SAVVY ANALYTIC SOLUTIONS — SAMPLE WORK
Portfolio Sample — Public CMS Data, Multilevel Modeling

Is a Hospital's Excess-Readmission Flag a Real Signal, or Just Volume?

A mixed-effects analysis of CMS's Hospital Readmissions Reduction Program, decomposing excess-readmission risk into discharge volume, condition, and hospital-level quality performance — then applied to one hospital's case profile.

Why this analysis

Every year, CMS publishes an excess readmission ratio for each hospital and condition under HRRP — the number that determines up to a 3% Medicare payment penalty. Read alone, that ratio invites a simplistic story: this hospital is "good" or "bad" at preventing readmissions. This analysis asks a more useful question a hospital's own analytics team would ask: after accounting for how many patients a hospital sees and how it performs on related CMS quality measures, is there anything left over that's specific to this hospital — and if so, where should improvement effort actually go?

The HRRP Supplemental Data File is built from MedPAR claims that CMS adopts directly for the measurement period, rather than health-plan-submitted encounter records — the same distinction that makes it more reliable than Medicare Advantage encounter data for quality measurement, and the reason it was chosen as the foundation here.

DataCMS HRRP FY2026 Supplemental File + Unplanned Hospital Visits file (data.cms.gov)
Unit of analysisHospital-condition (up to 6 rows per hospital)
ModelsCondition-specific logistic; pooled mixed-effects logistic (melogit); covariate-adjusted mixed-effects logistic
SoftwareStata 19
Sample8,037 hospital-condition observations, 2,477 hospitals (Model 1)
Case profilePalomar Health Downtown Campus, CA (CCN 050115)

Of 4,802 matched facility records, 3,045 hospitals (63.4%) appear in both source files; the remainder split between hospitals covered only by the broader Unplanned Visits measure set and a small number covered only by HRRP. The two files were reconciled on a common six-digit CCN, reshaped long-to-wide and back to long by condition, and modeled at the hospital-condition level.

OR 0.56Discharge volume (log) — higher-volume hospitals have markedly lower odds of excess readmissions, pooled across conditions
τ² 0.96 → 0.07Hospital-level random-effect variance before vs. after adding 8 standardized quality covariates
OR 1.66Hospital-wide mortality performance (z-scored) — the strongest single quality predictor of excess readmissions
3,879 obsCovariate-adjusted model sample — reduced from 8,037 by listwise deletion on suppressed low-volume measures

01

Data Sources and File Construction

Two public CMS hospital-level files were used: the FY2026 HRRP Supplemental Data File and the Unplanned Hospital Visits — Hospital file. HRRP reports, for six conditions and procedures (AMI, CABG, COPD, heart failure, hip/knee replacement, and pneumonia), each hospital's excess readmission ratio — predicted-to-expected 30-day readmissions given that hospital's case mix — along with predicted and expected rates, discharge counts, and readmission counts. The Unplanned Visits file reports standardized scores, denominators, and national comparison flags across fourteen measures, including excess-days-in-acute-care (EDAC) for AMI, heart failure, and pneumonia; a hybrid hospital-wide readmission/mortality measure; and outpatient procedure follow-up measures for colonoscopy, chemotherapy, and surgery.

Facility identifiers were reconciled to a common six-digit, zero-padded CMS Certification Number; the HRRP file's numeric ID was converted to this format before merging. Non-numeric placeholder text ("Not Available," "Too Few to Report") was forced to missing during numeric conversion, reflecting CMS's low-volume suppression rules.

Each source file was reshaped long-to-wide so one row represented one hospital, with condition- or measure-specific variables distinguished by suffix. The two wide files were merged 1:1 on CCN, then the merged file was reshaped back to long format on the six HRRP conditions — producing one row per hospital per condition. Hospital-level covariates from the Unplanned Visits file (EDAC scores, the hybrid mortality measure, outpatient procedure measures) are invariant across a hospital's six condition-rows and were retained unchanged through this reshape.

