Primary Submission Category: Sensitivity Analysis
Sensitivity Analysis with Likelihood Ratio Test and Pearson’s chi-square Test from IxJ Tables
Authors: Elaine Chiu, Hyunseung Kang,
Presenting Author: Elaine Chiu*
Examining associations between categorical variables via contingency tables is common in clinical and social science research. Typically, the strength of these associations is measured using a Likelihood ratio test (LRT) or Pearson’s chi-square test. However, in observational studies, these associations do not imply causation due to unmeasured confounding and a sensitivity analysis seeks to understand how the associations can be nullified by an unmeasured confounder. This paper proposes a non-asymptotic, exact sensitivity analysis for tests of associations in IxJ contingency tables. In particular, we extend the Rosenbaum sensitivity model to allow for (a) non-binary, potentially un-ordered, exposures, (b) a larger class of test statistics, and (c) two-sided alternatives typically implied in an LRT or the Pearson’s chi-square test. We apply our method to assess the association between three types of pre-kindergarten (pre-k) care and students’ overall math achievement, measured on a discrete scale, from the Early Childhood Longitudinal Study-Kindergarten cohort. After controlling for socioeconomic and demographic factors, we find that the association between pre-k programs and math performance is strong, especially for black and Hispanic female students (two-sided p-values: 0.0034 and 0.0086 when γ=0), and the observed association is insensitive up to a Rosenbaum’s Γ of 2.