医学诊断试验评价的ROC分析—重复测量诊断数据的ROC曲线

目的 探讨诊断试验中重复有序分类测量数据的ROC分析方法。方法 在有序模型基础上构造相应的ROC模型,然后选用累积logistic模型作为联系函数,采用GEE方法进行参数估计。结果 通过累积logistic模型的参数估计,能够得到ROC曲线方程、ROC曲线下面积及标准误。结论 上术方法影像诊断试验中常见的重复测量数据进行有效地分析与处理。     

Analysis of a cluster randomized trial with binary outcome data using a multi-level model

The use of multi-level logistic regression models was explored for the analysis of data from a cluster randomized trial investigating whether a training programme for general practitioners' reception staff could improve women's attendance at breast screening. Twenty-six general practices were randomized with women nested within them, requiring a two-level model which allowed for between-practice variability. Comparisons were made with fixed effect (FE) and random effects (RE) cluster summary statistic methods, ordinary logistic regression and a marginal model based on generalized estimating equations with robust variance estimates. An FE summary statistic method and ordinary logistic regression considerably understated the variance of the intervention effect, thus overstating its statistical significance. The marginal model produced a higher statistical significance for the intervention effect compared to that obtained from the RE summary statistic method and the multi-level model. Because there was only a moderate number of practices and these had unbalanced cluster sizes, reliable asymptotic properties for the robust standard errors used in the marginal model may not have been achieved. While the RE summary statistic method cannot handle multiple covariates easily, marginal and multi-level models can do so. In contrast to multi-level models however, marginal models do not provide direct estimates of variance components, but treat these as nuisance parameters. Estimates of the variance components were of particular interest in this example. Additionally, parametric bootstrap methods within the multi-level model framework provide confidence intervals for these variance components, as well as a confidence interval for the effect of intervention which allows for the imprecision in the estimated variance components. The assumption of normality of the random effects can be checked, and the models extended to investigate multiple sources of variability.     

Goodness-of-fit for GEE: an example with mental health service utilization

Suppose we use generalized estimating equations to estimate a marginal regression model for repeated binary observations. There are no established summary statistics available for assessing the adequacy of the fitted model. In this paper we propose a goodness-of-fit test statistic which has an approximate chi-squared distribution when we have specified the model correctly. The proposed statistic can be viewed as an extension of the Hosmer and Lemeshow goodness-of-fit statistic for ordinary logistic regression to marginal regression models for repeated binary responses. We illustrate the methods using data from a study of mental health service utilization by children. The repeated responses are a set of binary measures of service use. We fit a marginal logistic regression model to the data using generalized estimating equations, and we apply the proposed goodness-of-fit statistic to assess the adequacy of the fitted model.     

ORDINAL REGRESSION METHODOLOGY FOR ROC CURVES DERIVED FROM CORRELATED DATA

We present an approach for the analysis of correlated ROC data, using ordinal regression models in conjunction with generalized estimating equations. The approach applies to the analysis of degree-of-suspicion data derived from multiple interpretations of the same diagnostic study and from the examination of the same patients with multiple diagnostic modalities. The regression models make it possible to incorporate patient and reader characteristics into the analysis, without having to resort to stratification. We illustrate the potential of the approach with analysis of data from two studies in diagnostic oncology.     

Familial associations of lipid profiles: a generalized estimating equations approach

Elevated plasma levels of apolipoproteins A1 (apoA1) and B (apoB) are important protective factors and risk factors, respectively, for atherosclerosis and coronary heart disease. It is well known that both apoA1 and apoB reveal strong familial aggregation. Our goal was to investigate whether exogenous variables influence these associations. We used marginal regression models for the mean and association structure (generalized estimating equations 2; GEE2) to analyse data from 1435 family members within 469 families of different sizes included in the Donolo-Tel Aviv Three-Generation Offspring Study. The usual robust variance matrix was approximated by extensions of jack-knife estimators of variance to GEE2 models. Estimation of standard errors in models with quite complex correlation structures was possible using this approach. All analyses were easily carried out using a menu-driven stand-alone software tool for marginal regression modelling. We demonstrate that a variety of hypotheses can be tested using Wald statistics by modelling regression matrices for the association structure. We show that correlation for apoB between parent-offspring pairs increased with decreasing age difference and that pairs with individuals of the same gender had more similar apoA1 levels than individuals of different gender. Associations between different relative pairs did not all agree with those expected from differences in kinship coefficients. The analysis using GEE2 models revealed structures that would not have been detected by other models and should therefore be used in addition to traditional approaches of analysing family data. GEE2 should be considered a standard method for the investigation of familial aggregation.     

