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Cardinality matching is a computational method for finding the largest possible number of matched pairs of exposed and unexposed individuals from an observational dataset, with specified patterns of baseline characteristics that represent a target population for analysis. This article explains the process of cardinality matching and how it simultaneously addresses the concerns of balance, sample size, and representativeness of matched samples in observational studies.

Difference in breast cancer survival by race is a recognized problem among Medicare beneficiaries.To determine if racial disparity in breast cancer survival is primarily attributable to differences in presentation characteristics at diagnosis or subsequent treatment.Comparison of 7375 black women 65 years and older diagnosed between 1991 to 2005 and 3 sets of 7375 matched white control patients selected from 99,898 white potential controls, using data for 16 US Surveillance, Epidemiology and End Results (SEER) sites in the SEER-Medicare database. All patients received follow-up through December 31, 2009, and the black case patients were matched to 3 white control populations on demographics (age, year of diagnosis, and SEER site), presentation (demographics variables plus patient comorbid conditions and tumor characteristics such as stage, size, grade, and estrogen receptor status), and treatment (presentation variables plus details of surgery, radiation therapy, and chemotherapy).5-Year survival.The absolute difference in 5-year survival (blacks, 55.9%; whites, 68.8%) was 12.9% (95% CI, 11.5%-14.5%; P .001) in the demographics match. This difference remained unchanged between 1991 and 2005. After matching on presentation characteristics, the absolute difference in 5-year survival was 4.4% (95% CI, 2.8%-5.8%; P .001) and was 3.6% (95% CI, 2.3%-4.9%; P .001) lower for blacks than for whites matched also on treatment. In the presentation match, fewer blacks received treatment (87.4% vs 91.8%; P .001), time from diagnosis to treatment was longer (29.2 vs 22.8 days; P .001), use of anthracyclines and taxols was lower (3.7% vs 5.0%; P .001), and breast-conserving surgery without other treatment was more frequent (8.2% vs 7.3%; P = .04). Nevertheless, differences in survival associated with treatment differences accounted for only 0.81% of the 12.9% survival difference.In the SEER-Medicare database, differences in breast cancer survival between black and white women did not substantially change among women diagnosed between 1991 and 2005. These differences in survival appear primarily related to presentation characteristics at diagnosis rather than treatment differences.