Concordance-assisted learning for estimating optimal individualized treatment regimes

We propose new concordance-assisted learning for estimating optimal individualized treatment regimes. We first introduce a type of concordance function for prescribing treatment and propose a robust rank regression method for estimating the concordance function. We then find treatment regimes, up to a threshold, to maximize the concordance function, named the prescriptive index. Finally, within the class of treatment regimes that maximize the concordance function, we find the optimal threshold to maximize the value function. We establish the rate of convergence and asymptotic normality of the proposed estimator for parameters in the prescriptive index. An induced smoothing method is developed to estimate the asymptotic variance of the estimator. We also establish the (Formula presented.) -consistency of the estimated optimal threshold and its limiting distribution. In addition, a doubly robust estimator of parameters in the prescriptive index is developed under a class of monotonic index models. The practical use and effectiveness of the methodology proposed are demonstrated by simulation studies and an application to an acquired immune deficiency syndrome data set.