Introduction One of the limitations of the statistical methods that use propensity scores, such as those involving adjustment for the propensity score, matching, subclassification, and inverse probability of treatment weighting, is that they do not achieve exact balance with respect to the measured confounders. Empirical likelihood is a nonparametric method with desirable statistical properties that is perfectly suited to perform the reweighting of the data as to achieve exact balance on measured confounders.
Methods We describe statistical methods that use empirical likelihood to construct weights that add up to one and produce exact balance when applied to the data. For the case involving only categorical confounders, the empirical likelihood based methods produce weights similar to those generated by the inverse probability weighting or standardisation methods. The new methods can handle both categorical and continuous confounders in a unified manner, and allow the incorporation of balancing constraints ranging from simple equalities of means/proportions to more complex constraints related to the comparison of distributions.
Results Under different scenarios of interest, we perform simulations to compare the statistical properties of the proposed method with the inverse probability weighting method. For comparative purposes we also use both methods to evaluate the association between cardiac malformations and birthweight using data from the Washington-Baltimore Infant Study.
Conclusion The proposed empirical likelihood based method performs well and should be used as complementary to the currently available propensity score based methods.
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