A New Construction of Evidence Factors in an Observational Study of Light Daily Alcohol Consumption and Longevity

Does light daily alcohol consumption lengthen life? In any observational study of this question, we expect drinking behavior – i.e., treatment assignment – to be confounded by measured and unmeasured covariates. An observational study has two evidence factors if there are two essentially independent tests of the same null hypothesis about causal effects, where the two tests are susceptible to different unmeasured biases in treatment assignment. Because they are independent, two evidence factors may be combined using meta-analytic techniques, despite being two analyses of the same data, and they may consequently provide mutual support and increased power; however, they may alternatively undermine one another by suggesting that unmeasured bias is present. In the study of light daily alcohol, two evidence factors are formed from two control groups, and the evidence factors provide mutual support for one outcome, HDL-cholesterol, and clash for another, survival. Evidence factors have typically been derived from the orthogonality of nominal factors in balanced designs that resemble simple experiments. In this paper, evidence factors are obtained in a new and completely different way. A recently proposed conditioning tactic creates test statistics with superior design sensitivity, and it turns out that this tactic partitions the sample space in a manner that yields evidence factors. The method is evaluated using an asymptotic measure, the design sensitivity, and using the simulated finite-sample power of sensitivity analyses. An R package alcoholSurv contains the data, implements the method, and replicates the analysis.