A Robust Alternative to the Schemper–Henderson Estimator of Prediction Error

Summary In clinical applications, the prediction error of survival models has to be taken into consideration to assess the practical suitability of conclusions drawn from these models. Different approaches to evaluate the predictive performance of survival models have been suggested in the literature. In this article, we analyze the properties of the estimator of prediction error developed by Schemper and Henderson (2000 , Biometrics 56, 249–255), which quantifies the absolute distance between predicted and observed survival functions. We provide a formal proof that the estimator proposed by Schemper and Henderson is not robust against misspecification of the survival model, that is, the estimator will only be meaningful if the model family used for deriving predictions has been specified correctly. To remedy this problem, we construct a new estimator of the absolute distance between predicted and observed survival functions. We show that this modified Schemper–Henderson estimator is robust against model misspecification, allowing its practical application to a wide class of survival models. The properties of the Schemper–Henderson estimator and its new modification are illustrated by means of a simulation study and the analysis of two clinical data sets.     

血清泌乳素水平对泌乳素瘤患者的临床价值研究

目的:分析术前血清泌乳素水平对泌乳素瘤患者的临床价值。方法:选择2011年1月至2016年12月于青岛大学附属医院行垂体腺瘤切除术且术前测得泌乳素(prolactin,PRL)水平、术后行病理免疫组化染色的垂体腺瘤164例,通过Spearman相关分析PRL水平与肿瘤大小的相关性,通过Kappa值判断PRL水平与病理诊断的一致性。采用ROC曲线获得PRL水平最佳临床诊断临界值。结果:(1)164例垂体瘤患者中,病理诊断单激素PRL瘤25例,主要表现为男性性功能低下及头痛、头晕,女性月经紊乱、闭经、泌乳;(2)术前PRL水平与年龄、性别无显著相关性(P均0.05),与肿瘤大小呈中度正相关(r=0.530,P0.05);(3)以正常范围上限值(23.3 ng/m L)为基线,分别以PRL23.3 ng/mL(1倍)、46.6 ng/m L(2倍)、69.9 ng/ml(3倍)、100 ng/mL、150 ng/m L、200 ng/mL为诊断标准,与病理免疫组化的一致性分析显示PRL69.9ng/m L作为诊断标准时符合率和Kappa系数最高,分别为82.3%和0.533;(4)以病理免疫组化作为诊断金标准作泌乳素瘤ROC曲线,以血清PRL为69.785 ng/m L作为诊断标准时,曲线下面积最大,此时符合率和Kappa系数分别为82.3%和0.553,灵敏度49.1%,特异度98.3%。结论:泌乳素瘤血清学诊断与病理免疫组化诊断一致性较高,血清PRL水平69.9 ng/mL(3倍于正常上限值)是诊断泌乳素瘤的最佳参考值。     

眼镜蛇入蛰前和出蛰后血液粘性的变化

利用血液流变学的理论和技术对入蛰前和出蛰后的眼镜蛇血液进行粘滞性、浓稠性及血细胞聚集性的比较分析,发现:(一)眼镜蛇的血液处于低粘滞性、低浓稠性及血细胞低聚集性的状态。(二)眼镜蛇出蛰后血液粘性比入蛰前非常显著增高,血液流速减慢,致使组织器官血液供应不足,影响了眼镜蛇出蛰后的活动,故其活动能力比入蛰前差。     

Using calibration weighting to adjust for nonresponse under a plausible model

When we estimate the population total for a survey variableor variables, calibration forces the weighted estimates of certaincovariates to match known or alternatively estimated populationtotals called benchmarks. Calibration can be used to correctfor sample-survey nonresponse, or for coverage error resultingfrom frame undercoverage or unit duplication. The quasi-randomizationtheory supporting its use in nonresponse adjustment treats responseas an additional phase of random sampling. The functional formof a quasi-random response model is assumed to be known, itsparameter values estimated implicitly through the creation ofcalibration weights. Unfortunately, calibration depends uponknown benchmark totals while the covariates in a plausible modelfor survey response may not be the benchmark covariates. Moreover,it may be prudent to keep the number of covariates in a responsemodel small. We use calibration to adjust for nonresponse whenthe benchmark model and covariates may differ, provided thenumber of the former is at least as great as that of the latter.We discuss the estimation of a total for a vector of surveyvariables that do not include the benchmark covariates, butthat may include some of the model covariates. We show how tomeasure both the additional asymptotic variance due to the nonresponsein a calibration-weighted estimator and the full asymptoticvariance of the estimator itself. All variances are determinedwith respect to the randomization mechanism used to select thesample, the response model generating the subset of sample respondents,or both. Data from the U.S. National Agricultural StatisticalService's 2002 Census of Agriculture and simulations are usedto illustrate alternative adjustments for nonresponse. The paperconcludes with some remarks about adjustment for coverage error.     

Empirical Bayes Gibbs sampling

The wide applicability of Gibbs sampling has increased the use of more complex and multi-level hierarchical models. To use these models entails dealing with hyperparameters in the deeper levels of a hierarchy. There are three typical methods for dealing with these hyperparameters: specify them, estimate them, or use a 'flat' prior. Each of these strategies has its own associated problems. In this paper, using an empirical Bayes approach, we show how the hyperparameters can be estimated in a way that is both computationally feasible and statistically valid.     

Robustness of an S‐Estimator in the One‐Way Random Effects Model

An S‐estimator is defined for the one‐way random effects model, analogous to an S‐estimator in the model of i.i.d. random vectors. The estimator resembles the multivariate S‐estimator with respect to existence and weak continuity. The proof of existence of the estimator yields in addition an upper bound for the breakdown point of the S‐estimator of one of the variance components which is rather low. An improvement of the estimator is proposed which overcomes this deficiency. Nevertheless this estimator is an example that new problems of robustness arise in more structured models.