 0.914) | −0.900 (p< 0.001) |
| Single | 0.309 (p= 0.047) | −1.129 (p< 0.001) |
| Unknown | 0.844 (p= 0.015) | 0.599 (p= 0.029) |
| Homeless (ref=Not homeless) | ||
| Homeless or at risk of homelessness | −0.118 (p= 0.671) | −1.290 (p< 0.001) |
| Unknown | −1.098 (p< 0.001) | −3.034 (p< 0.001) |
| Food Insecurity (ref=Not food insecure) | ||
| Yes, Food insecurity | 0.770 (p= 0.232) | 0.209 (p= 0.664) |
| Unknown, Food insecurity | −0.335 (p= 0.109) | −0.328 (p= 0.055) |
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Table 3 shows, for both cardiology and orthopedic services, unadjusted mean wait times, adjusted mean wait times, within-facility differences, and the between-facility differences for White, Black and Hispanic Veterans. First, both Hispanic Veterans using cardiology and Black Veterans using orthopedics had noticeably longer wait times compared to White Veterans, 2.32 days for Hispanic Veterans in cardiology and 3.44 for Black Veterans in orthopedics. In both cases, the entire disparity was due to within-facility differences. And, in both cases, the between-facility differences were slightly negative, indicating each group disproportionately used facilities with shorter wait times for all Veterans. This is the reason that the within-facility difference was slightly larger than the overall difference in wait times (2.44 days for Hispanic Veterans and 3.49 days for Black Veterans). Second, for both Black Veterans using cardiology services and Hispanic Veterans using orthopedic services, mean adjusted wait times were almost the same as White Veteran mean adjusted wait times (0.12 days shorter and 0.23 days longer, respectively). However, within-facility differences for Hispanic Veterans using cardiology services were 0.57 days, over double the overall difference. This difference was offset by a negative between-facility difference (−0.34). And, third, at the overall system level (i.e., summarized over facilities), mean unadjusted (col. 2) and mean adjusted wait times (col. 3) were the same. This unsurprising result was because ordinary least squares was used to estimate parameters in a linear model. However, the decomposition results were very different when using mean adjusted wait time data (cols. 5 and 6) compared to unadjusted wait time data (cols 7 and 8). At the facility-level, the distribution of covariates in different race and ethnicity groups was different than the distribution in the overall data (i.e., there were significant case-mix differences between different groups at different facilities). The larger percent of the overall difference attributed to between-facility differences when using unadjusted wait times reflects these case-mix differences. The adjusted wait time data removes these case-mix differences from the decomposition analysis, similar to how risk adjustment removes case mix differences between facilities, providing more valid comparisons of quality.
Table 3:
Mean unadjusted wait times, mean adjusted wait times, and adjusted and unadjusted within-facility effects and between-facility effects
| Mean Adjusted Wait Times | Unadjusted Wait Times | ||||||
|---|---|---|---|---|---|---|---|
| Mean Unadjusted Wait Time | Mean Adjusted Wait Time | Race/Ethnic Group Wait Time minus White Veteran Wait Time | Within-Facility Differences | Between-Facility Differences | Within-Facililty Differences | Between-Facility Differences | |
| CARDIOLOGY | |||||||
| White Veterans | 34.04 | 34.04 | |||||
| Black Veteran | 33.92 | 33.92 | −0.12 | −0.01 | −0.11 | −0.96 | 0.84 |
| Hispanic Veterans | 36.35 | 36.35 | 2.32 | 2.44 | −0.12 | −0.42 | 2.74 |
| ORTHOPEDICS | |||||||
| White Veterans | 33.42 | 33.43 | |||||
| Black Veterans | 36.85 | 36.86 | 3.44 | 3.49 | −0.05 | 1.68 | 1.75 |
| Hispanic Veterans | 33.65 | 33.66 | 0.23 | 0.57 | −0.34 | 1.43 | −1.20 |
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Table 4 compares 2 ways of selecting facilities for interventions based on mean adjusted wait times for the 2 situations in which there were notable differences in wait times: the left-hand panel contains data on the 10 facilities with the largest within-facility differences, while the right-hand panel contains data on the 10 facilities with the largest difference in mean adjusted wait times. For Hispanic vs. White Veterans using cardiology (Table 4, Part A), the top 10 facilities accounted for over 37% of the overall within-facility difference and were utilized by 53% of Hispanic Veterans vs. 11% of White Veterans. The average of the mean adjusted wait times across the 10 facilities was 2.76 days longer for Hispanic than for White Veterans. The right-hand panel shows that when the selection criterion for facilities was the greatest difference in mean adjusted wait times, the average of the mean adjusted wait times for the 10 facilities was 3.25 days, about half a day longer than when within-facility differences were used as the selection criterion. However, the 10 facilities selected by the second method served only 23% of Hispanic Veterans and 6% of White Veterans, and accounted for only 20% of the overall within-facility difference.