Analysing repeated measurements data: a practical comparison of methods.

A variety of methods are available for analysing repeated measurements data where the outcome is continuous. However, there is little information on how established methods, such as summary statistics and repeated measures analysis of variance (RMAOV), compare in practice with methods that have become available to applied statisticians more recently, such as marginal models (based on generalized estimating equation methodology) and multilevel models (that is, hierarchical random effects models). The aim of this paper is to exemplify the use of these methods, and directly compare their results by application to a clinical trial data set. The focus is on practical aspects rather than technical issues. The data considered were taken from a clinical trial of treatments for asthma in 240 children, in which a baseline and four post-randomization measurements of outcomes were taken. The simplicity of the method of summary statistics using the post-randomization mean of observations provided a useful initial analysis. However, fixed time effects or treatment-time interactions cannot be included in such an analysis, and choice of appropriate weighting when there is substantial missing data is problematic. RMAOV, marginal models and multilevel models generally provided similar estimates and standard errors for the treatment effects, although in one example with a relatively complex variance structure the marginal model produced less efficient estimates. Two advantages of multilevel models are that they provide direct estimates of variance components which are often of interest in their own right, and that they can be naturally extended to handle multivariate outcomes.     

A general regression methodology for ROC curve estimation

A method for applying generalized ordinal regression models to categorical rating data to estimate and analyze receiver operating characteristic (ROC) curves is presented. These models permit parsimonious adjustment of ROC curve parameters for relevant covariates through two regression equations that correspond to location and scale. Particular shapes of ROC curves are interpreted in relation to the kind of covariates included in the two regressions. The model is shown to be flexible because it is not restricted to the assumption of binormality that is commonly employed in smoothed ROC curve estimation, although the binormal model is one particular form of the more general model. The new method provides a mechanism for pinpointing the effect that interobserver variability has on the ROC curve. It also allows for the adjustment of ROC curves for temporal variation and case mix, and provides a way to assess the incremental diagnostic value of a test. The new methodology is recommended because it substantially improves the ability to assess diagnostic tests using ROC curves.     

A GENERALIZED LINEAR MODEL FOR ANALYSING RECEIVER OPERATING CHARACTERISTIC CURVES

We present a continuation ratio model for analysing ordinal categorical data and we apply the model to the problem of estimating receiver operating characteristic (ROC) curves. We apply the methods to post-prandial capillary blood glucose measurements as a criterion for a potential screening test for diabetes mellitus. One can obtain point estimates of sensitivity and specificity and their associated standard errors at any value along the observed range of post-prandial capillary blood glucose measurements. Also, in comparison to the models for ROCs described by Tosteson and Begg, ROC curves based on the continuation ratio model have the desired features that allow ROCs to be concave but not necessarily symmetric.     

A Bayesian approach to a general regression model for ROC curves.

A fully Bayesian approach to a general nonlinear ordinal regression model for ROC-curve analysis is presented. Samples from the marginal posterior distributions of the model parameters are obtained by a Markov-chain Monte Carlo (MCMC) technique--Gibbs sampling. These samples facilitate the calculation of point estimates and credible regions as well as inferences for the associated areas under the ROC curves. The analysis of an example using freely available software shows that the use of noninformative vague prior distributions for all model parameters yields posterior summary statistics very similar to the conventional maximum-likelihood estimates. Clinically important advantages of this Bayesian approach are: the possible inclusion of prior knowledge and beliefs into the ROC analysis (via the prior distributions), the possible calculation of the posterior predictive distribution of a future patient outcome, and the potential to address questions such as: "What is the probability that a certain diagnostic test is better in one setting than in another?"     

An appraisal of methods for the analysis of longitudinal categorical data with MAR drop-outs

A number of methods for analysing longitudinal ordinal categorical data with missing-at-random drop-outs are considered. Two are maximum-likelihood methods (MAXLIK) which employ marginal global odds ratios to model associations. The remainder use weighted or unweighted generalized estimating equations (GEE). Two of the GEE use Cholesky-decomposed standardized residuals to model the association structure, while another three extend methods developed for longitudinal binary data in which the association structures are modelled using either Gaussian estimation, multivariate normal estimating equations or conditional residuals. Simulated data sets were used to discover differences among the methods in terms of biases, variances and convergence rates when the association structure is misspecified. The methods were also applied to a real medical data set. Two of the GEE methods, referred to as Cond and ML-norm in this paper and by their originators, were found to have relatively good convergence rates and mean squared errors for all sample sizes (80, 120, 300) considered, and one more, referred to as MGEE in this paper and by its originators, worked fairly well for all but the smallest sample size, 80.     

