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Cardiac rehabilitation (CR) is a medically supervised program designed to improve heart health after a cardiac event. Despite its demonstrated clinical benefits, CR participation among eligible patients remains poor due to low referral rates and individual barriers to care. To evaluate CR participation by patients who receive care from hospital-integrated physicians compared with independent physicians, and subsequently, to examine CR and recurrent cardiac hospitalizations. This retrospective cohort study evaluated Medicare Part A and Part B claims data from calendar years 2016 to 2019. All analyses were conducted between January 1 and April 30, 2024. Patients were included if they had a qualifying event for CR between 2017 and 2018, and qualifying events were identified using diagnosis codes on inpatient claims and procedure codes on outpatient and carrier claims. Eligible patients also had to continuously enroll in fee-for-service Medicare for 12 months or more before and after the index event. Physicians’ integration status and patients’ CR participation were determined during the 12-month follow-up period. The study covariates were ascertained during the 12 months before the index event. ExposureHospital-integration status of the treating physician during follow-up. Main Outcomes and MeasuresPostindex CR participation was determined by qualifying procedure codes on outpatient and carrier claims. ResultsThe study consisted of 28 596 Medicare patients eligible for CR. Their mean (SD) age was 74.0 (9.6) years; 16 839 (58.9%) were male. A total of 9037 patients (31.6%) were treated by a hospital-integrated physician, of which 2995 (33.1%) received CR during follow-up. Logistic regression via propensity score weighting showed that having a hospital-integrated physician was associated with an 11% increase in the odds of receiving CR (odds ratio [OR], 1.11; 95% CI, 1.05-1.18). Additionally, CR participation was associated with a 14% decrease in the odds of recurrent cardiovascular-related hospitalizations (OR, 0.86; 95% CI, 0.81-0.91). The findings of this cohort study suggest that hospital integration has the potential to facilitate greater CR participation and improve heart care. Several factors may help explain this positive association, including enhanced care coordination and value-based payment policies. Further research is needed to assess the association of integration with other appropriate high-quality care activities. 

Identifying cause-effect relations among variables is a key step in the decision-making process. Whereas causal inference requires randomized experiments, researchers and policy makers are increasingly using observational studies to test causal hypotheses due to the wide availability of data and the infeasibility of experiments. The matching method is the most used technique to make causal inference from observational data. However, the pair assignment process in one-to-one matching creates uncertainty in the inference because of different choices made by the experimenter. Recently, discrete optimization models have been proposed to tackle such uncertainty; however, they produce 0-1 nonlinear problems and lack scalability. In this work, we investigate this emerging data science problem and develop a unique computational framework to solve the robust causal inference test instances from observational data with continuous outcomes. In the proposed framework, we first reformulate the nonlinear binary optimization problems as feasibility problems. By leveraging the structure of the feasibility formulation, we develop greedy schemes that are efficient in solving robust test problems. In many cases, the proposed algorithms achieve a globally optimal solution. We perform experiments on real-world data sets to demonstrate the effectiveness of the proposed algorithms and compare our results with the state-of-the-art solver. Our experiments show that the proposed algorithms significantly outperform the exact method in terms of computation time while achieving the same conclusion for causal tests. Both numerical experiments and complexity analysis demonstrate that the proposed algorithms ensure the scalability required for harnessing the power of big data in the decision-making process. Finally, the proposed framework not only facilitates robust decision making through big-data causal inference, but it can also be utilized in developing efficient algorithms for other nonlinear optimization problems such as quadratic assignment problems. History: Accepted by Ram Ramesh, Area Editor for Data Science and Machine Learning. Funding: This work was supported by the Division of Civil, Mechanical and Manufacturing Innovation of the National Science Foundation [Grant 2047094]. Supplemental Material: The online supplements are available at https://doi.org/10.1287/ijoc.2022.1226 .