Keywords: Precision medicine, statistical inference, confidence measure, adaptive design
Personalized decision rule in precision medicine can be viewed as a “discrete parameter”, for which theoretical development for statistical inference is lagged behind. In this talk, we propose a new way to quantify the estimation uncertainty in a personalized decision based on recent developments of confidence distribution (CD). Specifically, in a parametric regression model setup, suppose the decision for treatment versus control for an individual xa is determined by a linear decision rule Da = I(xa ß> xa ?), where ß and ? are unknown regression coefficients in models for potential outcomes of treatment and control, respectively. The data-driven decision hat-Da relies on the estimates of ß and ?, which in turn introduces uncertainty on the decision. In this work, we propose to find a CD for ?a =xaß - xa? and compute a “confidence measure” of the decision {Da = 1} = {?a > 0}. This measure has a value between 0 and 1, and provides a frequency-based assessment on how reliable our decision is. For example, if the confidence measure of the decision {Da = 1} is 63%, then we know that, out of 100 patients who are the same as patient xa, 63 will benefit to have the treatment and 38 will be better off to be in the control group. Numerical study suggests that this new measurement is inline with classical assessments (such as sensitivity, specificity, etc.), but different from the classical assessments, this measurement can be directly computed from the observed data without the need to know the truth of {Da = 1} or {Da = 0}. Utility of this new measure will also be demonstrated in an application of an adaptive-design clinical trial. (Joint work with Yilei Zhan and Sijian Wang)