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区间删失数据的统一非参数 fiducial 推断AI 解读

Censored data, where the event time is partially observed, are challenging for survival probability estimation. In this article, we introduce a novel nonparametric fiducial approach to interval-censored data, including right-censored, current status, case II censored, and mixed case censored data. The proposed approach leveraging a simple Gibbs sampler has a useful property of being “one size fits all,” that is, the proposed approach automatically adapts to all types of…

用 V-learning 估计移动健康中的动态处理策略AI 解读

The vision for precision medicine is to use individual patient characteristics to inform a personalized treatment plan that leads to the best possible health-care for each patient. Mobile technologies have an important role to play in this vision as they offer a means to monitor a patient's health status in real-time and subsequently to deliver interventions if, when, and in the dose that they are needed. Dynamic treatment regimes formalize individualized treatment plans as…

中等高维核机器中的特征剔除AI 解读

We develop an approach for feature elimination in statistical learning with kernel machines, based on recursive elimination of features. We present theoretical properties of this method and show that it is uniformly consistent in finding the correct feature space under certain generalized assumptions. We present a few case studies to show that the assumptions are met in most practical situations and present simulation results to demonstrate performance of the proposed…

竞争风险子分布的加权非参数极大似然估计AI 解读

Direct regression modeling of the subdistribution has become popular for analyzing data with multiple, competing event types. All general approaches so far are based on non-likelihood based procedures and target covariate effects on the subdistribution. We introduce a novel weighted likelihood function that allows for a direct extension of the Fine-Gray model to a broad class of semiparametric regression models. The model accommodates time-dependent covariate effects on the…

用于估计个体化治疗规则的残差加权学习AI 解读

Personalized medicine has received increasing attention among statisticians, computer scientists, and clinical practitioners. A major component of personalized medicine is the estimation of individualized treatment rules (ITRs). Recently, Zhao et al. (2012) proposed outcome weighted learning (OWL) to construct ITRs that directly optimize the clinical outcome. Although OWL opens the door to introducing machine learning techniques to optimal treatment regimes, it still has…

评论：多阶段化疗方案的 Q-learning 与 O-learningAI 解读

Xu, Müller, Wahed, and Thall proposed a Bayesian model to analyze an acute leukemia study involving multi-stage chemotherapy regimes. We discuss two alternative methods, Q-learning and O-learning, to solve the same problem from the machine learning point of view. The numerical studies show that these methods can be flexible and have advantages in some situations to handle treatment heterogeneity while being robust to model misspecification.

不同模型误设程度下变点模型的渐近理论AI 解读

Change-point models are widely used by statisticians to model drastic changes in the pattern of observed data. Least squares/maximum likelihood based estimation of change-points leads to curious asymptotic phenomena. When the change-point model is correctly specified, such estimates generally converge at a fast rate ($n$) and are asymptotically described by minimizers of a jump process. Under complete mis-specification by a smooth curve, that is, when a change-point model is…

In this paper, we introduce a new type of tree-based method, reinforcement learning trees (RLT), which exhibits significantly improved performance over traditional methods such as random forests (Breiman, 2001) under high-dimensional settings. The innovations are three-fold. First, the new method implements reinforcement learning at each selection of a splitting variable during the tree construction processes. By splitting on the variable that brings the greatest future…

估计最优动态治疗方案的新统计学习方法AI 解读

Dynamic treatment regimes (DTRs) are sequential decision rules for individual patients that can adapt over time to an evolving illness. The goal is to accommodate heterogeneity among patients and find the DTR which will produce the best long-term outcome if implemented. We introduce two new statistical learning methods for estimating the optimal DTR, termed backward outcome weighted learning (BOWL), and simultaneous outcome weighted learning (SOWL). These approaches convert…

潜在监督学习AI 解读

training labels which serve as surrogates for the unobserved class labels. A specific model is investigated where the surrogate variable arises from a two-component Gaussian mixture with unknown means and variances, and the component membership is determined by a hyperplane in the covariate space. The estimation of the separating hyperplane and the Gaussian mixture parameters forms what shall be referred to as the change-line classification problem. A data-driven sieve…

使用结局加权学习估计个体化治疗规则AI 解读

There is increasing interest in discovering individualized treatment rules for patients who have heterogeneous responses to treatment. In particular, one aims to find an optimal individualized treatment rule which is a deterministic function of patient specific characteristics maximizing expected clinical outcome. In this paper, we first show that estimating such an optimal treatment rule is equivalent to a classification problem where each subject is weighted proportional…

递归插补生存树AI 解读

We propose recursively imputed survival tree (RIST) regression for right-censored data. This new nonparametric regression procedure uses a novel recursive imputation approach combined with extremely randomized trees that allows significantly better use of censored data than previous tree based methods, yielding improved model fit and reduced prediction error. The proposed method can also be viewed as a type of Monte Carlo EM algorithm which generates extra diversity in the…

