Title: Pairwise Inverse Probability Weighted and Quadruply Robust Kendall’s Tau for Conditional Dependence

Abstract: Studying the associations between variables is a fundamental problem in multivariate data analysis. Conditional associations measure relationships between bivariate outcomes after adjusting for the impacts of covariates and provide insights on more direct relationships between bivariate outcomes than marginal associations. In this talk, we study conditional associations based on Kendall’s Tau.  First, we adjust the traditional Kendall's tau coefficient by inverse probability weighting with pairwise propensity scores and propose a statistic PIP-tau in the form of U-statistic that is an unbiased estimator of the average conditional Kendall's tau. The PIP-tau statistic can be used to measure nonlinear conditional association between bivariate outcomes. The pairwise propensity scores in our statistic can be estimated flexibly by both parametric and non-parametric methods. Our proposed measure of conditional association has zero expectation under conditional independence, as long as either one of the propensity score models is correctly specified. In addition, we show that our proposed statistic is asymptotically normal under the null hypothesis, which provides a valid test if models for both propensity scores are correct and if the estimates of propensity scores are consistent. Simulation studies show that our test controls Type I error rate and has competitive power. Furthermore, our test is more robust to model misspecifications than other existing methods.

If time allows, we also present a quadruply robust association test by combining the PIP-tau method with the Kendall's tau correlation coefficient on the residuals to employ information from both propensity scores and outcome models. The new measure is quadruply robust because it has zero expectation under conditional independence, as long as either one of the propensity score models, or either one of the outcome models is correctly specified. And our proposed test statistic is shown to be asymptotically normal under the null hypothesis, which provides a valid test when models for both propensity scores or models for both outcomes are correctly specified. We present the performance of our proposed test in a series of simulation studies and show that our test controls Type I error rate, is powerful and is robust.