Factors Associated With Disparities in Hospital Readmission Rates Among US Adults Dually Eligible for Medicare and Medicaid

Key Points Question To what extent are state- and community-level factors associated with within-hospital disparities in hospital readmission for dual-eligible Medicare patients? Findings In this cohort study of 2.5 million US adults aged 65 years or older, within-hospital disparities in 30-day readmission for dual-eligible patients persisted after accounting for state- and community-level social and health service availability factors. There was no meaningful change in hospital ranking or between hospital variation in disparity performance when adjustments for community-level factors were included. Meaning Hospital disparities in 30-day readmission rates for dual-eligible patients are not fully explained by differences in community-level factors, and this persistent variation suggests continued opportunities for hospital efforts to advance equity in health care outcomes.

These represent the predicted risk for patient i using hospital j's specific latent quality and the risk predicted for the same patient assuming he or she were treated at a hospital with average latent quality. Once these are calculated, they are used to construct a standardized risk ratio (SRR) for each hospital j: SRR j = (ΣP ij )/(Σ E ij ) (2) where the sum is over all patients at hospital j. This is usually multiplied by the overall crude rate mean (Y ij ) to produce a risk-standardized readmission rate (RSRR), which is reported.

Disparity Model
Model (1) can be expanded to include an additional risk factor X (for example, dual eligibility), which captures the fixed effect of X on patient outcomes: Here, β X represents the overall disparity effect. While important to assess, it is a fixed effect, which is the same for all hospitals. To assess within-hospital disparities related to patient attribute X (for example, dual eligibility), we assume that in addition to the hospital-specific effect described above and the fixed effect β X, there is an additional latent disparity trait at each hospital, such that patients with X=1 have an increased or decreased risk of the outcome specific to that hospital: logit(Pr[Y ij =1]) = β 0 + BZ ij +(β X + ε j ) X ij + γ j (4) where ε j is the hospital-specific disparity effect (or within-hospital disparity effect), and represents the latent disparity trait for each hospital. Model (4) is known as a "mixed effects random slope model". There are different ways of specifying the same model, but for purposes of estimation we use a form that separates the between-hospital effect (effect of being at a hospital with a high proportion of patients with the risk factor) from the within-hospital effect (effect of having the social risk factor at a particular hospital). In order to better interpret the results, we also center all factors Z ij on their overall mean. Thus, our final model is: is the indicator of social risk factor (for example, 1=dual, 0=non-dual or 1=Black, 0=White) for case i at hospital j; is the proportion of cases with social risk factors in hospital j and is the average of all hospitals proportion of cases with social risk factors; In this model, the fixed effect reflects overall disparity; that is, the average disparity effect across all hospitals. The random slope reflects hospital i's hospital-specific disparity effect; that is the degree to which the disparity in outcomes in hospital j differs from the average disparity. By combining these two, we can estimate the disparity effect at a given hospital.

Reporting
Once model (5) is estimated, we report the hospital disparity using in a metric that is both accurate and accessible to consumers: the rate difference (RD). The rate difference is calculated from model (5) by predicting the probability of a positive outcome under two different assumptions and calculating the difference. In both cases, we assume Z=mean(Z ij ), the average value of all risk factors in the population, and include the hospital-specific quality effect γ j and hospital-specific disparity ε j . For one, we assume X ij = 0, that the hypothetical patient has no disparity risk factor, and for the other we assume X ij =1, that the hypothetical average patient has the disparity risk factor. The difference between these two predicted probabilities is the rate difference, which can be intuitively interpreted as the difference in outcome rates for "average patients" treated at that hospital with and without the social risk factor.

Appendix B: Estimates of Medicaid Enrollment by Eligibility Pathway for Older Adult Dual Eligible Medicare Beneficiaries
We categorized states based on Medicaid income or asset eligibility pathways for older adults (>65 years). Using publicly available data sources 1,2,3 , supplemented by manual review of state Medicaid websites, we characterized state income and asset thresholds for two eligibility groups, those that are categorically eligible by income or asset level (eTable 1, columns B and C) and those eligible through medically-needy determinations (eTable 1, columns D and E). We also categorized states based on the type of authorities used for establishing enrollment, resulting in three groups: those that use a single federal application and federal criteria (Section 1634), those that use a separate state application and federal criteria (SSI Criteria), and those that use state-specific application and criteria (Section 209b) (eTable 1, Column F). An entry of "N/A" signifies that the state does not participate in the eligibility pathway. To assess the validity of this approach, we used the 2012 Medicaid Analytic eXtract (MAX) dataset to examine enrollment differences across these two eligibility groups. MAX contains patient-level demographic, enrollment, and utilization information obtained from the State Medicaid Statistical Information System. We selected the 2012 version of the dataset as it contains the most comprehensive state-level information available.
We included 45 states and DC in this analysis. We excluded three states (Colorado, Rhode Island, and Kansas) for which data were unavailable in our version of the dataset at the time of analysis and two additional states (Idaho and Missouri) where anomalies in dual eligibility reporting have been previously identified in the 2012 MAX files. Collectively, the excluded states account for only 5% of the total U.S. population.
We used the Medicare crossover variable to categorize beneficiaries into (a) full benefit dual eligible and (b) all other beneficiaries. This information uses data derived from the Medicare Modernization Act information submitted to CMS by each State Medicaid Agency, and is considered the gold standard for identifying dual eligible enrollees in Medicare data.
The Medicaid eligibility pathway and type of dual eligibility were obtained using the most recent monthly enrollment indicator available for the beneficiary. We excluded individuals with more than a two-month gap in enrollment.
In total, we identified 3.4 million beneficiaries 65 years and older as of January 1, 2012 who received full Medicaid and Medicare benefits and met inclusion criteria. We categorized these individuals into mutually exclusive groupings based on their eligibility pathway: (a) categorically eligible/poverty level, (b) medically needy, and (c) other (including all other pathways). For the purposes of data presentation, we combined aged, blind, and disabled individuals into one group, given that we limited the cohort to 65 years and older.
The figure below depicts the cumulative percentage of older adult dual eligible population by eligibility category. The darker the shading of blue, the more the eligibility pathway accounts for the total dual eligible population.
The figure shows that nationally: • Two-thirds (66.2%) of older adults who qualify for full Medicaid and Medicare benefits qualified for Medicaid benefits as a result of receiving SSI benefits or meeting state-specific 209(b) eligibility thresholds ("categorically eligible") or resided in a state that expanded the categorically eligible group to allow income levels up to the federal poverty level.
• Thirteen percent (13.0%) of older adults who qualify for full Medicaid and Medicare benefits received Medicaid benefits under the medically needy ("spend down") pathway.

Eligibility Pathways and Variation in State Policies for Older Adults with Full Medicaid and Medicare Benefits
Appendix C: Additional Analytic Results