Individual risk prediction: Comparing random forests with Cox proportional-hazards model by a simulation study

With big data becoming widely available in healthcare, machine learning algorithms such as random forest (RF) that ignores time-to-event information and random survival forest (RSF) that handles right-censored data are used for individual risk prediction alternatively to the Cox proportional hazards (Cox-PH) model. We aimed to systematically compare RF and RSF with Cox-PH. RSF with three split criteria [log-rank (RSF-LR), log-rank score (RSF-LRS), maximally selected rank statistics (RSF-MSR)]; RF, Cox-PH, and Cox-PH with splines (Cox-S) were evaluated through a simulation study based on real data. One hundred eighty scenarios were investigated assuming different associations between the predictors and the outcome (linear/linear and interactions/nonlinear/nonlinear and interactions), training sample sizes (500/1000/5000), censoring rates (50%/75%/93%), hazard functions (increasing/decreasing/constant), and number of predictors (seven, 15 including noise variables). Methods' performance was evaluated with time-dependent area under curve and integrated Brier score. In all scenarios, RF had the worst performance. In scenarios with a low number of events (⩽70), Cox-PH was at least noninferior to RSF, whereas under linearity assumption it outperformed RSF. Under the presence of interactions, RSF performed better than Cox-PH as the number of events increased whereas Cox-S reached at least similar performance with RSF under nonlinear effects. RSF-LRS performed slightly worse than RSF-LR and RSF-MSR when including noise variables and interaction effects. When applied to real data, models incorporating survival time performed better. Although RSF algorithms are a promising alternative to conventional Cox-PH as data complexity increases, they require a higher number of events for training. In time-to-event analysis, algorithms that consider survival time should be used.     

Bias-reduced estimators of conditional odds ratios in matched case-control studies with unmatched confounding

We study bias-reduced estimators of exponentially transformed parameters in general linear models (GLMs) and show how they can be used to obtain bias-reduced conditional (or unconditional) odds ratios in matched case-control studies. Two options are considered and compared: the explicit approach and the implicit approach. The implicit approach is based on the modified score function where bias-reduced estimates are obtained by using iterative procedures to solve the modified score equations. The explicit approach is shown to be a one-step approximation of this iterative procedure. To apply these approaches for the conditional analysis of matched case-control studies, with potentially unmatched confounding and with several exposures, we utilize the relation between the conditional likelihood and the likelihood of the unconditional logit binomial GLM for matched pairs and Cox partial likelihood for matched sets with appropriately setup data. The properties of the estimators are evaluated by using a large Monte Carlo simulation study and an illustration of a real dataset is shown. Researchers reporting the results on the exponentiated scale should use bias-reduced estimators since otherwise the effects can be under or overestimated, where the magnitude of the bias is especially large in studies with smaller sample sizes.     

Model misspecification and bias for inverse probability weighting estimators of average causal effects

Commonly used semiparametric estimators of causal effects specify parametric models for the propensity score (PS) and the conditional outcome. An example is an augmented inverse probability weighting (IPW) estimator, frequently referred to as a doubly robust estimator, because it is consistent if at least one of the two models is correctly specified. However, in many observational studies, the role of the parametric models is often not to provide a representation of the data-generating process but rather to facilitate the adjustment for confounding, making the assumption of at least one true model unlikely to hold. In this paper, we propose a crude analytical approach to study the large-sample bias of estimators when the models are assumed to be approximations of the data-generating process, namely, when all models are misspecified. We apply our approach to three prototypical estimators of the average causal effect, two IPW estimators, using a misspecified PS model, and an augmented IPW (AIPW) estimator, using misspecified models for the outcome regression (OR) and the PS. For the two IPW estimators, we show that normalization, in addition to having a smaller variance, also offers some protection against bias due to model misspecification. To analyze the question of when the use of two misspecified models is better than one we derive necessary and sufficient conditions for when the AIPW estimator has a smaller bias than a simple IPW estimator and when it has a smaller bias than an IPW estimator with normalized weights. If the misspecification of the outcome model is moderate, the comparisons of the biases of the IPW and AIPW estimators show that the AIPW estimator has a smaller bias than the IPW estimators. However, all biases include a scaling with the PS-model error and we suggest caution in modeling the PS whenever such a model is involved. For numerical and finite sample illustrations, we include three simulation studies and corresponding approximations of the large-sample biases. In a dataset from the National Health and Nutrition Examination Survey, we estimate the effect of smoking on blood lead levels.     