Table 4:
Highest-ranked 10 facilities based on within-facility difference and on the difference in mean adjusted wait times
| A. Cardiology: Hispanic/White Veteran Comparison | ||||||||
|---|---|---|---|---|---|---|---|---|
| Highest-ranked 10 Facilities Based on the Within-Facility Difference | Highest-ranked 10 Facilities Based on the Difference in Mean Adjusted Wait Times | |||||||
| Facility ID | Within-Facility Difference | Proportion of Hispanic Veterans | Proportion of White Veterans | Difference in Mean Adjusted Wait Times | Facility ID | Proportion of Hispanic Veterans | Proportion White Veterans | Difference in Mean Adjusted Wait Times |
| 123 | 0.267 | 0.161 | 0.001 | 3.294 | 6 | 0.004 | 0.005 | 3.451 |
| 137 | 0.128 | 0.090 | 0.006 | 2.673 | 47 | 0.023 | 0.012 | 3.383 |
| 122 | 0.101 | 0.065 | 0.010 | 2.674 | 58 | 0.001 | 0.003 | 3.332 |
| 126 | 0.092 | 0.050 | 0.021 | 2.600 | 61 | 0.000 | 0.006 | 3.295 |
| 47 | 0.059 | 0.023 | 0.012 | 3.383 | 123 | 0.161 | 0.001 | 3.294 |
| 100 | 0.056 | 0.023 | 0.017 | 2.813 | 12 | 0.000 | 0.004 | 3.262 |
| 124 | 0.055 | 0.026 | 0.019 | 2.468 | 14 | 0.003 | 0.011 | 3.214 |
| 76 | 0.052 | 0.033 | 0.010 | 2.402 | 10 | 0.023 | 0.004 | 3.095 |
| 133 | 0.044 | 0.029 | 0.009 | 2.344 | 98 | 0.017 | 0.008 | 3.083 |
| 138 | 0.043 | 0.027 | 0.003 | 2.899 | 5 | 0.000 | 0.004 | 3.075 |
| Summary | ||||||||
| Cumulative % of Within-Facility Difference: | 0.367 | 0.195 | ||||||
| Total Proportion of Hispanic Veterans: | 0.528 | 0.233 | ||||||
| Total Proportion of White Veterans: | 0.107 | 0.058 | ||||||
| Average of the Difference in Mean Adjusted Wait Times: | 2.755 | 3.248 | ||||||
| B. Orthopedics: Black/White Veteran Comparison | ||||||||
| Highest-ranked 10 Facilities Based on the Within-Facility Difference | Highest-ranked 10 Facilities Based on the Difference in Mean Adjusted Wait Times | |||||||
| Facility ID | Within-Facility Difference | Proportion of Black Veterans | Proportion of White Veterans | Difference in Mean Adjusted Wait Times | Facility ID | Proportion of Black Veterans | Proportion of White Veterans | Difference in Wait Times |
| 114 | 0.090 | 0.035 | 0.016 | 3.565 | 100 | 0.010 | 0.017 | 4.314 |
| 60 | 0.084 | 0.033 | 0.013 | 3.607 | 118 | 0.007 | 0.007 | 4.221 |
| 57 | 0.082 | 0.027 | 0.015 | 3.881 | 33 | 0.013 | 0.006 | 4.207 |
| 54 | 0.073 | 0.029 | 0.010 | 3.748 | 32 | 0.001 | 0.014 | 4.178 |
| 15 | 0.073 | 0.037 | 0.007 | 3.346 | 126 | 0.013 | 0.015 | 4.173 |
| 84 | 0.068 | 0.034 | 0.006 | 3.482 | 90 | 0.011 | 0.002 | 4.159 |
| 125 | 0.066 | 0.023 | 0.013 | 3.663 | 124 | 0.014 | 0.013 | 4.145 |
| 17 | 0.064 | 0.029 | 0.006 | 3.720 | 138 | 0.006 | 0.004 | 4.132 |
| 100 | 0.060 | 0.010 | 0.017 | 4.313 | 3 | 0.000 | 0.011 | 4.118 |
| 50 | 0.058 | 0.023 | 0.008 | 3.804 | 76 | 0.008 | 0.007 | 4.046 |
| 105 | 0.058 | 0.025 | 0.007 | 3.585 | 25 | 0.003 | 0.005 | 4.025 |
| Summary | ||||||||
| Cumulative % of Within-Facility Difference: | 0.206 | 0.107 | ||||||
| Total Proportion of Black Veterans: | 0.305 | 0.085 | ||||||
| Total Proportion of White Veterans: | 0.118 | 0.101 | ||||||
| Average of the Difference in Mean Adjusted Wait Times: | 3.701 | 4.156 | ||||||
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Table 4, Part B shows a similar pattern when considering Black vs. White Veterans receiving orthopedic consults. The highest-ranked 10 facilities based on their within-facility difference were utilized by 31% of Black Veterans and 12% of White Veterans; the highest-ranked 10 facilities based on their difference in mean adjusted wait times were utilized by 9% of Black Veterans and 10% of White Veterans. Although the average of the mean adjusted wait time difference between Black and White Veterans in these 10 facilities (4.2 days) was longer than in the 10 facilities selected using within-facility differences (3.7 days), the percentage of the overall within-facility difference accounted for was smaller (11% vs. 21%).
