A comparison of several methods of estimating the survival function when there is extreme right censoring

When there is extreme censoring on the right, the Kaplan-Meier product-limit estimator is known to be a biased estimator of the survival function. Several modifications of the Kaplan-Meier estimator are examined and compared with respect to bias and mean squared error.     

What price Kaplan-Meier?

The asymptotic efficiency of the Kaplan-Meier product-limit estimator, relative to the maximum likelihood estimator of a parametric survival function, is examined under a random-censoring model.     

Nonparametric estimation of the survival function when cause of death is uncertain

A nonparametric estimator for the survival function, accommodating censored survival times and uncertainty in the assignment of cause of death, is proposed. For example, in a carcinogenicity experiment the data on each animal may consist of an observed age-at-death and some indication of the probability that the tumor type under study caused death. An estimator of the net survival function, for time-to-death due to the cause of interest, is developed. Under certain assumptions, the proposed estimator is consistent and asymptotically normally distributed. Monte Carlo simulations were used to compare this estimator with the Kaplan-Meier estimator. Forcing the cause of death to be specified with certainty, as required by the Kaplan-Meier estimator, may result in substantial biases.     

Dynamic comparison of Kaplan-Meier proportions: monitoring a randomized clinical trial with a long-term binary endpoint.

The approach to early termination for efficacy in a trial where events occur over time but the primary question of interest relates to a long-term binary endpoint is not straightforward. This article considers comparison of treatment groups with Kaplan-Meier (KM) proportions evaluated at increasing times from randomization, at increasing calendar testing times. This strategy is employed to improve the ability to detect important treatment effects and provide critical treatments to patients in a timely manner. This dynamic Kaplan-Meier (DKM) approach is shown to be robust; that is, it produces high power and early termination time across a wide range of circumstances. In contrast, a fixed time KM comparison and the log-rank test are both shown to be more variable in performance. Practical considerations of implementing the DKM method are discussed.     

Estimating number of events from the Kaplan-Meier curve for incorporation in a literature-based meta-analysis: what you don't see you can't get!

In literature-based meta-analyses of time-to-event data, the number of events in the treated and control groups together with the total number of patients randomized to the two treatment arms are often used as summary statistics. If interest is in mortality at a specified moment in time, the number of events can, in most cases, only be obtained from the Kaplan-Meier curve. The estimated number of events, however, is typically larger than the true number of events. The effect of this overestimation on the Mantel-Haenszel test and the odds ratio is studied in this paper. From these results, it can be concluded that the number of events should not be estimated from the Kaplan-Meier curves for meta-analytic purposes unless virtually no patients are lost to follow-up or censored and there are still many patients at risk in the two groups at the time at which the number of events is to be determined.     

Population-based rates of revision of primary total hip arthroplasty: a systematic review

Background

Most research on failure leading to revision total hip arthroplasty (THA) is reported from single centers. We searched PubMed between January 2000 and August 2010 to identify population- or community-based studies evaluating ten-year revision risks. We report ten-year revision risk using the Kaplan-Meier method, stratifying by age and fixation technique.

Results

Thirteen papers met the inclusion criteria. Cemented prostheses had Kaplan-Meier estimates of revision-free implant survival of ten years ranging from 88% to 95%; uncemented prostheses had Kaplan-Meier estimates from 80% to 85%. Estimates ranged from 72% to 86% in patients less than 60 years old and from 90 to 96% in older patients.

Conclusion

Data reported from national registries suggest revision risks of 5 to 20% ten years following primary THA. Revision risks are lower in older THA recipients. Uncemented implants may have higher ten-year rates of revision, regardless of age.     

Simultaneous inferences on the contrast of two hazard functions with censored observations

In survival analysis, often times the pattern of instantaneous risk over time is more interesting than that of the cumulative risk. For this case, a nonparametric hazard function estimate is more appropriate for summarizing the risk experience of a group of patients than the corresponding Kaplan-Meier estimate. In comparing a new treatment with a standard therapy, it is important to know if the treatment loses it potency during the follow-up period, and if it does, one would like to know when it becomes ineffective. Unfortunately, with a plot of the differences of two Kaplan-Meier curves, it is rather difficult to capture such temporal trends. In this article, we propose simple procedures for constructing confidence bands for the contrast of two hazard functions with censored data. The simultaneous interval estimates are quite useful for identifying possible values of the contrast over time with a certain degree of confidence. The new proposals are illustrated with an example and a small simulation study.     