具有节点偏置的高阶神经网络模型

在汪涛文献基础上提出了一个具有节点偏置的高阶神经网络模型、给出了模型的哈密顿量和学习算法,证明了学习算法的收敛性,该模型能对每一神经元自动引入一个节点偏置使得网络能够存储所有学习图样包括相关图样,其存储容量远高于Hebb—rule—like学习算法下的高阶神经网络模型.对由30个神经元组成的二阶神经网络进行了计算机仿真,结果证实了上述结论.此外,对初始突触强度对学习效果的影响和不同存储图样数目下的平均吸引半径进行了仿真计算并分析了所得结果.新模型的特点使其具有良好的应用前景     

脑部磁刺激场的理论模型

作为脑部磁刺激研究的一项基础工作,建立了刺激磁场中的球形头模型、对方形线圈在其内产生的时变磁场和感应电场进行了理论研究.导出(?).(?).(?)的解析表达式,分析了场的特性和刺激强度的分布规律.为进一步探索时变磁场对人脑的最佳刺激方式和作用机理提供了初步的理论基础.     

一种感知视觉运动信息的简化脑模型

视觉运动信息的感知过程,包括从局域运动检测到对模式整体运动的感知过程.我们以蝇视觉系统的图形-背景相对运动分辨的神经回路网络为基本框架,采用初级运动检测器的六角形阵列作为输入层,构造了一种感知视觉运动信息的简化脑模型,模拟了运动信息应该神经计算模型各个层次上的处理.该模型对差分行为实验结果作出了正确预测.本文并对空间生理整合的神经机制作了讨论.     

用胆固醇代谢的房室模型速率系数来分析动脉粥样硬化程度

理论上认为胆固醇逆向转运的速率与动脉粥样硬化程序呈负相关。但目前尚无完善的测试血浆脂蛋白－胆固醇体内代谢的方法。我们运用同位素＾３Ｈ－胆固醇示踪方法,建立房室模型,选取健康兔与ＡＳ兔对照,研究血浆脂蛋白转运胆固醇能力的差异,并结合ＡＳ兔主动脉斑块程度对比,结果验证了上述理论,此法如改用短半衰期同位素或稳定性同位素标记的胆固醇,就可用于人体,这可为临床判断ＡＳ程度提供一种无创性的新方法。     

东海带鱼的最适可捕规格

带鱼是中国东海的重要经济渔获种类,其可捕规格会随不同时期的捕捞强度而变化。为确定目前东海带鱼最适可捕规格,根据2016—2020年拖网、帆张网及延绳钓等主捕带鱼作业方式采集的带鱼样品和数据,利用FiSAT II软件对其生长、死亡参数进行估算,进而计算可捕规格。结果表明: 带鱼的拐点肛长、临界肛长、1龄鱼肛长分别为382.84、397.12、216.05 mm,50%带鱼性成熟肛长为230.38 mm,最小可捕肛长为219.23 mm。利用Beverton-Holt模型分析带鱼单位补充量渔获量可知,带鱼当前渔业参考点为:t_c=0.38 a,F=2.11,处于捕捞过度区域,并得出最适可捕肛长为364.64 mm。但过高的可捕规格会导致短期内带鱼产量急剧下降,渔民难以接受,因此,本研究综合考虑采用接近1龄鱼肛长与50%性成熟肛长作为最适可捕规格较为合适,即220 mm。     

免疫反应动力学的几个数学模型

免疫系统对抗原刺激的应答过程非常复杂,由抗原刺激导致抗体产生的现象,可借助数学模型的研究获得有意义的结果。本文讨论有关抗体产生与免疫反应的动力学的问题,介绍有关的数学模型,并根据近斯免疫学研究的进展分析了若干模型。     

相关遗传力抽样方差的估计

本文给出了单因子组和系统模型下有关相关传力及相关环境力抽样方差的估计方法。有关该参数在育种中的潜在应用其它与遗传相关之产间的相互关系也给予了一定的讨论。概括地来讲,相关遗传力具有遗传力和遗传相关的双重特征。遗传力是相关遗传力的一个特例而相关遗传力则是遗传力概念本身的扩展。用相关遗传力来表达性状间的相关遗传变异要比通常所用的遗传相关更准确一些。