具有协变量或干扰因素的诊断试验数据的ROC分析

目的 探讨具有协变量或干扰因素的诊断试验的评价问题。建立相应的统计模型及分析方法。方法 基于ROC分析给出变量ROC模型，采用有序logistic连续函数，利用SAS软件进行参数估计，得到有协为量情况下的ROC曲线方程及曲线下面积。文中结合检测动脉硬化的数据，说明了其用法。结果 采用文中给出的方法，可以有效地扣除协变量的影响，准确地评价诊断的作用。结论 本文提供的方法能够有效地解决诊断试验中具有干扰因素影响的问题。     

A comparison of methods for correlated ordinal measures with ophthalmic applications

For many clinical trials and epidemiologic investigations in the field of ophthalmology, paired ordinal data are often collected through the detailed grading of retinal photographs. One method for analysis of these data is the extension of the generalized estimating equation (GEE) methodology to multinomial data with cumulative link functions. Prior to the development of this advanced technique, however, ophthalmologists developed a method of combining the ordinal responses of both eyes of a patient into a single person-level response on a new ordinal scale. A relationship between the regression coefficients of these two methods is derived as a function of the correlation between eyes. We investigate the applicability of this result and the relationship of the standard errors in simulation experiments and in an example from the Wisconsin Epidemiologic Study of Diabetic Retinopathy.     

The analysis of the influence of birth order and other factors in multiple birth data

We compare three methods which can be used to analyse the influence of birth order and other factors on health outcomes in multiple birth data. We consider marginal models based on generalized estimating equations (GEE) and two kinds of conditional models; conditional logistic regression (CLR) and mixed effects models (MEM). Although the models may be written similarly, there are differences in both the interpretation and the numerical values assigned to the parameters. Our main conclusion is that GEE and MEM are preferable to CLR since they provide more flexibility in dealing with missing values and covariates. The choice between GEE and MEM is less obvious and depends on the data, the parameter of interest and statistical power.     

Conditional analysis of multiple quantitative traits based on marginal GWAS summary statistics

There has been an increasing interest in joint association testing of multiple traits for possible pleiotropic effects. However, even in the presence of pleiotropy, most of the existing methods cannot distinguish direct and indirect effects of a genetic variant, say single‐nucleotide polymorphism (SNP), on multiple traits, and a conditional analysis of a trait adjusting for other traits is perhaps the simplest and most common approach to addressing this question. However, without individual‐level genotypic and phenotypic data but with only genome‐wide association study (GWAS) summary statistics, as typical with most large‐scale GWAS consortium studies, we are not aware of any existing method for such a conditional analysis. We propose such a conditional analysis, offering formulas of necessary calculations to fit a joint linear regression model for multiple quantitative traits. Furthermore, our method can also accommodate conditional analysis on multiple SNPs in addition to on multiple quantitative traits, which is expected to be useful for fine mapping. We provide numerical examples based on both simulated and real GWAS data to demonstrate the effectiveness of our proposed approach, and illustrate possible usefulness of conditional analysis by contrasting its result differences from those of standard marginal analyses.     

金标准为等级变量时诊断试验的评价及其在冠心病诊断试验中的应用

目的利用金标准为等级变量时诊断试验的评价方法 ,评价氧化低密度脂蛋白ELISA检测试剂盒在冠心病诊断中的诊断价值。方法共入选1190例观察对象,根据金标准检测结果分为3个不同状态,从ROC曲线下面积的定义出发,利用R软件,获得金标准为等级变量时氧化低密度脂蛋白ROC曲线下面积的非参数估计值。结果无论国产或瑞士产氧化低密度脂蛋白试剂盒,均说明氧化低密度脂蛋白对冠心病的不同疾病或健康状态具有区分能力,与AUC=0.5比较均具有统计学意义(P<0.001),且随着状态间的差距越大,其区分能力增强。两试剂盒与金标准相比的准确性分别为0.8797和0.8883,且具有统计学意义(P<0.001)。结论本研究为类似的研究提供了方法学参考。     

Latent variables, measurement error and methods for analysing longitudinal binary and ordinal data

We explore structural equations with latent variables for modelling between-individual variability and measurement error in the analysis of longitudinal binary and ordinal data. The structural equation formulation provides insight into the assumptions and differences in interpretation of methods that are popular for longitudinal data analysis. Introducing the concept of continuous latent variables makes it clear that marginal and cluster-specific models differ because their predicted variables are scaled to different standard deviations, and that adjustment for measurement error in the outcome involves a change in scale as well. We apply both structural equation modelling and common longitudinal modelling approaches to data from a study of sleep disorders. In the process, we compare results from marginal modelling using an SAS GEE routine (Karim and Zeger, 1988), Qu's GAUSS program (Qu, 1992) for generalized mixed models using GEE, the MIXOR package for cluster-specific mixed effects models (Hedeker and Gibbons, 1994), and LISCOMP for structural models (Muthén, 1988).     