Survival estimation using splines

A nonparametric maximum likelihood procedure is given for estimating the survivor function from right-censored data. It approximates the hazard rate by a simple function such as a spline, with different approximations yielding different estimators. A special case is that proposed by Nelson (1969, Journal of Quality Technology 1, 27-52) and Altshuler (1970, Mathematical Biosciences 6, 1-11). The estimators are uniformly consistent and have the same asymptotic weak convergence properties as the Kaplan-Meier (1958, Journal of the American Statistical Association 53, 457-481) estimator. However, in small and in heavily censored samples, the simplest spline estimators have uniformly smaller mean squared error than do the Kaplan-Meier and Nelson-Altshuler estimators. The procedure is extended to estimate the baseline hazard rate and regression coefficients in the Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-220) proportional hazards model and is illustrated using experimental carcinogenesis data.     

JMJD6在胃癌组织中的表达及意义

目的:检测JMJD6蛋白在胃癌组织及相应癌旁正常组织中的表达情况,并分析JMJD6蛋白表达与胃癌患者临床病理参数及预后的关系。方法:应用免疫组织化学方法检测JMJD6蛋白在胃癌组织及相应癌旁正常组织中的表达情况,进一步用Kaplan-Meier生存分析、COX比例风险回归模型等统计学方法研究JMJD6表达与胃癌患者临床病理参数及预后的关系。结果:JMJD6在胃癌组织中的表达阳性率显著高于癌旁正常组织(P=0.001);JMJD6在胃癌组织的高表达与肿瘤临床分期(P=0.008)、病理分级(P=0.001)、局部浸润深度(P=0.028)、有无淋巴结转移(P=0.001)等显著相关;Kaplan-Meier生存分析结果表明JMJD6高表达的胃癌患者术后总体生存率显著低于JMJD6低表达的患者(P=0.023)。结论:JMJD6在胃癌的发生发展中可能发挥了癌基因样作用,可能作为胃癌治疗的潜在靶点。     

Inference for the proportional hazards model with misclassified discrete-valued covariates

We consider the Cox proportional hazards model with discrete-valued covariates subject to misclassification. We present a simple estimator of the regression parameter vector for this model. The estimator is based on a weighted least squares analysis of weighted-averaged transformed Kaplan-Meier curves for the different possible configurations of the observed covariate vector. Optimal weighting of the transformed Kaplan-Meier curves is described. The method is designed for the case in which the misclassification rates are known or are estimated from an external validation study. A hybrid estimator for situations with an internal validation study is also described. When there is no misclassification, the regression coefficient vector is small in magnitude, and the censoring distribution does not depend on the covariates, our estimator has the same asymptotic covariance matrix as the Cox partial likelihood estimator. We present results of a finite-sample simulation study under Weibull survival in the setting of a single binary covariate with known misclassification rates. In this simulation study, our estimator performed as well as or, in a few cases, better than the full Weibull maximum likelihood estimator. We illustrate the method on data from a study of the relationship between trans-unsaturated dietary fat consumption and cardiovascular disease incidence.     

Maximum of the weighted Kaplan-Meier tests with application to cancer prevention and screening trials

A class of maximum weighted Kaplan-Meier test statistics is described where the weight functions are chosen from a family of smooth functions. The investigated test statistic is robust and sensitive to a variety of alternatives that are often observed in cancer prevention and screening trials. A simulation study is performed to compare the size and power properties between the proposed test statistics and some existing ones. We illustrate the procedure using data from a clinical trial of a breast cancer screening program.     

Comparative experience with smooth and polyurethane breast implants using the Kaplan-Meier method of survival analysis.

Smooth-walled silicone implants have been widely used in breast surgery. Capsular contracture, causing undesirable firmness and spherical deformity, has been a common problem. Recent studies suggest that polyurethane-covered breast implants are associated with a lower incidence of capsular contracture. The statistical methodology employed in some of these studies, however, may be subject to criticism. Between July of 1984 and June of 1990 (72 months), 427 polyurethane breast implants were used in 279 patients and 439 smooth prostheses were used in 250 patients for a variety of aesthetic and reconstructive procedures. The occurrence of capsular contracture was carefully monitored and then analyzed using the Kaplan-Meier method of survival analysis. This method is particularly well suited to analysis of these types of clinical data because it allows for the fact that contractures occur at varying intervals after surgery and that follow-up of patients is incomplete. The probability of capsular contracture with smooth-walled prostheses was found to be significantly greater than with polyurethane-covered implants in each group of patients studied (p less than 0.05). Other complications occurred at a similar rate regardless of prosthesis type. This study supports the belief that polyurethane breast implants have a lower contracture rate; furthermore, it introduces the Kaplan-Meier method for analyzing the outcome of alternative plastic surgical therapies.     

