Matching (statistics)

The matching is a statistical technique which is used to evaluate the effect of a treatment by comparing the treated and the non-treated in non experimental design (when the treatment is not randomly assigned). People use this technique with observational data (ie non experimental data). The idea is to find for any treated unit a similar non treated unit with similar observable characteristics. By matching them and looking at their average difference, one can evaluate under some conditions the pure effect of being treated. This is one way to identify the Rubin Potential Outcome model if there is selection on observable characteristics in the treatment.

The matching has been promoted by Donald Rubin.^[1] It has been discredited by LaLonde in 1986.^[2] In this article LaLonde compares experimental estimates with matching methods and show that matching methods are biased in this case. Dehejia and Wahba reevalutes LaLonde's critique and show that matching is a good solution.^[3]

Analysis

Paired difference tests can be applied to analyze such matched studies. Forming matched pairs for paired difference testing is an example of a general approach for using matching to reduce the effects of confounding when making comparisons.^[4][5][6]

Overmatching

Overmatching is matching for an apparent confounder that actually is a result of the exposure. True confounders are associated with both the exposure and the disease, but if the exposure itself leads to the confounder, or has equal status with it, then stratifying by that confounder will also partly stratify by the exposure, resulting in an obscured relation of the exposure to the disease.^[7] Overmatching thus causes statistical bias.^[7]

For example, matching the control group by gestation length and/or the number of multiple births when estimating perinatal mortality and birthweight after in vitro fertilization (IVF) is overmatching, since IVF itself increases the risk of premature birth and multiple birth.^[8]

It may be regarded as a sampling bias in decreasing the external validity of a study, because the controls become more similar to the cases in regard to exposure than the general population.

References

1. ^ PR Rosenbaum; DB Rubin (1983). "The central role of the propensity score in observational studies for causal effects". Biometrika. 
2. ^ LaLonde, Robert J. (1986). "Evaluating the Econometric Evaluations of Training Programs with Experimental Data". The American Economic Review 76 (4): 604–620. JSTOR 1806062. 
3. ^ RH Dehejia; S Wahba (1999). "Causal Effects in Nonexperimental Studies: Reevaluating the Evaluation of Training Programs.". Journal of the American Statistical Association. .
4. ^ Rubin, Donald B. (1973). "Matching to Remove Bias in Observational Studies". Biometrics 29 (1): 159–183. doi:10.2307/2529684. JSTOR 2529684. 
5. ^ Anderson, Dallas W.; Kish, Leslie; Cornell, Richard G. (1980). "On Stratification, Grouping and Matching". Scandinavian Journal of Statistics 7 (2): 61–66. JSTOR 4615774. 
6. ^ Kupper, Lawrence L.; Karon, John M.; Kleinbaum, David G.; Morgenstern, Hal; Lewis, Donald K. (1981). "Matching in Epidemiologic Studies: Validity and Efficiency Considerations". Biometrics 37 (2): 271–291. doi:10.2307/2530417. JSTOR 2530417. PMID 7272415. 
7. ^ ^{a b} Removal of radiation dose response effects: an example of over-matching. Marsh JL, Hutton JL, Binks K. PMID: 12169512
8. ^ The danger of overmatching in studies of the perinatal mortality and birthweight of infants born after assisted conception. Gissler M, Hemminki E. PMID: 8902436