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STOR Colloquium: Bikram Karmakar, University of Pennsylvania
January 11, 2019 @ 2:30 pm - 3:30 pm
Statistics Department, The Wharton School,
University of Pennsylvania
Evidence factors for observational studies: methodology, computation and applications.
Observational studies aim to elucidate cause-and-effect relationships from situations in which treatment is not randomly assigned. A sensitivity analysis for an observational study assesses how much bias, due to non-random assignment of treatment, would be necessary to change the conclusions of an analysis that assumes treatment assignment was effectively random. Causal conclusions gain strength from a demonstration that they are insensitive to small or moderate violations of non-random treatment assignment, especially if that happens in each of several statistically independent analyses that depend upon very different assumptions. In particular, causal conclusions gain strength when evidence factors concur and are insensitive to bias, where a study is said to contain two or more evidence factors if it provides two or more tests of the null hypothesis of no treatment effect that would be (essentially) independent were there no effect. Previous work with evidence factors has not addressed the problem that they involve multiple testing and how to control the type-I error to obtain valid inference. We develop a powerful method for controlling the familywise error rate for sensitivity analyses with evidence factors. We show that the Bahadur efficiency of sensitivity analysis for the combined evidence is greater than for any one evidence factor alone, so that even though using two or more evidence factors requires multiple testing, a study is better off asymptotically using two or more evidence factors than just one factor.
We also develop methods to widen the applicability of evidence factors to various designs for causal assessment, including designs with instrumental variables, and case-control studies. Computationally however it is often very hard to build these designs optimally. Even the simplest addition to a one treatment-control comparison – a second comparison – creates design problems without polynomial-time solutions. We develop an “approximation algorithm” that provides a solution in polynomial time that is probably not much worse than the unattainable optimal solution.
We illustrate our methodological and computational developments for evidence factors in two observational studies: (i) the effect of exposure to radiation on solid cancers and (ii) the effect of having a side airbag on the chance of dying in a car crash.
Refreshments will be served at 3:00pm in the 3rd floor lounge of Hanes Hall