Methods for comparing cumulative hazard functions in a semi-proportional hazard model.

Graphical methods based on the analysis of differences between log cumulative hazard functions are considered for a two-group semi-proportional hazard model which allows for interaction between treatments and covariates. Confidence procedures and test statistics that can be used to test for interaction and for main effects are developed. Their use is illustrated by applying them to the analysis of kidney transplant data from the University of California, San Francisco.     

Power analysis for multivariable Cox regression models

In power analysis for multivariable Cox regression models, variance of the estimated log-hazard ratio for the treatment effect is usually approximated by inverting the expected null information matrix. Because, in many typical power analysis settings, assumed true values of the hazard ratios are not necessarily close to unity, the accuracy of this approximation is not theoretically guaranteed. To address this problem, the null variance expression in power calculations can be replaced with one of the alternative expressions derived under the assumed true value of the hazard ratio for the treatment effect. This approach is explored analytically and by simulations in the present paper. We consider several alternative variance expressions and compare their performance to that of the traditional null variance expression. Theoretical analysis and simulations demonstrate that, whereas the null variance expression performs well in many nonnull settings, it can also be very inaccurate, substantially underestimating, or overestimating the true variance in a wide range of realistic scenarios, particularly those where the numbers of treated and control subjects are very different and the true hazard ratio is not close to one. The alternative variance expressions have much better theoretical properties, confirmed in simulations. The most accurate of these expressions has a relatively simple form. It is the sum of inverse expected event counts under treatment and under control scaled up by a variance inflation factor.     

非随机化医学研究中风险比的一种估计方法

目的提出一种适用于非随机化医学研究的,结合倾向指数与非参数生存分析估计风险比的方法.方法首先对倾向指数进行估计,然后对倾向指数分布分层以消除比较两组间协变量分布的不均衡.其次对分层样本用非参数生存分析的方法估计两组间发病或死亡的风险比.最后比较本法与常用的Cox模型方法并探讨其适用性.结果将本法应用于一项评价某降血脂新药效果的4期临床试验数据后显示:(1)对倾向指数分布分层后基本上消除了由于随机分组方案失败导致的新药组与传统药物组之间协变量分布的不均衡性,使得非参数生存分析方法得以应用;(2)由本法得到的新药效果的估计-风险比与由Cox模型得到的结果基本一致.结论对于非随机化医学研究,结合倾向指数进行非参数生存分析是一种新的可选择的统计方法.     

Parsimonious analysis of time-dependent effects in the Cox model

Cox's proportional hazards model can be extended to accommodate time-dependent effects of prognostic factors. We briefly review these extensions along with their varying degrees of freedom. Spending more degrees of freedom with conventional procedures (a priori defined interactions with simple functions of time, restricted natural splines, piecewise estimation for partitions of the time axis) allows the fitting of almost any shape of time dependence but at an increased risk of over-fit. This results in increased width of confidence intervals of time-dependent hazard ratios and in reduced power to confirm any time-dependent effect or even any effect of a prognostic factor. By means of comparative empirical studies the consequences of over-fitting time-dependent effects have been explored. We conclude that fractional polynomials, and similarly penalized likelihood approaches, today are the methods of choice, avoiding over-fit by parsimonious use of degrees of freedom but also permitting flexible modelling if time dependence of a usually a priori unknown shape is present in a data set. The paradigm of a parsimonious analysis of time-dependent effects is exemplified by means of a gastric cancer study.     

统计软件配伍组秩和检验及多重比较

目的：针对医学研究中常见配伍组设计等级资料数据分析工作存在的一些问题，给予统计软件技术上正确且实用的支持。方法：灵活结合秩变换理论和软件本身的一些特点，分别在统计软件SAS、SPSS以及Stata中实现配伍组设计秩和检验及其多重比较。结果：3种软件对同一数据资料进行处理，所得结论基本相同。结论：本文提供了统计软件实现该种数据分析的详细的程序、具体的操作步骤和结果解释，相关研究工作和数据分析人员可以结合不同的工作条件和个人喜好，应用不同的软件正确地完成此类数据的分析工作。     

