DEVELOPING
1,159
84.2%
0 of 1,376 CAHs clear the benchmark.
Across the national Critical Access Hospital roster, no facility currently satisfies CAHSP ≥ 85 with both mandate floors held (FI ≥ 0.50 and QI ≥ 0.50). The baseline is not a forecast — it is what the published CMS and MBQIP data say, scored through the model in this repository.
Band distribution
MODERATE
202
14.7%
HIGH
15
1.1%
BENCHMARK SOLVED
0
0.0%
CAHSP distribution
MEAN
46.17
MEDIAN
45.5
MIN
15.0
MAX
78.17
Binding constraint — which index is lowest, per facility
QI BINDS
742
Quality is the lowest index.
FI BINDS
506
Financial margin is the lowest.
OI BINDS
69
Operations is the lowest.
WI BINDS
59
Workforce is the lowest.
Correction the national data forces
The binding‑constraint count makes QI look like the dominant blocker (742 vs. 506). At the 2‑part mandate gate the picture inverts: only 66 facilities are QI‑only blockers versus 505 FI‑only. Margin interventions move more facilities across the gate than quality interventions do. FI is the bottleneck — even in 3 of the 15 High‑band facilities.
The 2‑part mandate and the math behind it.
A CAH solution is only Solved when the composite clears the benchmark and both mandate floors are held simultaneously. Financial without quality does not count; quality without financial does not count. The dual mandate is a gate, not a preference.
Mandate definition
CAHSP >= 85 AND FI >= 0.50 AND QI >= 0.50
Source: cahsp_score.py:14, :51, :53‑55
Composite index weights
| INDEX | NAME | WEIGHT | IN MANDATE GATE |
|---|---|---|---|
| FI | Financial Index | 0.30 | Yes (floor 0.50) |
| QI | Clinical Quality Index (MBQIP‑weighted) | 0.30 | Yes (floor 0.50) |
| OI | Operations Index | 0.20 | No |
| WI | Workforce Index | 0.10 | No |
| CI | Confidence Index | 0.10 | No |
Objective
R(x) = alpha_1 * CMI * (ADC * 365 / ALOS)
+ alpha_2 * ED_visits
+ alpha_3 * OP_visits
+ alpha_4 * swing_beds * swing_occupancy * 365
+ alpha_transfer * transfer_volume
C(x) = beta_1 * nursing_FTE + beta_2 * provider_FTE
+ beta_3 + beta_4 * ADC * 365
+ beta_transfer * transfer_volume
M(x) = (R(x) - C(x)) / R(x) # operating margin
Q(x) = sum_i w_i * normalize(measure_i(x)) # quality composite
J(x) = theta * Q(x) + (1 - theta) * M_hat(x) # default theta = 0.6
Constraints
- acute_beds + swing_beds ≤ 25 — 42 CFR § 485.620/645
- ADC ≤ 0.85 * acute_beds
- nursing_FTE / ADC ≥ 0.5 — Aiken 2014
- provider_FTE ≥ 2.0; ED / provider ≤ 5000
- transfer ≤ 0.15 * ADC * 365 — MBQIP corridor
- nursing_FTE + provider_FTE ≤ 120 — MV‑CAHI workforce
- M(x) ≥ 0.05 — margin floor
Solver stack
| COMPONENT | MODULE | METHOD |
|---|---|---|
| Deterministic optimum | solver.py | Multi‑start SLSQP with Charnes‑Cooper reformulation of the margin ratio |
| Quality‑margin frontier | pareto.py | Augmented ε‑constraint (Mavrotas 2009) |
| Uncertainty & CIs | robust.py | Bertsimas‑Sim budget of uncertainty + Monte Carlo |
Source: docs/MATH_AND_MANDATE.md §1‑§4
1,376 facilities, four cohorts, one gate.
Partitioning the national roster against the dual mandate — FI ≥ 0.50 and QI ≥ 0.50 — produces four cohorts. Clearing the gate is the entry criterion; climbing to CAHSP ≥ 85 requires OI, WI, and CI progress on top.
Cohorts
DUAL_SOLVED
762
55.4%
Mandate cleared. Defend the floor.
FI_ONLY_BLOCKER
505
36.7%
Margin push required to unlock mandate.
QI_ONLY_BLOCKER
66
4.8%
Quality push required to unlock mandate.
BOTH_BLOCKERS
43
3.1%
Dual push required.
Quick wins
11
facilities within 0.05 of both floors. All eleven sit at FI = 0.4833 and QI = 0.50 exactly, concentrated in Alaska and Arizona IHS/tribal facilities.
Audit‑then‑act. The narrow numerical stripe likely reflects an ownership‑bias default and a QI pinned at the neutral 0.50, not eleven independent measurements. Reconcile scoring before any field push.
Cohort‑specific action program
| COHORT | PRIMARY TOOL | FIELD ACTIONS | SUCCESS METRIC |
|---|---|---|---|
| fi_only_blocker (505) | CAHOptimizer.optimize() · Charnes‑Cooper | Revenue‑cycle diagnostic, swing‑bed expansion, payer‑mix renegotiation, cost‑based reimbursement audit | FI crosses 0.50 without QI slipping below 0.50 |
| qi_only_blocker (66) | Solver with θ shifted toward quality | HCAHPS rounding, 30‑day readmission bundle, ED‑2b throughput, opioid stewardship | QI crosses 0.50 without FI slipping below 0.50 |
| both_blockers (43) | pareto.py + robust.py | If front never crosses (0.50, 0.50), escalate to Flex Program, state rural grant, or affiliation | Feasible point above both floors exists |
| dual_solved (762) | robust.py under uncertainty | Defend the floor, then attack OI and WI to climb toward CAHSP ≥ 85 | Band moves Developing → Moderate → High |
| quick_wins (11 AK/AZ) | Data audit | Reconcile IHS/tribal FI scoring and QI default before any field action | Scoring confirmed or corrected |
Dual mandate met ≠ Solved
762 facilities (55.4%) clear both floors. Zero clear the full benchmark gate. The 2‑part mandate is the entry criterion; the path from mandate‑met to CAHSP ≥ 85 requires progress on OI, WI, and CI on top of the held floor.