Outcome and predictors

The outcome was a binary indicator of excess readmissions — coded 1 if a hospital's excess readmission ratio exceeded 1.0 for a given condition, 0 otherwise. Records with a missing ratio (typically low-volume suppression) were excluded from the corresponding model. Discharge volume was log-transformed for right skew; condition entered as a categorical predictor (AMI as reference); the eight hospital-level quality covariates were standardized (z-scored) so odds ratios are interpretable per one SD change, given their non-comparable native scales (days per 100 discharges, percentages, and standardized ratios).

02

Modeling Strategy

Three sets of models were estimated. First, condition-specific logistic regressions predicted excess readmission status from log discharge volume alone, fit separately for each of the six conditions. Second, a pooled mixed-effects logistic regression (melogit) was fit across all six conditions jointly — log discharge volume and condition as fixed effects, a random intercept for hospital — to test whether hospital performance correlates across conditions net of volume and condition. Third, the pooled model was re-estimated with the eight standardized quality covariates added as fixed effects, to see how much of the hospital-level random-effect variance from the second model is explained by these measured quality domains. Predicted probabilities and empirical Bayes posterior means of the random effects (BLUPs) were extracted from the final model for hospital-specific case profiling.

Table 1 — Condition-specific logistic regressions (outcome: excess readmissions; predictor: log discharge volume)
ConditionNORp95% CI
Heart attack (AMI)1,2400.386<.0010.313–0.475
Bypass surgery (CABG)3630.107<.0010.060–0.190
COPD1,5450.549<.0010.450–0.668
Heart failure2,3160.691<.0010.624–0.764
Hip/knee replacement2530.049<.0010.023–0.106
Pneumonia2,3200.818.0010.729–0.917

Odds ratios below 1.0 indicate higher discharge volume associated with lower odds of excess readmissions — a volume effect strong enough to specifically flag hip/knee replacement and CABG as the most volume-sensitive programs.

Table 2 — Pooled mixed-effects logistic regression, Model 1 (volume + condition, random intercept for hospital)
PredictorORp95% CI
Discharge volume (log)0.564<.0010.517–0.615
Condition: CABG (ref. AMI)1.174.2520.893–1.543
Condition: COPD (ref. AMI)0.779.0040.656–0.926
Condition: Heart failure (ref. AMI)0.974.7530.827–1.147
Condition: Hip/knee (ref. AMI)1.099.5630.798–1.513
Condition: Pneumonia (ref. AMI)0.972.7330.825–1.144
Constant26.787<.00116.883–42.504

N = 8,037 hospital-condition observations, 2,477 hospitals. Hospital-level variance = 0.962 (SE 0.096); LR test vs. standard logistic regression: χ²(1) = 246.02, p < .001 — hospital identity matters, net of volume and condition.

Table 3 — Pooled mixed-effects logistic regression, Model 2 (adding 8 standardized hospital-level quality covariates)
PredictorORp95% CI
Discharge volume (log)0.681<.0010.596–0.778
Condition: CABG (ref. AMI)1.256.1510.920–1.714
Condition: COPD (ref. AMI)0.723.0040.578–0.904
Condition: Heart failure (ref. AMI)0.815.0920.642–1.034
Condition: Hip/knee (ref. AMI)0.963.8510.650–1.426
Condition: Pneumonia (ref. AMI)0.856.1900.679–1.080
EDAC, heart attack (z)1.316<.0011.201–1.441
EDAC, heart failure (z)1.461<.0011.283–1.665
EDAC, pneumonia (z)1.555<.0011.375–1.758
Hospital-wide mortality (z)1.656<.0011.528–1.795
Outpatient colonoscopy follow-up (z)0.992.7860.937–1.051
Outpatient chemo admissions (z)0.992.8060.928–1.060
Outpatient chemo ED visits (z)0.912.0160.846–0.983
Outpatient surgery follow-up (z)0.997.9250.929–1.070
Constant9.039<.0014.388–18.621

N = 3,879 hospital-condition observations, 929 hospitals. Hospital-level variance = 0.073 (SE 0.065); LR test vs. standard logistic: χ²(1) = 1.43, p = .116. "(z)" denotes a standardized (mean 0, SD 1) covariate.

