#### Abstract

In many analyses, one has data on one level but desires to draw inference on another level. For example, in genetic association studies, one observes units of DNA referred to as SNPs, but wants to determine whether genes that are comprised of SNPs are associated with disease. While there are some available approaches for addressing this issue, they usually involve making parametric assumptions and are not easily generalizable. A statistical test is proposed for testing the association of a set of variables with an outcome of interest. No assumptions are made about the functional form relating the variables to the outcome. A general function is fit using any statistical learning algorithm, with the SuperLearner algorithm suggested. The parameter of interest is the cross-validated risk and this is compared to an expected risk. A Wald test is proposed using the influence curve of the cross-validated risk to obtain the variance. It is shown both theoretically and via simulation that the test maintains appropriate type I error control and is more powerful than parametric tests under more general alternatives. The test is applied to an MS candidate gene study. Three separate analyses are performed highlighting the flexibility of the approach.

#### Disciplines

Genetics | Statistical Methodology | Statistical Theory

#### Suggested Citation

Goldstein, Benjamin A.; Hubbard, Alan E.; and Barcellos, Lisa F., "A Generalized Approach for Testing the Association of a Set of Predictors with an Outcome: A Gene Based Test" (January 2011). *U.C. Berkeley Division of Biostatistics Working Paper Series.* Working Paper 274.

http://biostats.bepress.com/ucbbiostat/paper274