Sensitivity Analysis for Multiple Comparisons in Matched Observational Studies through Quadratically Constrained Linear Programming

A sensitivity analysis in an observational study assesses the robustness of significant findings to unmeasured confounding. While sensitivity analyses in matched observational studies have been well addressed when there is a single outcome variable, accounting for multiple comparisons through the existing methods yields overly conservative results when there are multiple outcome variables of interest. This stems from the fact that unmeasured confounding cannot affect the probability of assignment to treatment differently depending on the outcome being analyzed. Existing methods allow this to occur by combining the results of individual sensitivity analyses to assess whether at least one hypothesis is significant, which in turn results in an overly pessimistic assessment of a study's sensitivity to unobserved biases. By solving a quadratically constrained linear program, we are able to perform a sensitivity analysis while enforcing that unmeasured confounding must have the same impact on the treatment assignment probabilities across outcomes for each individual in the study. We show that this allows for uniform improvements in the power of a sensitivity analysis not only for testing the overall null of no effect, but also for null hypotheses on \textit{specific} outcome variables while strongly controlling the familywise error rate. We illustrate our method through an observational study on the effect of smoking on naphthalene exposure

Historical Statistics of the United States Chapter on Voluntary, Nonprofit, and Religious Entities and Activities: Underlying Concepts, Concerns, and Opportunities

This paper is a draft of the introduction to the chapter on voluntary, nonprofit, and religious entities and activities slated to appear in the Millennial Edition of Historical Statistics of the United States (forthcoming, Cambridge University Press). Conceding the various problematic definitions of the "nonprofit sector," the essay offers a rationale for the broadly inclusive approach to the selection of historical statistics of institutions and activities presented in the chapter. In addition, it reviews the challenges and opportunities for researchers working on the statistical aspects of nonprofit, voluntary, and religious organizations. The essay includes samples of the statistical series that will appear in HSUS.This publication is Hauser Center Working Paper No. 14. The Hauser Center Working Paper Series was launched during the summer of 2000. The Series enables the Hauser Center to share with a broad audience important works-in-progress written by Hauser Center scholars and researchers

The Diffusion of Cattle Ranching and Deforestation – Prospects for a Hollow Frontier in Mexico’s Yucatán

This article investigates the behavioral drivers of pasture creation and associated implications for deforestation in a 22,000 km2 agricultural frontier spanning the base of Mexico‘s southern Yucatán. After developing a theoretical model that highlights the role of social networks and information spillovers with respect to the decision to begin cattle ranching, we use household data to estimate an econometric duration model of the determinants of pasture creation. Although pasture fi ts well with the typical household‘s resource constraints, its continued expansion contributes to a hollow frontier dynamic in which the spread of low-value cattle ranching coincides with decreasing population.Pasture creation; information spillovers; duration analysis; farm households; Mexico

Budget Imbalance Criteria for Auctions: A Formalized Theorem

We present an original theorem in auction theory: it specifies general conditions under which the sum of the payments of all bidders is necessarily not identically zero, and more generally not constant. Moreover, it explicitly supplies a construction for a finite minimal set of possible bids on which such a sum is not constant. In particular, this theorem applies to the important case of a second-price Vickrey auction, where it reduces to a basic result of which a novel proof is given. To enhance the confidence in this new theorem, it has been formalized in Isabelle/HOL: the main results and definitions of the formal proof are re- produced here in common mathematical language, and are accompanied by an informal discussion about the underlying ideas.Comment: 6th Podlasie Conference on Mathematics 2014, 11 page