Flexible estimation of the mean outcome under a treatment regimen (i.e., value function) is the key step toward personalized medicine. We define our target parameter as a conditional value function given a set of baseline covariates which we refer to as a stratum based value function. We focus on semiparametric class of decision rules and propose a sieve based nonparametric covariate adjusted regimen-response curve estimator within that class. Our work contributes in several ways. First, we propose an inverse probability weighted nonparametrically efficient estimator of the smoothed regimen-response curve function. We show that asymptotic linearity is achieved when the nuisance functions are undersmoothed sufficiently. Asymptotic and finite sample criteria for undersmoothing are proposed. Second, using Gaussian process theory, we propose simultaneous confidence intervals for the smoothed regimen-response curve function. Third, we provide consistency and convergence rate for the optimizer of the regimen-response curve estimator; this enables us to estimate an optimal semiparametric rule. The latter is important as the optimizer corresponds with the optimal dynamic treatment regimen. Some finite-sample properties are explored with simulations.

翻译：治疗方案下平均结局（即价值函数）的灵活估计是实现个性化医疗的关键步骤。我们将目标参数定义为给定一组基线协变量的条件价值函数，并称之为基于分层的价值函数。本文聚焦于半参数类决策规则，并在此框架内提出了一种基于筛选的非参数协变量调整治疗方案-响应曲线估计量。我们的贡献体现在以下几个方面：首先，我们提出了光滑治疗方案-响应曲线函数的逆概率加权非参数有效估计量。研究表明，当干扰函数得到充分欠光滑处理时，可实现渐近线性性。我们进一步提出了欠光滑处理的渐近与有限样本准则。其次，基于高斯过程理论，我们构建了光滑治疗方案-响应曲线函数的联合置信区间。第三，我们证明了治疗方案-响应曲线估计量优化器的一致性与收敛速率，从而能够估计最优半参数规则。后者具有重要意义，因为优化器对应于最优动态治疗方案。通过模拟研究，我们探索了部分有限样本性质。