Conditional Permutation Tests and the Propensity Score in Observational Studies.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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In observational studies, the distribution of treatment assignments is unknown, and therefore randomization tests are not generally applicable. However, permutation tests that condition on sample information about the treatment assignment mechanism can be applicable in observational studies, providing treatment assignment is strongly ignorable. These tests use the conditional distribution of the treatment assignments given a sufficient statistic for the unknown parameter of the propensity score. Several tests that are commonly used in observational studies are particular instances of this general procedure moreover, conditional permutation tests and covariance adjustment are closely related. A backtrack algorithm is developed to permit efficient calculation of the exact conditional significance level, and two approximations are discussed. A clinical study of treatments for lung cancer is used to illustrate the technique. Conditional permutation tests extend previous large sample results on the propensity score by providing a general basis for exact inference in small observational studies when treatment assignment is strongly ignorable. Author
- Statistics and Probability