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We propose new optimal matching techniques for large administrative data sets. In current practice, very large matched samples are constructed by subdividing the population and solving a series of smaller problems, for instance, matching men to men and separately matching women to women. Without simplification of some kind, the time required to optimally match 𝑇 treated individuals to 𝑇 controls selected from 𝐶 ≥ 𝑇 potential controls grows much faster than linearly with the number of people to be matched—the required time is of order 𝑂{(𝑇+𝐶)3}—so splitting one large problem into many small problems greatly accelerates the computations. This common practice has several disadvantages that we describe. In its place, we propose a single match, using everyone, that accelerates the computations in a different way. In particular, we use an iterative form of Glover's algorithm for a doubly convex bipartite graph to determine an optimal caliper for the propensity score, radically reducing the number of candidate matches; then we optimally match in a large but much sparser graph. In this graph, a modified form of near-fine balance can be used on a much larger scale, improving its effectiveness. We illustrate the method using data from US Medicaid, matching children receiving surgery at a children's hospital to similar children receiving surgery at a hospital that mostly treats adults. In the example, we form 38,841 matched pairs from 159,527 potential controls, controlling for 29 covariates plus 463 Principal Surgical Procedures, plus 973 Principal Diagnoses. The method is implemented in an R package bigmatch available from CRAN.

Donor-derived fecal microbiota treatments are efficacious in preventing recurrent Clostridioides difficile infection (rCDI), but they have inherently variable quality attributes, are difficult to scale and harbor the risk of pathogen transfer. In contrast, VE303 is a defined consortium of eight purified, clonal bacterial strains developed for prevention of rCDI. In the phase 2 CONSORTIUM study, high-dose VE303 was well tolerated and reduced the odds of rCDI by more than 80% compared to placebo. VE303 organisms robustly colonized the gut in the high-dose group and were among the top taxa associated with non-recurrence. Multi-omic modeling identified antibiotic history, baseline stool metabolites and serum cytokines as predictors of both on-study CDI recurrence and VE303 colonization. VE303 potentiated early recovery of the host microbiome and metabolites with increases in short-chain fatty acids, secondary bile acids and bile salt hydrolase genes after antibiotic treatment for CDI, which is considered important to prevent CDI recurrences. These results support the idea that VE303 promotes efficacy in rCDI through multiple mechanisms. Results of multi-omic profiling of the microbiome and host immunity of individuals treated with VE303 to prevent recurrent Clostridioides difficile infection in the context of a phase 2 trial show robust colonization of VE303 and indicate potential biomarkers of response.

Every newly trained surgeon performs her first unsupervised operation. How do the health outcomes of her patients compare with the patients of experienced surgeons? Using data from 498 hospitals, we compare 1252 pairs comprised of a new surgeon and an experienced surgeon working at the same hospital. We introduce a new form of matching that matches patients of each new surgeon to patients of an otherwise similar experienced surgeon at the same hospital, perfectly balancing 176 surgical procedures and closely balancing a total of 2.9 million categories of patients; additionally, the individual patient pairs are as close as possible. A new goal for matching is introduced, called \"refined covariate balance,\" in which a sequence of nested, ever more refined, nominal covariates is balanced as closely as possible, emphasizing the first or coarsest covariate in that sequence. A new algorithm for matching is proposed and the main new results prove that the algorithm finds the closest match in terms of the total within-pair covariate distances among all matches that achieve refined covariate balance. Unlike previous approaches to forcing balance on covariates, the new algorithm creates multiple paths to a match in a network, where paths that introduce imbalances are penalized and hence avoided to the extent possible. The algorithm exploits a sparse network to quickly optimize a match that is about two orders of magnitude larger than is typical in statistical matching problems, thereby permitting much more extensive use of fine and near-fine balance constraints. The match was constructed in a few minutes using a network optimization algorithm implemented in R. An R package called rcbalance implementing the method is available from CRAN.

