Hospital Outcome Prediction Equation (HOPE) model, version 7.

Background: The hospital standardised mortality ratio (HSMR) is a simple ratio, yet, plagued by sparsity, dimensionality, over-dispersion, exclusivity, and clinical controversy. We describe the Hospital Outcome Prediction Equation, version-7 (HOPE-7) methodology, derived from jurisdictional administrative data, which addresses many of these limitations. Methods: Population included all adult acute-care hospital separations in State of Victoria (population 6.8 million), Australia, over 5-years July 2018-June 2023. Multistage model development included: (a) aggregation of 12,145 principal diagnoses (reason for hospital admission) from International Classification of Disease version 10 into twenty categories ranked according to estimated risk of death; (b) fixed-effect logistic regression (with adjustment for clustering at hospital level) fitted to a randomly selected (75%) training dataset, with low-risk (case fatality rate, CFR <0.02%) diagnosis groups allocated to a zero risk category; (c) and model performance tested in (remaining 25%) validation dataset. Calibration assessed by Hosmer-Lemeshow goodness-of-fit [H10], Brier score, calibration plot; model discrimination by area under precision-recall (AUCPR) and receiver-operator (AUCROC) curves; and model classification at the hospital level by dispersion value [tor], standard deviation of random effect [SD]) and proportion of in-control hospitals. Ideal model characteristics: Brier score ~0, H10 p-value >0.05, AUCPR>0.30, AUCROC >0.80, tor approximates unity, SD approximates zero; and <1% hospitals outside +/-3SD of benchmark. Results: 315 hospitals treated 12.97-million adult acute-care separations with mean CFR 0.59% (95%CI = 0.58-0.60; n=77,637). 4,211 (34.7%) principal diagnoses allocated to zero mortality-risk category (CFR 0.003%); 3,497 (28.8%) non-significant diagnoses allocated to baseline mortality risk category (CFR 0.50%); remaining 4,437 (36.5%) diagnoses aggregated into 18 ranked risk categories (CFR range: 0.08-32.5%). Final model, developed on 9.75-million records, included one continuous variable (age in years, transformed to square root); five binary demographic variables (sex, relationship status, unplanned admission, aged-care resident, hospital transfer); one interaction term (emergency-transfer); and twenty diagnosis-risk categories, of which, only one was allocated to each record. Validation cohort (n= 3.25 million) parameters included: Brier score =0.015; H10 =14.88 (p=0.094); AUCPR =0.28 +0.01; AUCROC =0.90 +0.007; tor; =4.3 and SD =0.24; before and after (multiplicative) adjustment for over-dispersion 280 (88.9%) and 313 (99.1%) hospitals, respectively, remained within 3SD benchmark over all five years. Conclusion: HOPE-7, a parsimonious and pragmatic HSMR based on administrative data common to all jurisdictions, displayed satisfactory calibration, classification, and discrimination metrics, addressed many common HSMR limitations, and complements existing methods.