网格现时状态数据的似然推断：边界现象与自适应程序AI 解读

In this paper, we study the nonparametric maximum likelihood estimator for an event time distribution function at a point in the current status model with observation times supported on a grid of potentially unknown sparsity and with multiple subjects sharing the same observation time. This is of interest since observation time ties occur frequently with current status data. The grid resolution is specified as cn−γ with c > 0 being a scaling constant and γ > 0 regulating the…

评论AI 解读

Inspired by the non-regular framework studied in Laber and Murphy (2011), we propose a family of adaptive classifiers. We discuss briefly their asymptotic properties and show that under the non-regular framework these classifiers have an "oracle property," and consequently have smaller asymptotic variance and smaller asymptotic test error variance than those of the original classifier. We also show that confidence intervals for the test error of the adaptive classifiers,…

删失数据的逆回归估计AI 解读

An inverse regression methodology for assessing predictor performance in the censored data setup is developed along with inference procedures and a computational algorithm. The technique developed here allows for conditioning on the unobserved failure time along with a weighting mechanism that accounts for the censoring. The implementation is nonparametric and computationally fast. This provides an efficient methodological tool that can be used especially in cases where the…

半参数模型失去可识别性时的渐近最优检验AI 解读

We consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models, where regularity conditions for profile likelihood theory fail. Exponential average tests based on integrated profile likelihood are constructed and shown to be asymptotically optimal under a weighted average power criterion with respect to a prior on the nonidentifiable aspect of the model. These results extend existing results for parametric models, which…

后验剖面分布的一般频率学派性质AI 解读

In this paper, inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution is thoroughly investigated from the frequentist viewpoint. The higher-order validity of the profile sampler obtained in Cheng and Kosorok [Ann. Statist. 36 (2008)] is extended to semiparametric models in which the infinite dimensional nuisance parameter may not have a root-n convergence rate. This is a nontrivial extension because it…

利用剖面采样器进行高阶半参数频率学推断AI 解读

We consider higher order frequentist inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution. The first order validity of this procedure established by Lee, Kosorok and Fine in [J. American Statist. Assoc. 100 (2005) 960–969] is extended to second-order validity in the setting where the infinite-dimensional nuisance parameter achieves the parametric rate. Specifically, we obtain higher order estimates of the…

“大维度、小样本”范式的边际渐近理论及微阵列应用AI 解读

The “large $p$, small $n$” paradigm arises in microarray studies, image analysis, high throughput molecular screening, astronomy, and in many other high dimensional applications. False discovery rate (FDR) methods are useful for resolving the accompanying multiple testing problems. In cDNA microarray studies, for example, $p$-values may be computed for each of $p$ genes using data from $n$ arrays, where typically $p$ is in the thousands and $n$ is less than 30. For FDR…

右删失下具有协变量阈值变点的变换模型推断AI 解读

We consider linear transformation models applied to right censored survival data with a change-point in the regression coefficient based on a covariate threshold. We establish consistency and weak convergence of the nonparametric maximum likelihood estimators. The change-point parameter is shown to be n-consistent, while the remaining parameters are shown to have the expected root-n consistency. We show that the procedure is adaptive in the sense that the nonthreshold…

现时状态数据下部分线性变换模型的惩罚对数似然估计AI 解读

We consider partly linear transformation models applied to current status data. The unknown quantities are the transformation function, a linear regression parameter and a nonparametric regression effect. It is shown that the penalized MLE for the regression parameter is asymptotically normal and efficient and converges at the parametric rate, although the penalized MLE for the transformation function and nonparametric regression effect are only n1/3 consistent. Inference…

单变量比例风险脆弱性回归模型的稳健推断AI 解读

We consider a class of semiparametric regression models which are one-parameter extensions of the Cox [J. Roy. Statist. Soc. Ser. B 34 (1972) 187–220] model for right-censored univariate failure times. These models assume that the hazard given the covariates and a random frailty unique to each individual has the proportional hazards form multiplied by the frailty. The frailty is assumed to have mean 1 within a known one-parameter family of distributions. Inference is based…

生存分析中由函数索引的一般非参数检验类AI 解读

Many of the popular nonparametric test statistics for censored survival data used in two-sample, $k$-sample trend and continuous covariate situations are special cases of a general statistic, differing only in the choice of the covariate-based label and the weight function. A weight function determines the asymptotic efficiency of its corresponding statistic in this general class. Since the true alternatives are often unknown, we may not be able to foresee which weight…

函数索引加权对数秩统计量的多适应性AI 解读

Two-sample weighted log-rank statistics are used in the presence of right censoring to test whether failure times from two populations have different survival distributions. Kosorok has showed that large families of these statistics form stochastic processes indexed by weight functions, and that these function-indexed statistics can be used to construct versatile test procedures simultaneously sensitive to a wide array of both ordered hazards and stochastic ordering…