SeekingChartis Quant Stack
ECONOMETRICS
- OLS with VIF + state R²
- Ridge regression + elastic net
- Per-hospital residual analysis
- Cross-sectional price elasticity
BIOSTATISTICS
- Beta-Binomial partial pooling
- Gamma-Lognormal hierarchies
- Survival/hazard for margin runway
- Missing-data scoring (MNAR)
OPERATIONS RESEARCH
- M/M/c queueing (Erlang C)
- Little's Law backlog analysis
- DEA efficiency frontier
- Staffing optimization
MACHINE LEARNING
- K-means hospital clustering
- Logistic distress prediction
- Ensemble (Ridge + k-NN + median)
- Conformal prediction intervals
CAUSAL INFERENCE
- Interrupted Time Series
- Difference-in-Differences
- Counterfactual estimation
- Cross-deal learning / shrinkage
SIMULATION
- Two-source Monte Carlo
- Latin Hypercube sampling
- Correlated lever draws
- P10/P50/P90 EBITDA/MOIC/IRR
Bayesian Calibration (Beta-Binomial Partial Pooling)
Denial rate estimation under varying data quality. With strong data, posterior converges to observed. With weak/no data, posterior shrinks toward peer-group prior (8.5% for medium hospitals). Shrinkage factor = how much weight goes to prior vs data. 90% credible intervals widen with uncertainty.
| Scenario | Observed | n | Prior | Posterior | 90% CI | Shrinkage | Quality |
|---|---|---|---|---|---|---|---|
| Strong data (n=500) | 12.0% | 500 | 8.5% | 11.8% | [9.5%, 14.1%] | 6% | strong |
| Moderate data (n=50) | 12.0% | 50 | 8.5% | 10.7% | [5.0%, 16.3%] | 38% | moderate |
| Weak data (n=5) | 12.0% | 5 | 8.5% | 9.0% | [1.1%, 16.9%] | 86% | weak |
| No data (prior only) | 0.0% | 0 | 8.5% | 8.5% | [0.3%, 16.7%] | 100% | prior_only |
| Low observed (n=100) | 3.0% | 100 | 8.5% | 4.3% | [1.4%, 7.2%] | 23% | strong |
| High observed (n=100) | 25.0% | 100 | 8.5% | 21.2% | [15.3%, 27.1%] | 23% | strong |
Operational Efficiency Frontier (DEA)
Data Envelopment Analysis: 30 hospitals on the efficient frontier, 0 in the bottom 30%. Inputs: beds + operating expenses. Outputs: net patient revenue + patient days.
| Hospital | State | Efficiency | Percentile | Frontier |
|---|---|---|---|---|
| PAM REHAB HOSPITAL OF DOVER | DE | 1.000 | P100 | ★ |
| FIRSTHEALTH MONTGOMERY MEMORIAL CAH | NC | 1.000 | P100 | ★ |
| BIG SANDY MEDICAL CENTER | MT | 1.000 | P100 | ★ |
| ADVENTHEALTH ORLANDO | FL | 1.000 | P100 | ★ |
| PH GREER MEMORIAL HOSPITAL | SC | 1.000 | P100 | ★ |
| WOMANS HOSPITAL OF TEXAS | TX | 1.000 | P100 | ★ |
| MIDWESTERN REGIONAL MEDICAL CENTER | IL | 1.000 | P100 | ★ |
| EASTERN MAINE MEDICAL CENTER | ME | 1.000 | P100 | ★ |
| ST. LUKES HOSPITAL | PA | 1.000 | P100 | ★ |
| BANNER ESTRELLA MEDICAL CENTER | AZ | 1.000 | P100 | ★ |
| SPARROW SPECIALTY HOSPITAL | MI | 1.000 | P100 | ★ |
| ST. JOSEPHS COMM. HOSPT. | WI | 1.000 | P100 | ★ |
| MUSCOGEE CREEK NATION LONG TERM CARE | OK | 1.000 | P100 | ★ |
| CORNERSTONE SPECIALTY MUSKOGEE | OK | 1.000 | P100 | ★ |
| SUNRISE HAVEN | WA | 1.000 | P100 | ★ |
| NEW YORK PRESBYTERIAN HOSPITAL | NY | 1.000 | P100 | ★ |
| PROFFESIONAL HOSPITAL | PR | 1.000 | P100 | ★ |
| LEO N LEVI MEMORIAL HOSPITAL | AR | 1.000 | P100 | ★ |
| ALHAMBRA | CA | 0.994 | P100 | ★ |
| FLOYD MEDICAL CENTER | GA | 0.991 | P100 | ★ |
State Market Intelligence
52 markets analyzed. HHI (Herfindahl-Hirschman Index) measures concentration: >2500 = highly concentrated, >1500 = moderate. Investability combines market depth, growth, health, and payer quality.
