Department of Biostatistics, University Of North Carolina, Chapel Hill, NC, United States.
Lifetime Data Anal. 2022 Oct;28(4):744-763. doi: 10.1007/s10985-022-09566-4. Epub 2022 Aug 8.
There is a growing interest in precision medicine, where a potentially censored survival time is often the most important outcome of interest. To discover optimal treatment regimens for such an outcome, we propose a semiparametric proportional hazards model by incorporating the interaction between treatment and a single index of covariates through an unknown monotone link function. This model is flexible enough to allow non-linear treatment-covariate interactions and yet provides a clinically interpretable linear rule for treatment decision. We propose a sieve maximum likelihood estimation approach, under which the baseline hazard function is estimated nonparametrically and the unknown link function is estimated via monotone quadratic B-splines. We show that the resulting estimators are consistent and asymptotically normal with a covariance matrix that attains the semiparametric efficiency bound. The optimal treatment rule follows naturally as a linear combination of the maximum likelihood estimators of the model parameters. Through extensive simulation studies and an application to an AIDS clinical trial, we demonstrate that the treatment rule derived from the single-index model outperforms the treatment rule under the standard Cox proportional hazards model.
人们对精准医学越来越感兴趣，而潜在删失的生存时间通常是最受关注的重要结果。为了发现此类结果的最佳治疗方案，我们通过未知单调链接函数将治疗与单个协变量指数之间的交互作用纳入半参数比例风险模型。该模型足够灵活，可以允许非线性的治疗-协变量交互作用，同时为治疗决策提供了一个临床可解释的线性规则。我们提出了一种筛子最大似然估计方法，其中基线风险函数采用非参数估计，未知链接函数通过单调二次 B 样条进行估计。我们证明了所得到的估计量是一致的，并且具有渐近正态性，其协方差矩阵达到了半参数效率边界。最优治疗规则自然是模型参数的最大似然估计的线性组合。通过广泛的模拟研究和对艾滋病临床试验的应用，我们表明，单指数模型得出的治疗规则优于标准 Cox 比例风险模型下的治疗规则。