Table 4 — Hospital-level variance across models
ModelN (obs)N (hospitals)Hospital varianceLR test vs. logistic
Model 1: volume + condition only8,0372,4770.962 (SE 0.096)χ²=246.02, p<.001
Model 2: adding quality covariates3,8799290.073 (SE 0.065)χ²=1.43, p=.116
Hospital-level variance drops by roughly 92% once the eight quality covariates enter the model — most of what looked like an unexplained "hospital effect" in Model 1 is actually volume and measurable quality performance. But the sample also shrinks from 2,477 to 929 hospitals through listwise deletion on suppressed low-volume measures, so this reduction in variance should be read alongside the change in sample composition, not as variance-explained alone.

03 — Applied Case Study

From Model to Hospital: Palomar Health Downtown Campus

A statistical model is only useful if it can answer a question about one real hospital, not just a population average. Palomar Health Downtown Campus in California was selected at random from hospitals with complete model data and a mixed performance profile — some conditions above the national benchmark, others below — specifically because it was representative, not because its results were unusually strong or weak.

Instead of asking whether the hospital's readmission rate is above or below benchmark, the model asks a sharper question: given this hospital's patient volume and quality-measure profile, how much readmission risk should we expect — and do the actual results line up?

Case Profile — CCN 050115

Palomar Health Downtown Campus, California

Condition
CMS ratio
Actual outcome
Model's expected risk
Heart attack (AMI)
1.02
Excess
~37% chance of excess
COPD
0.96
Not excess
~37% chance of excess
Heart failure
1.10
Excess
~28% chance of excess
Pneumonia
0.86
Not excess
~26% chance of excess
Bypass surgery (CABG)
0.96
Not excess
Volume too low to model
Hip/knee replacement
1.14
Excess
Volume too low to model

Two things stand out. First, heart failure was expected to be the lowest-risk of the four modelable conditions, yet it's the one where the hospital exceeds benchmark — a clear gap between expectation and reality, and one that lines up with a specific driver identified below. Second, CMS suppresses case counts for bypass surgery and hip/knee replacement at this hospital due to low volume, so the model can't evaluate those two — their results are real, but rest on a thinner evidence base than the other four.

Is this hospital unusual?

The model separates readmission performance into measurable factors (volume, related quality scores) and whatever hospital-specific effect is left over once those are accounted for — in effect, asking whether something unique to this hospital is driving its results. For Palomar Downtown, that residual hospital-specific effect (its empirical Bayes random-effect estimate) is essentially zero and not statistically distinguishable from an average hospital. There's no sign of a hidden, unmeasured issue — its performance is fully explained by volume and the related quality measures already in the model.

What drives the hospital's risk?

Covariate contribution decomposition

Which measured factors move the needle

Factor
Direction
Size of effect
Patient volume
Protective
By far the largest factor
Overall hospital mortality performance
Protective
Second-largest factor
Pneumonia follow-up care (return visits)
Protective
Modest
Heart attack follow-up care (return visits)
Roughly neutral
Negligible
Heart failure follow-up care (return visits)
Working against
The one factor pushing risk up

Patient volume is the strongest factor by a wide margin — it outweighs any single quality measure in the model. Overall hospital mortality performance is next, and works in the hospital's favor: hospitals with better mortality outcomes tend to have fewer excess readmissions, and that pattern holds here. The one factor working against the hospital is return visits after heart failure care — patients returning to the ED, observation, or inpatient care within 30 days of a heart failure discharge. That's the only measured factor raising this hospital's risk, and it's exactly what shows up in the heart-failure benchmark gap noted above. Return visits after heart attack care, by contrast, barely move this hospital's risk at all — even though they matter across hospitals generally, which is a useful reminder that an industry-level driver isn't automatically the driver for every individual hospital.

Bottom line. Palomar Downtown's readmission performance is largely explained by two favorable factors — patient volume and overall mortality performance — and one unfavorable factor: patient outcomes in the 30 days after a heart failure hospitalization. There's no evidence of an unexplained, hospital-specific issue. The most targeted opportunity for improvement is the heart failure discharge and follow-up process.

A plain-language version of this case profile, written for a non-technical hospital administrator audience, accompanies the full technical write-up in this portfolio's companion documents.