The estimation of average hazard ratios by weighted Cox regression

Often the effect of at least one of the prognostic factors in a Cox regression model changes over time, which violates the proportional hazards assumption of this model. As a consequence, the average hazard ratio for such a prognostic factor is under‐ or overestimated. While there are several methods to appropriately cope with non‐proportional hazards, in particular by including parameters for time‐dependent effects, weighted estimation in Cox regression is a parsimonious alternative without additional parameters. The methodology, which extends the weighted k‐sample logrank tests of the Tarone‐Ware scheme to models with multiple, binary and continuous covariates, has been introduced in the nineties of the last century and is further developed and re‐evaluated in this contribution. The notion of an average hazard ratio is defined and its connection to the effect size measure P(X<Y) is emphasized. The suggested approach accomplishes estimation of intuitively interpretable average hazard ratios and provides tools for inference. A Monte Carlo study confirms the satisfactory performance. Advantages of the approach are exemplified by comparing standard and weighted analyses of an international lung cancer study. SAS and R programs facilitate application. Copyright © 2009 John Wiley & Sons, Ltd.     

A Monte Carlo approach for change-point detection in the Cox proportional hazards model

Detecting a time lag of treatment effect or identifying change points in a hazard function is of great interest and importance in survival analysis. The testing procedures hereto are primarily based on analytical approximations for the asymptotic null distribution of either the likelihood ratio test or the score test. In the presence of random censoring and/or covariates, however, the justification for the limiting distribution often requires some technical assumptions and conditions that are difficult to verify in practice. Moreover, a satisfactory asymptotic theory for testing the existence of multiple change points in hazard function has not emerged. In this paper, we consider maximal score tests for detecting change point(s) in the Cox proportional hazards model with censored data. We propose to use a simple Monte Carlo approach for assessing the statistical significance of tests. The proposed approach is applicable for testing a single change point in the Cox model with covariates and sample stratifications over various types of candidate regions, including discrete time-point sets or disjoint intervals. We also show that the proposed test statistics and the Monte Carlo procedure are well applicable under situations with multiple change points. Simulation studies and an analysis of a real data from a randomized cancer trial are conducted to demonstrate the finite-sample performance of the proposed approach.     

Practical recommendations for reporting Fine‐Gray model analyses for competing risk data

In survival analysis, a competing risk is an event whose occurrence precludes the occurrence of the primary event of interest. Outcomes in medical research are frequently subject to competing risks. In survival analysis, there are 2 key questions that can be addressed using competing risk regression models: first, which covariates affect the rate at which events occur, and second, which covariates affect the probability of an event occurring over time. The cause‐specific hazard model estimates the effect of covariates on the rate at which events occur in subjects who are currently event‐free. Subdistribution hazard ratios obtained from the Fine‐Gray model describe the relative effect of covariates on the subdistribution hazard function. Hence, the covariates in this model can also be interpreted as having an effect on the cumulative incidence function or on the probability of events occurring over time. We conducted a review of the use and interpretation of the Fine‐Gray subdistribution hazard model in articles published in the medical literature in 2015. We found that many authors provided an unclear or incorrect interpretation of the regression coefficients associated with this model. An incorrect and inconsistent interpretation of regression coefficients may lead to confusion when comparing results across different studies. Furthermore, an incorrect interpretation of estimated regression coefficients can result in an incorrect understanding about the magnitude of the association between exposure and the incidence of the outcome. The objective of this article is to clarify how these regression coefficients should be reported and to propose suggestions for interpreting these coefficients.     

The resolution of genotype x environment interaction in segregation analysis of nuclear families

A model is presented for the effects of one or two loci, a measured index of the environment and genotype x environment (G x E) interaction of risk for a discontinuous trait. Initial properties of the model are explored for the single locus case, with and without the effects of environment and G x E interaction. Seven data sets were simulated, each comprising 500 nuclear families on whom an environmental index has been measured. Maximum-likelihood estimation procedures were used to obtain parameter estimates under seven models for each data set. Likelihood ratio tests were constructed, and in all cases it was possible to identify the "correct" model for the simulated data. The matrices of information realized showed that the parameters could be estimated with acceptable precision and that the effects of genes, environment, and G x E interaction could be resolved in the simulated populations. The effects on conventional segregation analysis of ignoring the environment and G x E are considered.     