Figure 1 shows the relationship between the number of facilities selected for a possible intervention based upon their within-facility difference and the cumulative percent of the overall within-facility difference accounted for by these facilities, for both cardiology (where Hispanic Veteran wait times were compared to White Veteran wait times) and orthopedics (where Black Veteran wait times were compared to White Veteran wait times). The greater concentration of Hispanic Veterans in facilities with higher within-facility differences is apparent. For the Hispanic/White Veteran comparison, the highest-ranked 20 facilities accounted for approximately 51% of the overall within-facility difference; for the Black/White Veteran comparison, 32 facilities accounted for 51% of the overall with-in facility difference.
Figure 1:
Number of Facilities Selected For an Intervention and the Associated Cumulative Percentage of the Overall Within-Facility Difference
DISCUSSION
The advantage of the Kitagawa decomposition is that it results in estimates of within-facility and between-facility differences that are on the same scale as the difference in outcomes between the 2 groups being considered, which greatly facilitates interpretation. It is straightforward to determine the percentage of an overall disparity that is attributable to each component and to determine the impact on the overall disparity if one or the other component was reduced. Also, it allows easy identification of the extent to which each individual facility contributes to both the within-facility and between-facility components of the overall disparity.
The individual facility contribution to within-facility differences depends upon both the size of the disparity at the facility and the proportion of patients using the facility. If an organizational goal is overall system disparity reduction and there are limited resources for potential interventions, it is reasonable to select facilities with the largest contribution to the overall within-facility difference rather than those with just the largest facility-level disparity.
The way in which the Kitagawa decomposition calculates between-facility effects is useful. Typically, the concern about between-facility differences is that facilities with a relatively high proportion of at-risk patients deliver poorer quality of care to all patients. The number of patients seen by each facility is the appropriate denominator to use when calculating the proportions if the policy or research focus is on a population that consists of all patients, regardless of payer. However, if the focus is on the patients of a particular payer (e.g., Veterans paid for by VA), interest would likely shift to the question of whether facilities that treat a high proportion of that payer’s at-risk patients provide poorer quality of care to all of that payer’s patients. In this case, the payer’s at-risk population is the relevant denominator. This is the denominator used in calculating the Kitagawa between-facility difference.
Whereas we implemented the Kitagawa decomposition as the 2nd stage of a 2-stage process, the Blinder-Oaxaca decomposition implements the Kitagawa decomposition as part of the output of a multivariable regression model. The Blinder-Oaxaca approach is essential if there is substantive interest in the covariates in the model (i.e., variables other than the primary variables; in our case, variables other than the race and ethnicity categories and, if they are in the model, facility indicator variables) and the extent to which they might contribute to overall disparities. The decomposition has been extended to models that express an outcome as a non-linear function of a set of independent variable.22,23 There is a program in R, ‘oaxaca’, that produces decomposition results.
The advantage of our 2-stage process is that there is complete flexibility in the stage 1 model used to generate the individual-level predictions of the outcome (e.g., models using shrinkage methods like Lasso, tree-based methods with binary splits, neural networks could be used). To apply the decomposition all that is needed is a prediction of an outcome for each individual. The formulas used to go from individual-level predictions to decomposition results are relatively simple and can be easily implemented using Excel (or using the “oaxaca” function in the R program, with race and ethnicity category and facility as indicator variables). Thus, operations managers, policy makers and researchers without sophisticated modeling skills, once given the individual-level predictions, can easily identify those facilities that contribute most to both within-facility and between-facility differences and use this information in their decision-making.
