presents the rates of PARC use: institution (versus home) and SNF (versus IRF) care by race/ethnicity and condition. P-values (chi-square analyses) for differences in discharge by race/ethnicity are also presented. Average age and percent with a length of stay of more than 6 days are presented to illustrate differences in the populations; a complete list of summary statistics is available from the authors.
Rates of PARC Use: Institution versus Home and SNF versus IRF Care, by Race/Ethnicity and Condition
Institutional care varies considerably across the conditions, with 45.63 percent of joint replacement patients, 28.12 percent of stroke patients, and 86.05 percent of hip fracture patients receiving institutional care. Interestingly, there is no clear pattern across conditions in institutional care by race/ethnicity. Although whites are the least likely to receive institutional care for joint replacement, they are the most likely group for hip fracture. For stroke, African Americans are the most likely followed by whites and then Hispanics. For all three conditions, African Americans are more likely to receive institutional care than Hispanics. Whites are generally more likely to receive SNF versus IRF care, although there is no difference between whites and blacks with hip fracture.
The differences in utilization patterns may be caused by factors other than race/ethnicity per se. also includes sample means for selected variables that may influence PARC use. For example, white patients in the sample tend to be older and appear to have less severe conditions (e.g., shorter length of stay). Adjustment for these factors may alter the disparity magnitude.
For illustration, presents the results of the mixed effects logistic model for institutional PARC for joint replacement patients (white and black only). Covariates include a race indicator and other covariates hypothesized to influence utilization. Regression coefficients are presented as odds ratios, and the variation in the hospital-specific random intercept is presented as a median odds ratio (MOR) (Larsen and Merlo 2002
). Larger MORs indicate greater variance in the random hospital-specific intercepts. For simplicity, coefficient estimates for some variables, such as comorbidities and hospital characteristics, are not shown.
Black–White Decomposition for Institution, Joint Replacement
Consistent with the unadjusted results, blacks have a higher odds of institutional use. Other factors known to be associated with institutional use, such as female and older age, have the expected signs. The right panel of presents the decomposition results, in both absolute (difference in utilization rates) and relative (proportion of the unadjusted difference explained by the characteristics) terms. The final row presents the differences in the unadjusted rate of institutional use between blacks and whites (60.68–44.48 from ).
The absolute difference is interpreted as the change in the average probability of institutional use among whites if they had the same covariates as blacks. For example, because blacks were more likely to be female in the data (71 versus 59 percent) and females were more likely to receive institutional care (OR of 2.03 in ), if whites had a similar gender distribution as blacks, the average probability of institutional use would increase by 1.32 percentage points. This increase represents a change equal to 8.14 percent (relative difference) of the difference in unadjusted utilization rates between blacks and whites. In other words, after adjusting for gender, the black–white disparity in institutional use decreases.
Institution versus Home
presents the estimated decomposition effects (absolute differences) along with 95 percent bootstrapped confidence intervals for the institution versus home outcome. The top portion of the table contains the estimated absolute decomposition effects. The row “total explained” is the sum of the effects, and “total difference” refers to the unadjusted difference. The second portion of the table presents the observed rates for the racial/ethnic minority, the predicted rates for whites based on the distribution of the covariates of the minority group, and the observed rate for whites. The difference between the “predicted rate” and the “observed white” is the explained difference; the difference between the “observed minority” and the “predicted rate” is the unexplained difference. Finally, the relative percent of unadjusted disparity explained and unexplained is presented.
For all six models, the clinical effect is statistically significant. Although it only explains 5 percent of the white-Hispanic disparity (0.004/0.085) and 10 percent of the white–black disparity (0.016/0.162) for joint replacement, it explains much more of the disparity for stroke and hip fracture, particularly in regard to the white–black disparity. Age is another important contributor to the racial/ethnic differences seen in all models, allocating the ages of blacks or Hispanics to whites lowers the probability of institutional use. In some models where whites have a lower observed rate of institutional use (e.g., joint replacement), this adjustment exacerbates the difference. Although often statistically significant, differences in gender explain 1.3 percentage points or less of the white-minority disparities. These effects are also small on a relative basis, less than 10 percent of the total difference in unadjusted rates. Geography (state and metropolitan status) is an important explanatory factor in the joint replacement models, contributing the greatest percentage change, but is less important for stroke and hip fracture. Generally, observable acute hospital characteristics have little effect on the disparities, but differences in the otherwise unobserved tendency of the hospital to discharge to institution are important; whites tend to be discharged from acute hospitals that have an otherwise lower unobserved tendency to discharge to institution. For Hispanics, this difference is particularly important, explaining 30 percent of the relative differences for joint replacement (i.e., 0.027/0.085) and 23 and 17 percent, respectively, for stroke and hip fracture. The supply of PARC resources in the community and socioeconomics is statistically significant in half the models, but relatively small in importance, explaining less than 10 percent of the differences. With the exception of the white–black model for hip fracture (68 percent) and stroke (29 percent), the set of observed characteristics explains roughly 50 percent of the difference between institutional care use by whites and racial and ethnic minorities.
