Mutual Information Technique in Assessing Crosstalk through a Random-Pairing Bootstrap Method

Abstract

Crosstalk plays a critical role in prevention research to promote purposeful behavior change through randomized controlled trials. However, two challenges prevent researchers from assessing crosstalk between subjects in the intervention and the control conditions that may contaminate an intervention trial. First, it is very hard if not impossible to identify who in the intervention group have talked with whom in the control group; therefore the crosstalk effect cannot be statistically evaluated. Second no method is readily available to quantify crosstalk even if we know who has talked with whom. To overcome the challenges, we devised the random-pairing bootstrap (RPB) method based on statistical principles and adapted the mutual information (MI) technique from the information sciences. The established RPB method provides a novel approach for researchers to identify participants in the intervention and the control groups who might have talked with each other; the MI itself is an analytical method capable of quantifying both linear and nonlinear relationships on a variable between two groups of subjects who might have experienced information exchange. An MI measure therefore provides evidence supporting the effect from crosstalk on a target variable with data generated through RPB. To establish the PRB-MI methodology, we first conducted a systematic test with simulated data. We then analyzed empirical data from a randomized controlled trial (n=1360) funded by the National Institute of Health. Analytical results with simulated data indicate that RBP-MI method can effectively detect a known crosstalk effect with different effect sizes. Analytical results with empirical data show that effects from within-group crosstalk are greater than those of between-group crosstalk, which is within our expectation. These findings suggest the validity and utility of the RBP-MI method in behavioral intervention research. Further research is needed to improve the method.