One-stage parametric meta-analysis of time-to-event outcomes

Methodology for the meta-analysis of individual patient data with survival end-points is proposed. Motivated by questions about the reliance on hazard ratios as summary measures of treatment effects, a parametric approach is considered and percentile ratios are introduced as an alternative to hazard ratios. The generalized log-gamma model, which includes many common time-to-event distributions as special cases, is discussed in detail. Likelihood inference for percentile ratios is outlined. The proposed methodology is used for a meta-analysis of glioma data that was one of the studies which motivated this work. A simulation study exploring the validity of the proposed methodology is available electronically.     

噪声危害防护措施评价分析

目的通过对10个建设项目噪声危害管理措施进行评价,为控制职业病危害提供科学依据。方法采用职业卫生学调查、职业健康检查,分析和比较工作场所不同工艺条件下,对噪声危害的综合管理措施。结果 10个项目中,90%落实了噪声的危害告知和配置了护耳器;30%对部分超标噪声岗位限制作业时限,配置隔声、消声设施,并实施职业健康体检;20%改革工艺降低噪声强度。1 124人听力检查结果中,听阈提高及观察对象的检出率分别为21.8%及2.4%。结论超标岗位在目前生产工艺未达到有效防护措施前提下,加强个体防护是防治噪声危害最为经济的方法,但实际效果需要落实相应的职业卫生管理制度。     

Does the association between self-rated health and mortality vary by social class?

Self-rated health (SRH) predicts future mortality. Individuals in different social classes with similar physical health status may have different reference levels and criteria against which they judge their health, therefore the SRH–mortality relationship may vary according to social class. We examine the relationship between SRH and mortality by occupational social class in a prospective study of 22,457 men and women aged 39–79 years, without prevalent disease, living in the general community in Norfolk, United Kingdom, recruited using general practice age–sex registers in 1993–1997 and followed up for an average of 10 years. As expected, SRH was related to subsequent mortality. The age and sex adjusted hazard ratio for mortality for those with poor compared to those with excellent SRH was 4.35 (95% confidence interval 3.38–5.59, P < 0.001). The prevalence of poor or moderate SRH was higher in manual than in non-manual classes. However, SRH was similarly related to mortality in manual and non-manual classes: when non-manual classes are compared with manual classes for each category of SRH, the 95% confidence intervals for the mortality hazard ratios overlap. There was no evidence of an interaction between social class and SRH in either men or women. Thus in this population, SRH appears to predict mortality in a similar manner in non-manual and manual classes.     

Bias due to missing exposure data using complete-case analysis in the proportional hazards regression model

We studied bias due to missing exposure data in the proportional hazards regression model when using complete-case analysis (CCA). Eleven missing data scenarios were considered: one with missing completely at random (MCAR), four missing at random (MAR), and six non-ignorable missingness scenarios, with a variety of hazard ratios, censoring fractions, missingness fractions and sample sizes. When missingness was MCAR or dependent only on the exposure, there was negligible bias (2-3 per cent) that was similar to the difference between the estimate in the full data set with no missing data and the true parameter. In contrast, substantial bias occurred when missingness was dependent on outcome or both outcome and exposure. For models with hazard ratio of 3.5, a sample size of 400, 20 per cent censoring and 40 per cent missing data, the relative bias for the hazard ratio ranged between 7 per cent and 64 per cent. We observed important differences in the direction and magnitude of biases under the various missing data mechanisms. For example, in scenarios where missingness was associated with longer or shorter follow-up, the biases were notably different, although both mechanisms are MAR. The hazard ratio was underestimated (with larger bias) when missingness was associated with longer follow-up and overestimated (with smaller bias) when associated with shorter follow-up. If it is known that missingness is associated with a less frequently observed outcome or with both the outcome and exposure, CCA may result in an invalid inference and other methods for handling missing data should be considered.     