There are several “lessons learned” from our analysis: First, even though there are no overall differences in outcomes between 2 groups, it is still important to evaluate the results of a decomposition. It is possible that overall there could be no overall disparity, but substantial within-facility differences that are offset by negative between-facility differences. Second, even if unadjusted and adjusted data show similar levels of disparities at the overall system level, there could still be confounding when comparing outcomes at the facility level. Thus, results of the decomposition could be very different when using adjusted and unadjusted data. Risk adjusted data should be used for the decomposition if they are available. If they are not, it is important to keep in mind that much of the overall between-facility difference could be due to case-mix differences. Third, it is important to think carefully about the implications of including facility-level variables in the risk adjustment model. Facility-level variables will remove between-facility differences that exist in the data, which could lead to misleading results from the decomposition. Finally, although we only analyzed one outcome variable from 2 services, our finding that within-facility differences accounted for observed disparities is of managerial and policy importance. It does suggest a focus for next steps, at least in regard to wait time disparities in the 2 services we examined. Mixed methods studies to better understand the disparities in those facilities with large within-facility differences would be particularly useful to inform the development of effective interventions to reduce existing disparities.
In conclusion, our goal in this paper was to illustrate the value of the 2-stage Kitagawa decomposition when considering racial and ethnic disparities in healthcare delivery. More generally, this decomposition approach may be useful whenever disparities are measured by the difference in mean outcomes between 2 groups. It leads to a deeper understanding of the overall difference in outcomes and the extent to which within-facility and between-facility differences account for the overall difference. And, it allows identification of individual facilities contributing the most to the within- and between-facility differences and thus facilitates targeting of facilities for further study and when considering quality improvement initiatives.
Supplementary Material
SDC1
SDC1 Table: Orthopedics: Veteran-level variables by race/ethnicity group and standardized mean differences
Click here to view.(19K, xlsx)
SDC2
SDC2 Table: Regression coefficients and p-values from the model used for Hispanic/White Veteran orthopedic analysis and Black/White Veteran cardiology analysis
Click here to view.(18K, xlsx)
Acknowledgements:
This work was supported using resources and facilities at the VA Informatics and Computing Infrastructure (VINCI). Material in this article was presented at ISPOR Europe 2022, Vienna, Austria in a poster session, Nov 8, 2022.
This work was supported by the VA Office of Health Equity, Veterans Health Administration, U.S. Department of Veterans Affairs.
Footnotes
The authors have no conflicts of interest to report. The contents of this article do not represent the views of the U.S. Department of Veterans Affairs or the U.S. Government.
Contributor Information
Michael Shwartz, VA Boston Healthcare System, 150 South Huntington Avenue, Boston, MA 02130.
Richard D. Cohen, Boston University Questrom School of Business, 595 Commonwealth Avenue, Boston, MA 02215.
Amy K. Rosen, VA Boston Healthcare System, 150 South Huntington Avenue, Boston, MA 02130. Boston University School of Medicine, 72 E. Concord Street, Boston, MA 02118.
Erin Beilstein-Wedel, VA Boston Healthcare System, 150 South Huntington Avenue, Boston, MA 02130.
Heather Davila, VA Iowa City Health Care System, 601 US-6 West, Iowa City, IA 52246. University of Iowa Carver College of Medicine, 200 Hawkins Drive, Iowa City, IA 52242.
Alex HS Harris, Center for Innovation to Implementation, VA Palo Alto Healthcare System, 795 Willow Road, Menlo Park, CA 94025. Stanford-Surgery Policy Improvement Research and Education Center, Department of Surgery, C.J. Huang Building, 780 Welch Road, 3rd floor, Palo Alto, CA 94304.
Deborah Gurewich, VA Boston Healthcare System, 150 South Huntington Avenue, Boston, MA 02130. Boston University School of Medicine, 801 Massachusetts Avenue Crosstown Center, Boston, MA 02118.
REFERENCES
1. National Quality Forum. Developing and Testing Risk Adjustment Models for Social and Functional Status-Related Risk Within Healthcare Performance Measurement. Final Technical Guidance.
2. Centers for Medicare and Medicaid Services. What is the CMS National Quality Strategy?https://www.cms.gov/Medicare/Quality-Initiatives-Patient-Assessment-Instruments/Value-Based-Programs/CMS-Quality-Strategy.Published June 10,2022. Accessed01/11/23.