Figures 1–3 (Appendix SA3
) outline the cumulative effect of these various adjustments for the three diagnoses. The left x
-axis is the unadjusted rate of institutional use. Moving right along the x
-axis, the estimated probability of institutional use for whites changes as the characteristics of blacks (dotted line) and Hispanics (dashed line) are allocated to whites. The joint replacement and stroke figures demonstrate that the net effect of adjustment for the characteristics narrows the unexplained racial and ethnic differences. For hip fracture, the adjustment narrows the unexplained white-Hispanic difference, but it widens the white-African American difference. The figures underscore the relative contributions of the various factors. For example, in the joint replacement model, clinical factors make a small contribution with larger effects for age and geography.
SNF versus IRF Care
The decomposition results show a different pattern for the SNF versus IRF care models (). Clinical factors do not explain the disparities for joint replacement and stroke (although they are important for hip fracture, especially for blacks). Age is significant in all models and is particularly important in explaining differences in whites versus blacks rate of SNF care use for stroke and hip fracture. Gender is significant in many models, but it makes a relatively small contribution to differences in use of SNF care.
Geography is significant in the white–black comparison for joint replacement, having a large effect of 6 percentage points (although statistically significant for hip fracture, the effect size is small). The hospital random effect is also generally large in these models, with some at 5–10 percentage points. Hospital characteristics and random effects were significant contributors in explaining the white-Hispanic disparity in all three models. For joint replacement, the net effect of the acute hospital (i.e., characteristics and random intercept) for Hispanics was to increase the probability of SNF use by 10.9 percentage points, 36 percent of the total unadjusted effect. Socioeconomic factors were significant in all models but had minimal effect, with the exception of the stroke models, where its effect was modest. PARC supply was significant in two of the six models but only minimally explained differences.
Figures 4–6 (Appendix SA3
) present the decomposition results for SNF versus IRF care in a graphical format. Contrary to the results of institutional care (versus home), the bulk of the difference is attributable to three factors: hospital random effects (for blacks receiving joint replacement and Hispanics for all three conditions), hospital characteristics (for Hispanics for all three conditions), and geography (for blacks receiving joint replacement). With the exception of the white-Hispanic comparison for stroke and white–black comparison for hip fracture, the net effect of the adjustments is a reversal in the differences—although whites were more likely to be discharged to SNF than the other groups in the unadjusted results, after adjustment they are less
likely. Because of these reversals, greater than 100 percent of the unadjusted disparities for these four models are explained. While whites were slightly less likely to be discharged to a SNF after hip fracture, the net effect of the adjustment is a large decrease in the likelihood of whites to use SNF care. Thus, the conclusion for the SNF versus IRF models is that racial and ethnic minorities are more likely (not less likely) to be discharged to SNFs and whites are more likely to receive IRF care. With the exception of age in the white–black comparison for stroke, clinical factors, age, gender, and PARC supply explained little of the disparities.
Comparison of Techniques
presents differences in results between the presented results and two alternative techniques: both use logistic regression (ignoring the hospital random effect) and one does not account for the variance in the parameter estimates. Results are presented for the “Institution versus Home, Joint replacement” model. Overall, the results are largely consistent across the three models. Notably, the addition of the sampling variance adds little to the confidence intervals, likely due to the large sample in our specific application.
Comparison of Results across Methods for Institution versus Home, Joint Replacement
Comparing the multilevel decomposition with the logistic O-B model, the conclusions for the African American sample are largely consistent. Although the estimated decomposed effect due to clinical, for example, is 25 percent higher in the logistic model, the qualitative conclusions are identical between the two models. Only the multilevel model allows the identification of the role of the hospital intercept, an important element in this application, but conclusions are similar between the two models.
The Hispanic population yields much different effects. First, some factors are insignificant in the logit yet significant in the multilevel (e.g., clinical factors and PARC supply), while the converse is also true (hospital characteristics). Despite having similar sample sizes (7,793 versus 7,335), the relative comparability of the decomposition varies between the two populations.