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The Bias Due to Incomplete Matching

Rosenbaum, Paul R.; Rubin, Donald B.
Publication Year:
Report Number:
RR-83-37, PSRTR-83-41
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Data Analysis, Observational Studies, Prenatal Influences, Research Methodology, Sampling


Observational studies comparing groups of treated and control units are often used to estimate the effects caused by treatments. Matching is a method for sampling a large reservoir of potential controls to produce a control group of modest size that is ostensibly similar to the treated group. In practice, there is a trade-off between the desires to find matches for all treated units and to obtain matched treated-control pairs that are extremely similar to each other. We derive expressions for the bias in the average matched pair difference due to (1) the failure to match all treated units— incomplete matching, and (2) the failure to obtain exact matches—inexact matching. A practical example shows that the bias due to incomplete matching can be severe, and moreover, can be avoided entirely by using an appropriate multivariate nearest available matching algorithm, which in the examples, leaves only a small residual bias due to inexact matching. (32pp.)

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