Comparison of methods for analysing cluster randomized trials: an example involving a factorial design

BACKGROUND: Studies involving clustering effects are common, but there is little consistency in their analysis. Various analytical methods were compared for a factorial cluster randomized trial (CRT) of two primary care-based interventions designed to increase breast screening attendance. METHODS: Three cluster-level and five individual-level options were compared in respect of log odds ratios of attendance and their standard errors (SE), for the two intervention effects and their interaction. Cluster-level analyses comprised: (C1) unweighted regression of practice log odds; (C2) regression of log odds weighted by their inverse variance; (C3) random-effects meta-regression of log odds with practice as a random effect. Individual-level analyses comprised: (I1) standard logistic regression ignoring clustering; (I2) robust SE; (I3) generalized estimating equations; (I4) random-effects logistic regression; (I5) Bayesian random-effects logistic regression. Adjustments for stratification and baseline variables were investigated. RESULTS: As expected, method I1 was highly anti-conservative. The other, valid, methods exhibited considerable differences in parameter estimates and standard errors, even between the various random-effects methods based on the same statistical model. Method I4 was particularly sensitive to between-cluster variation and was computationally stable only after controlling for baseline uptake. CONCLUSIONS: Commonly used methods for the analysis of CRT can give divergent results. Simulation studies are needed to compare results from different methods in situations typical of cluster trials but when the true model parameters are known.     

比例优势模型实现ROC分析的方法及其应用前景分析

目的 探讨比例优势模型在ROC分析中的应用前景。方法 比较比例优势模型与双正态模型等经典方法所计算的ROC曲线下面积及其标准误；采用灵敏度残差平方和与决定系数两个指标评价参数模型的拟合优度。结果 在一般情况下，由比例优势模型所得到的Roe曲线指标结果与经典方法很接近；对于有序分类资料和连续型资料，该模型的拟合效果均较好；但由于该模型获得的Roe曲线形状单一，有些情况下该模型的拟合不理想。结论 与经典的方法相比，比例优势模型有其自身的特点，实际应用时应慎重做出选择。     

POPULATION-AVERAGED AND CLUSTER-SPECIFIC MODELS FOR CLUSTERED ORDINAL RESPONSE DATA

We compare population-averaged and cluster-specific models for clustered ordinal data. We consider generalized estimating equations and constrained equations maximum likelihood estimation of population-averaged cumulative logit regression models, and mixed effects estimation of cluster-specific cumulative logit regression models. A previously reported relationship between population-averaged and cluster-specific parameters for the binary logistic link appears to hold for analogous parameters under the cumulative logit link. We address these issues in the context of data from two cross-over clinical trials.     

Estimating and testing direct genetic effects in directed acyclic graphs using estimating equations

In genetic association studies, it is important to distinguish direct and indirect genetic effects in order to build truly functional models. For this purpose, we consider a directed acyclic graph setting with genetic variants, primary and intermediate phenotypes, and confounding factors. In order to make valid statistical inference on direct genetic effects on the primary phenotype, it is necessary to consider all potential effects in the graph, and we propose to use the estimating equations method with robust Huber–White sandwich standard errors. We evaluate the proposed causal inference based on estimating equations (CIEE) method and compare it with traditional multiple regression methods, the structural equation modeling method, and sequential G‐estimation methods through a simulation study for the analysis of (completely observed) quantitative traits and time‐to‐event traits subject to censoring as primary phenotypes. The results show that CIEE provides valid estimators and inference by successfully removing the effect of intermediate phenotypes from the primary phenotype and is robust against measured and unmeasured confounding of the indirect effect through observed factors. All other methods except the sequential G‐estimation method for quantitative traits fail in some scenarios where their test statistics yield inflated type I errors. In the analysis of the Genetic Analysis Workshop 19 dataset, we estimate and test genetic effects on blood pressure accounting for intermediate gene expression phenotypes. The results show that CIEE can identify genetic variants that would be missed by traditional regression analyses. CIEE is computationally fast, widely applicable to different fields, and available as an R package.