Imprinting effect in premature ovarian failure confined to paternally inherited fragile X premutations

Fragile X premutations are considered to be a risk factor for premature ovarian failure (POF), which is usually defined as menopause at age <40 years. Since premutations may be inherited from either the mother or the father, we evaluated the influence of the inheritance pattern on the duration of reproductive life in female carriers. The occurrence of POF and age at menopause in women with a paternally inherited fragile X premutation (PIP) were compared to those in women with a maternally inherited fragile X premutation (MIP). We identified 148 women in whom the parental origin of the premutation could be determined. In 109 of these women we were able to establish whether POF had occurred: 82 women had a PIP, and 27 had a MIP. Twenty-three of the women (28%) with a PIP had POF, versus only 1 (3.7%) with a MIP (two -tailed Fisher's exact test; P=. 007). Kaplan-Meier analysis of all 148 premutations showed that the age at menopause was significantly lower in the women with a PIP than in the woman with a MIP (Breslow test in Kaplan-Meier analysis; P=.003). Our data strongly suggest that, when POF occurs in fragile X premutation carriers, a considerable proportion of the premutations are inherited paternally (parent-of-origin effect). We hypothesize that this may be owing to a paternal genomic imprinting effect.     

CFHR3 is a potential novel biomarker for hepatocellular carcinoma

Complement factor H-related 3 (CFHR3) is a protein-coding gene acting in various diseases. However, its prognostic values of CFHR3 in hepatocellular carcinoma (HCC) are not understandable. Therefore, we present a further study on CFHR3 in HCC. CFHR3 expression data were acquired from The Cancer Genome Atlas (TCGA) and the International Cancer Genome Consortium (ICGC). We compared the differential expression of CFHR3 between the low-stage (stage I and II) and high-stage (stage III and IV) patients with HCC in the TCGA and ICGC cohorts. Furthermore, we assessed the CFHR3 expression as a prognostic marker using the Kaplan-Meier survival analysis, univariate, and multivariate analysis. The Kaplan-Meier analysis declared that CFHR3 overexpression was correlated with a good prognosis for HCC patients. Multivariate analysis proved the prognostic significance of CFHR3 expression levels (P < .001 and .003 for TCGA and ICGC, respectively). Immune-related scores in low-risk cohorts were higher than high-risk cohorts. Gene set enrichment analysis implied that the low CFHR3 expression phenotype was significantly enriched in critical biological functions and pathways and was associated with tumorigenesis, such as regulation of cell activation cycle, and the WNT and NOTCH signal pathway. Above all, CFHR3 could be a novel prognostic biomarker and therapeutic target for HCC.     

Metaplastic breast cancer: Treatment and prognosis by molecular subtype

BackgroundMetaplastic breast cancer (MBC) is a rare and aggressive subtype of breast. However, the effect of molecular subtype on treatment and prognosis of MBC remains unclear.Patients and methodsThe Surveillance, Epidemiology, and End Results database was used to analyze patients with MBC between 2010 and 2016. Molecular subtype was stratified to TN group (ER and PR-/HER2-), HER2 group (ER and PR-/HER2+, ER/PR+ and HER2+), and HR group (ER/PR+ and HER2-). The breast cancer-specific survival (BCSS) differences were estimated using multivariate Cox regression model and Kaplan-Meier curves.ResultsWe included 1665 patients with median follow-up time of 27 months (range 0–83 months). 1154 (69.3%), 65 (3.9%), and 446 (26.8%) patients presented in TN group, HER2 group, and HR group, respectively. On multivariate Cox analysis, the prognosis was related to age, tumor size, regional node metastasis, and surgery. Molecular subtype remained no impact on BCSS. Radiotherapy (RT) was associated with better prognosis. Patients cannot benefit from chemotherapy. In Kaplan-Meier curve, triple-negative (P = 0.047) and HR-positive (P = 0.006) patients receiving RT had a superior BCSS than that not RT. HER2-positive patients cannot benefit from RT. However, adjusted Kaplan-Meier survival model showed that triple-negative (P = 0.019) but not HER2-positive (P = 0.575) or HR-positive (P = 0.574) patients receiving RT had a superior BCSS than that not RT.ConclusionsMolecular subtype is not associated with the better prognosis of MBC. Patients could benefit from RT. However, triple-negative but not HR-positive or HER2-positive patients have superior survival after receiving RT.     