| State | Hospitals | Revenue | Median Margin | HHI | Concentration | Investability | Distress |
|---|---|---|---|---|---|---|---|
| UT | 59 | $11.72B | 8.0% | 892 | Competitive | 90 (A) | 25% |
| VA | 111 | $28.36B | 4.4% | 354 | Competitive | 87 (A) | 30% |
| FL | 261 | $74.71B | 3.2% | 159 | Competitive | 86 (A) | 30% |
| SC | 85 | $18.31B | 1.3% | 516 | Competitive | 83 (A) | 34% |
| WI | 150 | $26.37B | 0.4% | 317 | Competitive | 83 (A) | 34% |
| AZ | 124 | $25.48B | -0.8% | 342 | Competitive | 82 (A) | 36% |
| NC | 129 | $38.65B | -2.0% | 348 | Competitive | 82 (A) | 37% |
| NV | 58 | $7.85B | 0.4% | 549 | Competitive | 82 (A) | 38% |
| OH | 235 | $59.11B | -0.4% | 266 | Competitive | 82 (A) | 37% |
| IN | 171 | $30.26B | -1.1% | 302 | Competitive | 80 (A) | 42% |
| TX | 583 | $97.37B | -0.7% | 109 | Competitive | 80 (A) | 43% |
| WV | 62 | $8.52B | -0.3% | 805 | Competitive | 80 (A) | 42% |
| NM | 55 | $6.85B | -2.7% | 977 | Competitive | 80 (A) | 42% |
| TN | 141 | $24.61B | -0.6% | 682 | Competitive | 79 (A) | 43% |
| GA | 165 | $35.67B | -2.8% | 234 | Competitive | 79 (A) | 44% |
| KY | 114 | $19.50B | -0.6% | 494 | Competitive | 79 (A) | 45% |
| MN | 141 | $24.57B | -3.6% | 424 | Competitive | 79 (A) | 45% |
| LA | 212 | $17.61B | -3.5% | 338 | Competitive | 78 (A) | 46% |
| CO | 108 | $21.68B | -3.6% | 370 | Competitive | 78 (A) | 47% |
| ID | 51 | $7.39B | -3.5% | 1,032 | Competitive | 78 (A) | 46% |
RCM Queueing Analysis (M/M/c)
Operations research model of RCM workqueues as M/M/c systems. Shows utilization, wait times, SLA breach probability, and recommended staffing. Uses Erlang C formula + Little's Law. Inputs are configurable per hospital.
| Queue | Arrivals | Staff | Utilization | Avg Wait | SLA Breach | Rec. Staff | Status |
|---|---|---|---|---|---|---|---|
| Denial Appeals | 50/day | 5 | 83% | 0.1d | 0% | 5 | ✓ |
| Medical Coding | 200/day | 8 | 83% | 0.0d | 0% | 8 | ✓ |
| Prior Authorization | 30/day | 3 | 67% | 0.0d | 0% | 3 | ✓ |
| A/R Follow-Up | 100/day | 6 | 83% | 0.0d | 0% | 6 | ✓ |