3. Nerenz DR, Austin JM, Deutscher D, et al. Adjusting quality measures for social risk factors can promote equity in health care. Health Aff. 2021; 40 (no. 4): 637–644. [PubMed] [Google Scholar]
4. Normand S-LT, Glickman ME, and Gatsonis. Statistical methods for profiling providers of medical care: Issues and applications. JASA. 1997; 92 (no. 439): 803–814. [Google Scholar]
5. Shahian DM, Normand S-LT, Torchiana, et al. Cardiac surgery report cards: Comprehensive review and statistical critique. Ann Thorac Surg. 2001; 72: 2155–68. [PubMed] [Google Scholar]
6. Krumholz HM, Normand S-LT, Galusha DH, et al. Risk-Adjustment Models for AMI and HF 30-Day Mortality: Methodology. Qualitynet.cms.gov/inpatient/measures/mortality/methodology. (01/23/07).
7. Kitagawa EM. Components of a difference between two rates. J Am Statistical Assoc. 1955; 50 (no. 272): 1168–1194. [Google Scholar]
8. Shwartz M, Merrill JC, and Blake LK. DRG-based case mix and public hospitals. Med Care. 1984; 22 (no. 4): 283–299. [PubMed] [Google Scholar]
9. Blinder AS. Wage discrimination: reduced form and structural estimates. J Hum Resources. 1973; 8: 436–55. [Google Scholar]
10. Oaxaca RMale-female wage differentials in urban labor markets. Int Economic Rev. 1973; 14: 693–709. [Google Scholar]
11. Kirby JB, Taliaferro G, and Zuvekas. Explaining racial and ethnic disparities in health care. Med Care. 2006; 44 (5, Suppl): I64–72. [PubMed] [Google Scholar]
12. Hudson JL, Miller GE and Kirby JB. Explaining racial and ethnic differences in children’s use of stimulant of stimulant medications. Med Care. 2007; 45 (11): 1068–75. [PubMed] [Google Scholar]
13. O’Donnell O, van Doorslaer E, Wagstaff Aet al. Analyzing Health Equity Using Household Survey Data: A Guide to Techniques and Their Implementation. 2008; The World Bank, Washington DC. [Google Scholar]
14. Rahimi E and Nazari SSH. A detailed explanation and graphical representation of the Blinder-Oaxaca decomposition method with its application in health inequities. Emerg Themes Epidemiol. 2021; 18: 12–27. [PMC free article] [PubMed] [Google Scholar]
15. Nieuwenhuis R, Lancker WV, Collado Det al. Trends in women’s employment and poverty rates on OECD countries: A Kitagawa-Blinder-Oaxaca decomposition. Italian Economic Journal. 2020; 6: 37–61. [Google Scholar]
16. Gurewich D, Shwartz M, Beilstein-Wedel E, et al. Did access to care improve since passage of the Veteran’s Choice Act? Differences between rural and urban Veterans. Med. Care2021; 59 (suppl. 3): S270–S278. [PMC free article] [PubMed] [Google Scholar]
17. Gurewich D,Beilstein-Wedel E, Shwartz M, Davila H, Harris AHS, and Rosen AKDisparities in Wait Times for Care Among US Veterans by Race and Ethnicity. JAMA Network Open. 2023; 6(1): e2252061. [PMC free article] [PubMed] [Google Scholar]
18. Cohen JStatistical Power Analysis for the Behavioral Sciences. San Diego: Academic Press; 1969. [Google Scholar]
19. Griffith KN, Ndugga NJ, Pizer SD. Appointment wait times for specialty care in Veterans Health Administration facilities vs community medical centers. JAMA Network Open. 2020; 3; e2014313. [PMC free article] [PubMed] [Google Scholar]
20. Wagner TH, Upadhyay, Cowgill E, et al. Risk adjustment tools for learning health systems: a comparison of DxCG and CMS-HCC V21. Health Serv Res. 2016; 51: 2002–2019. [PMC free article] [PubMed] [Google Scholar]
21. https://www.va.gov/health-care/about-va-health-benefits/cost-of-care/.Accessed01/11/2023.
22. Fairlie RW. The absence of the African-American owned business: an analysis of the dynamics of self-employment. J Labor Econ. 1999; 17(1): 80–108. [Google Scholar]
23. Bauer TK and Sinning M. An extension of the Blinder-Oaxaca decomposition to nonlinear models. AStA. 2008; 92(2):197–206. [Google Scholar]