Tests for interaction in epidemiologic studies: a review and a study of power

Tests for statistical interaction have come into increasing use in epidemiologic analysis, with most based on either an additive or multiplicative model for joint effects. Further procedures have been proposed for testing the goodness-of-fit and comparing the fit of the latter models. This paper reviews the relationships between the various tests and model comparison methods, and, for the special case of two dichotomous risk factors, presents asymptotic power functions for tests of additivity and multiplicativity. For a range of sample sizes and factor effects, the powers of the tests are computed using both the asymptotic power function and simulation studies. The powers of the tests are very low in several commonly encountered situations. In addition, convergence to the asymptotic distribution appears slow for some of the statistics. The results also indicate that likelihood comparison procedures can provide a useful adjunct to the classical hypothesis-testing approach.     

Expected value of sample information calculations in medical decision modeling.

There has been an increasing interest in using expected value of information (EVI) theory in medical decision making, to identify the need for further research to reduce uncertainty in decision and as a tool for sensitivity analysis. Expected value of sample information (EVSI) has been proposed for determination of optimum sample size and allocation rates in randomized clinical trials. This article derives simple Monte Carlo, or nested Monte Carlo, methods that extend the use of EVSI calculations to medical decision applications with multiple sources of uncertainty, with particular attention to the form in which epidemiological data and research findings are structured. In particular, information on key decision parameters such as treatment efficacy are invariably available on measures of relative efficacy such as risk differences or odds ratios, but not on model parameters themselves. In addition, estimates of model parameters and of relative effect measures in the literature may be heterogeneous, reflecting additional sources of variation besides statistical sampling error. The authors describe Monte Carlo procedures for calculating EVSI for probability, rate, or continuous variable parameters in multi parameter decision models and approximate methods for relative measures such as risk differences, odds ratios, risk ratios, and hazard ratios. Where prior evidence is based on a random effects meta-analysis, the authors describe different ESVI calculations, one relevant for decisions concerning a specific patient group and the other for decisions concerning the entire population of patient groups. They also consider EVSI methods for new studies intended to update information on both baseline treatment efficacy and the relative efficacy of 2 treatments. Although there are restrictions regarding models with prior correlation between parameters, these methods can be applied to the majority of probabilistic decision models. Illustrative worked examples of EVSI calculations are given in an appendix.     

临床生存数据新视角:竞争风险模型

临床生存数据常常伴有多个结局,各结局间存在竞争关系,忽略竞争风险使用传统单因素Kaplan-Meier法会高估累积死亡率,使用传统多因素Cox有可能错误估计HR值。目前国内临床文献较少提及竞争风险且方法学均未提供具体实现程序,亦无解析主流模型应用条件与参数。为此本文旨在阐述竞争风险的概念与核心模型,以实例解析累积发生率、原因别风险模型、部分分布风险模型正确的应用,并提供相应SAS 9.4程序以便临床研究人员进行竞争风险建模时参考。     

Interim analysis on survival data: its potential bias and how to repair it

We consider interim analyses in clinical trials or observational studies with a time-to-event outcome variable where the survival curves are compared using the hazard ratio resulting from a proportional hazards (PH) model or tested with the logrank test or another two-sample test. We show and illustrate with an example that if the PH assumption is violated, the results of interim analyses can be heavily biased. This is due to the fact that the censoring pattern in interim analyses can be completely different from the final analysis. We argue that, when the PH assumption is violated, interim analyses are only sensible if a fixed time horizon for the final analysis is specified, and at the time of the interim analysis sufficient information is available over the whole time interval up to the horizon. We show how the bias can then be remedied by introducing in the estimation and testing procedures an appropriate weighting that reflects the weights to be expected in the final analysis. The consequences for design and analysis are discussed and some practical recommendations are given.     

Sex bias in the management of coronary artery disease in Quebec.

This study tests the hypothesis that, given the absence of financial barriers to major coronary procedures in Quebec, women are as likely as men to undergo such procedures. The use of coronary procedures in 33,940 patients with ischemic heart disease, admitted during 1 year to 78 Quebec hospitals, was analyzed. The male-to-female age- and severity-adjusted odds ratios for the use of these procedures were 1.47 for diagnostic procedures, 1.38 for therapeutic procedures, and 1.26 for diagnostic and therapeutic procedures. These results suggest that differences in the use of coronary procedures by sex are influenced by factors other than financial accessibility.