A sensitivity analysis displays the increase in uncertainty that attends an inference when a key assumption is relaxed. In matched observational studies of treatment effects, a key assumption in some analyses is that subjects matched for observed covariates are comparable, and this assumption is relaxed by positing a relevant covariate that was not observed and not controlled by matching. What properties would such an unobserved covariate need to have to materially alter the inference about treatment effects? For ease of calculation and reporting, it is convenient that the sensitivity analysis be of low dimension, perhaps indexed by a scalar sensitivity parameter, but for interpretation in specific contexts, a higher dimensional analysis may be of greater relevance. An amplification of a sensitivity analysis is defined as a map from each point in a low-dimensional sensitivity analysis to a set of points, perhaps a \"curve,\" in a higher dimensional sensitivity analysis such that the possible inferences are the same for all points in the set. Possessing an amplification, an investigator may calculate and report the low-dimensional analysis, yet have available the interpretations of the higher dimensional analysis.

BackgroundNursing resources, such as staffing ratios and skill mix, vary across hospitals. Better nursing resources have been linked to better patient outcomes but are assumed to increase costs. The value of investments in nursing resources, in terms of clinical benefits relative to costs, is unclear.ObjectiveTo determine whether there are differential clinical outcomes, costs, and value among medical patients at hospitals characterized by better or worse nursing resources.DesignMatched cohort study of patients in 306 acute care hospitals.PatientsA total of 74,045 matched pairs of fee-for-service Medicare beneficiaries admitted for common medical conditions (25,446 sepsis pairs; 16,332 congestive heart failure pairs; 12,811 pneumonia pairs; 10,598 stroke pairs; 8858 acute myocardial infarction pairs). Patients were also matched on hospital size, technology, and teaching status.Main MeasuresBetter (n = 76) and worse (n = 230) nursing resourced hospitals were defined by patient-to-nurse ratios, skill mix, proportions of bachelors-degree nurses, and nurse work environments. Outcomes included 30-day mortality, readmission, and resource utilization-based costs.Key ResultsPatients in hospitals with better nursing resources had significantly lower 30-day mortality (16.1% vs 17.1%, p < 0.0001) and fewer readmissions (32.3% vs 33.6%, p < 0.0001) yet costs were not significantly different ($18,848 vs 18,671, p = 0.133). The greatest outcomes and cost advantage of better nursing resourced hospitals were in patients with sepsis who had lower mortality (25.3% vs 27.6%, p < 0.0001). Overall, patients with the highest risk of mortality on admission experienced the greatest reductions in mortality and readmission from better nursing at no difference in cost.ConclusionsMedicare beneficiaries with common medical conditions admitted to hospitals with better nursing resources experienced more favorable outcomes at almost no difference in cost.

BackgroundTeaching hospitals typically pioneer investment in new technology and cultivate workforce characteristics generally associated with better quality, but the value of this extra investment is unclear.ObjectiveCompare outcomes and costs between major teaching and non-teaching hospitals by closely matching on patient characteristics.DesignMedicare patients at 339 major teaching hospitals (resident-to-bed (RTB) ratios ≥ 0.25); matched patient controls from 2439 non-teaching hospitals (RTB ratios < 0.05).ParticipantsForty-three thousand nine hundred ninety pairs of patients (one from a major teaching hospital and one from a non-teaching hospital) admitted for acute myocardial infarction (AMI), 84,985 pairs admitted for heart failure (HF), and 74,947 pairs admitted for pneumonia (PNA).ExposureTreatment at major teaching hospitals versus non-teaching hospitals.Main MeasuresThirty-day all-cause mortality, readmissions, ICU utilization, costs, payments, and value expressed as extra cost for a 1% improvement in survival.Key ResultsThirty-day mortality was lower in teaching than non-teaching hospitals (10.7% versus 12.0%, difference = − 1.3%, P < 0.0001). The paired cost difference (teaching − non-teaching) was $273 (P < 0.0001), yielding $211 per 1% mortality improvement. For the quintile of pairs with highest risk on admission, mortality differences were larger (24.6% versus 27.6%, difference = − 3.0%, P < 0.0001), and paired cost difference = $1289 (P < 0.0001), yielding $427 per 1% mortality improvement at 30 days. Readmissions and ICU utilization were lower in teaching hospitals (both P < 0.0001), but length of stay was longer (5.5 versus 5.1 days, P < 0.0001). Finally, individual results for AMI, HF, and PNA showed similar findings as in the combined results.Conclusions and RelevanceAmong Medicare patients admitted for common medical conditions, as admission risk of mortality increased, the absolute mortality benefit of treatment at teaching hospitals also increased, though accompanied by marginally higher cost. Major teaching hospitals appear to return good value for the extra resources used.

