Book contents
- Frontmatter
- Contents
- Contributor Acknowledgments
- Matched Sampling for Causal Effects
- My Introduction to Matched Sampling
- PART I THE EARLY YEARS AND THE INFLUENCE OF WILLIAM G. COCHRAN
- PART II UNIVARIATE MATCHING METHODS AND THE DANGERS OF REGRESSION ADJUSTMENT
- PART III BASIC THEORY OF MULTIVARIATE MATCHING
- PART IV FUNDAMENTALS OF PROPENSITY SCORE MATCHING
- 10 The Central Role of the Propensity Score in Observational Studies for Causal Effects
- 11 Assessing Sensitivity to an Unobserved Binary Covariate in an Observational Study with Binary Outcome
- 12 Reducing Bias in Observational Studies Using Subclassification on the Propensity Score
- 13 Constructing a Control Group Using Multivariate Matched Sampling Methods That Incorporate the Propensity Score
- 14 The Bias Due to Incomplete Matching
- PART V AFFINELY INVARIANT MATCHING METHODS WITH ELLIPSOIDALLY SYMMETRIC DISTRIBUTIONS, THEORY AND METHODOLOGY
- PART VI SOME APPLIED CONTRIBUTIONS
- PART VII SOME FOCUSED APPLICATIONS
- Conclusion: Advice to the Investigator
- References
- Author Index
- Subject Index
14 - The Bias Due to Incomplete Matching
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Contributor Acknowledgments
- Matched Sampling for Causal Effects
- My Introduction to Matched Sampling
- PART I THE EARLY YEARS AND THE INFLUENCE OF WILLIAM G. COCHRAN
- PART II UNIVARIATE MATCHING METHODS AND THE DANGERS OF REGRESSION ADJUSTMENT
- PART III BASIC THEORY OF MULTIVARIATE MATCHING
- PART IV FUNDAMENTALS OF PROPENSITY SCORE MATCHING
- 10 The Central Role of the Propensity Score in Observational Studies for Causal Effects
- 11 Assessing Sensitivity to an Unobserved Binary Covariate in an Observational Study with Binary Outcome
- 12 Reducing Bias in Observational Studies Using Subclassification on the Propensity Score
- 13 Constructing a Control Group Using Multivariate Matched Sampling Methods That Incorporate the Propensity Score
- 14 The Bias Due to Incomplete Matching
- PART V AFFINELY INVARIANT MATCHING METHODS WITH ELLIPSOIDALLY SYMMETRIC DISTRIBUTIONS, THEORY AND METHODOLOGY
- PART VI SOME APPLIED CONTRIBUTIONS
- PART VII SOME FOCUSED APPLICATIONS
- Conclusion: Advice to the Investigator
- References
- Author Index
- Subject Index
Summary
Abstract: 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 (i) the failure to match all treated units – incomplete matching, and (ii) 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 example, leaves only a small residual bias due to inexact matching.
INTRODUCTION
The Effects Caused by Treatments
A treatment is an intervention that can, in principle, be given to or withheld from any experimental unit under study. With an experimental treatment and a control treatment, each unit has two potential responses: a response r1 that would be observed if the unit received the experimental treatment, and a response r0 that would be observed if the unit received the control treatment.
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- Matched Sampling for Causal Effects , pp. 217 - 232Publisher: Cambridge University PressPrint publication year: 2006
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