Hospital standardised mortality ratio: a novel method and approach to risk adjustment

Hospital standardised mortality ratio (HSMR) is a simple ratio that is plagued by sparsity, dimensionality, overdispersion, exclusions and controversy.

Describe Hospital Outcome Prediction Equation V.7 (HOPE-7) methodology.

State of Victoria (Australia), population 6.8 million.

Multiphase process: (a) principal diagnoses aggregated into 406 clinical diagnosis groups (CDGs); (b) low case fatality rate (CFR<0.02%) CDGs set aside; (c) remaining CDGs ranked according to predicted risk; (d) final generalised linear model fitted to (75%) training dataset; (e) low-risk cases reinserted and allocated zero risk; (e) model performance in validation dataset assessed for calibration (Hosmer-Lemeshow goodness-of-fit (H₁₀), Brier score, calibration plot), discrimination (area under the receiver operator characteristic (AUCROC) and area under the precision recall (AUCPRC) curves) and classification (dispersion value (φ), SD random effect (τ)). Ideal model: Brier score~0, H₁₀ p value>0.05, AUCROC>0.80, AUCPRC>0.30, φ~1 and τ~0. Classification assessed by proportion of outlier CFR reclassified as inlier HSMR.

315 hospitals treated 12.97 million adult separations and 152 (48.3%) reported 63 806 in-hospital deaths, 0.49 (95% CI 0.48 to 0.50) per 100 separations. 10 722 principal diagnoses allocated to 198 non-significant CDGs, 45 low-risk CDGs (5.05 million cases) assigned zero risk and 163 significant CDGs aggregated to 20 risk ranks. Final model (development cohort 9.73 million) included demographic variables (age, birth sex, emergency, aged-care resident, hospital transfer, relationship status), one interaction term (emergency transfer) and 20 diagnosis-risk categories. Validation metrics (cohort 3.24 million): Brier score 0.015; H₁₀ p value 0.09; AUCROC 0.90 (95% CI 0.87 to 0.92); AUCPRC 0.28 (95% CI 0.25 to 0.31); φ=4.31 and τ=0.24. Study hospitals generated 2192 hospital quarters with 2053 (95.7%) outlier CFR values, of which 1975 (96.2%) reclassified as HSMR inliers.

HOPE-7 is a parsimonious and pragmatic HSMR model based on administrative data common to many jurisdictions that displayed satisfactory calibration, classification and discrimination metrics and addressed frequent HSMR limitations.