Improving hospital quality risk-adjustment models using interactions identified by hierarchical group lasso regularisation

Abstract

Background: Risk-adjustment (RA) models are used to account for severity of illness in comparing patient outcomes across hospitals. Researchers specify covariates as main effects, but they often ignore interactions or use stratification to account for effect modification, despite limitations due to rare events and sparse data. Three Agency for Healthcare Research and Quality (AHRQ) hospital-level Quality Indicators currently use stratified models, but their variable performance and limited interpretability motivated the design of better models.

Methods: We analysed patient discharge de-identified data from 14 State Inpatient Databases, AHRQ Healthcare Cost and Utilization Project, California Department of Health Care Access and Information, and New York State Department of Health. We used hierarchical group lasso regularisation (HGLR) to identify first-order interactions in several AHRQ inpatient quality indicators (IQI) - IQI 09 (Pancreatic Resection Mortality Rate), IQI 11 (Abdominal Aortic Aneurysm Repair Mortality Rate), and Patient Safety Indicator 14 (Postoperative Wound Dehiscence Rate). These models were compared with stratum-specific and composite main effects models with covariates selected by least absolute shrinkage and selection operator (LASSO).

Results: HGLR identified clinically meaningful interactions for all models. Synergistic IQI 11 interactions, such as between hypertension and respiratory failure, suggest patients who merit special attention in perioperative care. Antagonistic IQI 11 interactions, such as between shock and chronic comorbidities, illustrate that naïve main effects models overestimate risk in key subpopulations. Interactions for PSI 14 suggest key subpopulations for whom the risk of wound dehiscence is similar between open and laparoscopic approaches, whereas laparoscopic approach is safer for other groups. Model performance was similar or superior for composite models with HGLR-selected features, compared to those with LASSO-selected features.

Conclusions: In this application to high-profile, high-stakes risk-adjustment models, HGLR selected interactions that maintained or improved model performance in populations with heterogeneous risk, while identifying clinically important interactions. The HGLR package is scalable to handle a large number of covariates and their interactions and is customisable to use multiple CPU cores to reduce analysis time. The HGLR method will allow scholars to avoid creating stratified models on sparse data, improve model calibration, and reduce bias. Future work involves testing using other combinations of risk factors, such as vital signs and laboratory values. Our study focuses on a real-world problem of considerable importance to hospitals and policy-makers who must use RA models for statutorily mandated public reporting and payment programmes.

Keywords: Hierarchical group lasso regularisation; Hospital inpatient quality indicators; Interaction effects; Risk-adjustment models.

Fig. 1

Interaction plot of shock and respiratory failure identified by HGLR for IQI 11 composite

Fig. 2

Interaction plot of shock and other gastrointestinal disease identified by HGLR for IQI 11 composite

Fig. 3

IQI 11 composite- Calibration belts of logistic regression models using A) HGLR or B) LASSO selected features

Fig. 4

Interaction plot of MDC 08 (Diseases and Disorders of the Musculoskeletal System and Connective Tissue) and Population Strata identified by HGLR for PSI 14 composite

Fig. 5

Interaction plot of MDC 13 (Diseases and Disorders of the Female Reproductive System) and Population Strata identified by HGLR for PSI 14 composite

Fig. 6

Interaction plot of Modified DRG 1304 (Uterine and Adnexa Procedure for Non-Malignancy) and Population Strata identified by HGLR for PSI 14 composite

Fig. 7

PSI 14 composite- Calibration belts of logistic regression models using A) HGLR or B) LASSO selected features