Context: Disparities in breast cancer survival by socioeconomic status (SES) exist despite the \"safety net\" programs Medicare and Medicaid. What is less clear is the extent to which SES disparities affect various racial and ethnic groups and whether causes differ across populations. Methods: We conducted a tapered matching study comparing 1,890 low-SES (LSES) non-Hispanic white, 1,824 black, and 723 Hispanic white women to 60,307 not-low-SES (NLSES) non-Hispanic white women, all in Medicare and diagnosed with invasive breast cancer between 1992 and 2010 in 17 US Surveillance, Epidemiology, and End Results (SEER) regions. LSES Medicare patients were Medicaid dual-eligible and resided in neighborhoods with both high poverty and low education. NLSES Medicare patients had none of these factors. Measurements: 5-year and median survival. Findings: LSES non-Hispanic white patients were diagnosed with more stage IV disease (6.6% vs 3.6%; p < 0.0001), larger tumors (24.6 mm vs 20.2 mm; p < 0.0001), and more chronic diseases such as diabetes (37.8% vs 19.0%; p < 0.0001) than NLSES non-Hispanic white patients. Disparity in 5-year survival (NLSES — LSES) was 13.7% (p < 0.0001) when matched for age, year, and SEER site (a 42-month difference in median survival). Additionally, matching 55 presentation factors, including stage, reduced the disparity to 4.9% (p = 0.0012), but further matching on treatments yielded little further change in disparity: 4.6% (p = 0.0014). Survival disparities among LSES blacks and Hispanics, also versus NLSES whites, were significantly associated with presentation factors, though black patients also displayed disparities related to initial treatment. Before being diagnosed, all LSES populations used significantly less preventive care services than matched NLSES controls. Conclusions: In Medicare, SES disparities in breast cancer survival were large (even among non-Hispanic whites) and predominantly related to differences of presentation characteristics at diagnosis rather than differences in treatment. Preventive care was less frequent in LSES patients, which may help explain disparities at presentation.

In this cluster-randomized trial involving 63 internal-medicine residency programs governed by either the 2011 ACGME duty-hour rules or more flexible duty-hour rules, flexible duty-hour policies did not increase 30-day mortality or adversely affect several other patient safety outcomes.

We thank the discussants for their insightful and generous comments. We organized our reply around a few themes, rather than responding to issues one by one. In Section 2, we recap the major elements of the paper in light of the discussion. Then Section 3 reviews the several goals of matching. Finally. Section 4 discusses open questions.

BackgroundThere are known clinical benefits associated with investments in nursing. Less is known about their value.AimsTo compare surgical patient outcomes and costs in hospitals with better versus worse nursing resources and to determine if value differs across these hospitals for patients with different mortality risks.MethodsRetrospective matched-cohort design of patient outcomes at hospitals with better versus worse nursing resources, defined by patient-to-nurse ratios, skill mix, proportions of bachelors-degree nurses and nurse work environments. The sample included 62 715 pairs of surgical patients in 76 better nursing resourced hospitals and 230 worse nursing resourced hospitals from 2013 to 2015. Patients were exactly matched on principal procedures and their hospital’s size category, teaching and technology status, and were closely matched on comorbidities and other risk factors.ResultsPatients in hospitals with better nursing resources had lower 30-day mortality: 2.7% vs 3.1% (p<0.001), lower failure-to-rescue: 5.4% vs 6.2% (p<0.001), lower readmissions: 12.6% vs 13.5% (p<0.001), shorter lengths of stay: 4.70 days vs 4.76 days (p<0.001), more intensive care unit admissions: 17.2% vs 15.4% (p<0.001) and marginally higher nurse-adjusted costs (which account for the costs of better nursing resources): $20 096 vs $19 358 (p<0.001), as compared with patients in worse nursing resourced hospitals. The nurse-adjusted cost associated with a 1% improvement in mortality at better nursing hospitals was $2035. Patients with the highest mortality risk realised the greatest value from nursing resources.ConclusionHospitals with better nursing resources provided better clinical outcomes for surgical patients at a small additional cost. Generally, the sicker the patient, the greater the value at better nursing resourced hospitals.