An Overview of Precedence-Type Tests for Censored Data

Precedence tests are simple yet robust nonparametric procedures useful for comparing two or more distributions. In this paper precedence-type tests are considered when the data contain some censored observations. Generalizing the precedence statistic for uncensored data, the precedence tests for censored data are based on the Kaplan-Meier estimators of the respective distribution functions and the corresponding quantile functions. The literature is reviewed for some two-sample as well as some multi-sample problems.     

死亡相关的LncRNAs在甲状腺癌中的预后价值及预后风险模型构建

目的:探讨铁死亡相关的长链非编码RNAs(LncRNAs)在甲状腺癌中的预后价值并构建预后风险模型。方法:从癌症基因组图谱(TCGA)数据库下载甲状腺癌的转录本数据和临床数据,铁死亡相关的基因数据集是从铁死亡数据库(http://www.zhounan.org/ferrdb/)下载的259个基因集。得到铁死亡相关LncRNAs,与患者临床信息合并后,通过单因素Cox回归分析和Kaplan-Meier生存分析两种方法得到与甲状腺癌预后相关的铁死亡LncRNAs,通过R的survival包构建COX模型以此来建立最佳预后风险模型并予以验证。结果:获得30个铁死亡相关的LncRNAs,多因素cox分析得到10个与甲状腺癌预后相关的铁死亡LncRNAs,包括AL136366.1、AL162231.2、CRNDE、AC004918.3、LINC02471、AC092279.1、AC046143.1、LINC02454、DOCK9-DT、AC008063.1。Kaplan-Meier生存分析表明高风险组预后较差。单因素和多因素Cox分析表明风险评分可以作为独立预后因子。KEGG通路富集分析发现,差异基因可能与嘧啶代谢、核苷酸切除修复、NOTCH_信号通路等通路有关。结论:通过生物信息学方法筛选出10个与甲状腺癌预后的铁死亡相关LncRNAs,并成功构建预后风险模型。     

High expression of MUC20 drives tumorigenesis and predicts poor survival in endometrial cancer

Mucins (MUCs) have been reported to play a critical role in the tumorigenesis of different cancers. This study was performed to explore the effect of MUC20 in endometrial cancer (EC). A total of 541 patients with EC were examined from The Cancer Genome Atlas. The relationship between MUC20 expression and clinical characteristics was analyzed with the Wilcoxon signed-rank test and logistic regression. The Kaplan-Meier method and the Cox regression model was performed to evaluate the prognosis. Gene set enrichment analysis (GSEA) was conducted. MUC20 high expression was associated with age, histology, positive peritoneal cytology, advanced stage, and lymph node metastasis (P < 0.05). Kaplan-Meier survival showed that patients with MUC20 high expression had a poorer prognosis than those with MUC20 low expression. Furthermore, multivariate analysis showed that MUC20 high expression was an independent prognostic factor for worse overall survival (hazard ratio = 1.93, 95% confidence interval = 1.00-3.74). Moreover, interferon α/γ response, cell-cell adhesion, O-glycan processing, and reactive oxygen species (ROS) pathway were associated with MUC20 high expression. MUC20 high expression may be a potential prognostic molecular factor of poor survival. The interferon α/γ response, cell-cell adhesion, O-glycan processing, and ROS pathway may be the key processes regulated by MUC20 in EC.     

Regularized estimation in the accelerated failure time model with high-dimensional covariates

We consider two regularization approaches, the LASSO and the threshold-gradient-directed regularization, for estimation and variable selection in the accelerated failure time model with multiple covariates based on Stute's weighted least squares method. The Stute estimator uses Kaplan-Meier weights to account for censoring in the least squares criterion. The weighted least squares objective function makes the adaptation of this approach to multiple covariate settings computationally feasible. We use V-fold cross-validation and a modified Akaike's Information Criterion for tuning parameter selection, and a bootstrap approach for variance estimation. The proposed method is evaluated using simulations and demonstrated on a real data example.     

A Comparison of Robust Estimators in the Presence of Arbitrarily Right Censored Data

Robust estimation of a location parameter is considered when the data from an unknown symmetric population are subject to arbitrary right-censorship. Comparisons are made between various M-estimators, several L-estimators (trimmed means), and the Kaplan-Meier median. Ten sampling distributions, two uniform censoring distributions, and three sample sizes are examined. A Cauchy censoring distribution is also considered when the sample size is equal to twenty for each of the ten sampling distributions. Performance is based on the estimated mean square error.