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The test statistic can be thought of as the solution to an adversarial game, where the researcher determines the best linear combination of test statistics to combat nature\u2019s presentation of the worst-case pattern of hidden bias. The corresponding optimization problem is convex, and can be solved efficiently even for reasonably sized observational studies. Asymptotically, the test statistic converges to a chi-bar-squared distribution under the null, a common distribution in order-restricted statistical inference. The test attains the largest possible design sensitivity over a class of coherent test statistics, and facilitates one-sided sensitivity analyses for individual outcome variables while maintaining familywise error control through its incorporation into closed testing procedures.<\/jats:p>","DOI":"10.1093\/biomet\/asaa024","type":"journal-article","created":{"date-parts":[[2020,3,16]],"date-time":"2020-03-16T20:32:43Z","timestamp":1584390763000},"page":"809-825","source":"Crossref","is-referenced-by-count":2,"title":["Multivariate one-sided testing in matched observational studies as an adversarial game"],"prefix":"10.1093","volume":"107","author":[{"given":"P L","family":"Cohen","sequence":"first","affiliation":[{"name":"Operations Research and Statistics Group, Massachusetts Institute of Technology, 100 Main Street, Cambridge, Massachusetts 02142, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M A","family":"Olson","sequence":"additional","affiliation":[{"name":"The Voleon Group, 2170 Dwight Way, Berkeley, California 94704, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C B","family":"Fogarty","sequence":"additional","affiliation":[{"name":"Operations Research and Statistics Group, Massachusetts Institute of Technology, 100 Main Street, Cambridge, Massachusetts 02142, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,6,3]]},"reference":[{"key":"2020121116433560800_B1","first-page":"451","article-title":"Cancer risk assessment, indicators, and guidelines for polycyclic aromatic hydrocarbons in the ambient air","volume":"110","author":"Bostr\u00f6m,","year":"2002","journal-title":"Env. 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