In this article, we propose a 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 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 convergence rate 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 proposed estimator. We also establish the n1/3-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 proposed methodology are demonstrated by simulation studies and an application to an AIDS data.

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∑ i=1 (1 − ζ i)ξ i (τ) + o (ν,τU ] (1). 在给定 {A i , Y i , δ i , Z i } n i=1 的条件下, K * (τ) 弱收敛到一个均值为 0、 协方差矩阵Ω(s, t) = E{ξ i (s)ξ i (t) T } 的 Gauss 过程. 当给定的模型成立时, 对于 s, t ∈ [ν, τ U ],Ω(s, t) 几乎处处收敛到 Ω(s, t).

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