Operability region equivalence: simultaneous confidence bands for the equivalence of two regression models over restricted regions

In many scientific problems the purpose of comparing two linear regression models is to demonstrate that they have only negligible differences and so can be regarded as being practically equivalent. The frequently used statistical approach of testing the homogeneity null hypothesis of the two models by using a partial F test is not appropriate for this purpose. In this paper, a simultaneous confidence band is proposed which provides an upper bound on the largest possible difference between the two models, in units of the standard error of the observations, over a given region of the covariates. This is demonstrated to be a more practical method for assessing the equivalence of the two regression models.     

桑枝总黄酮的提取工艺研究

研究桑枝总黄酮的最佳提取工艺,本试验以桑枝（Tang10）为材料,以桑枝总黄酮得率为考察目标,采用二次回归正交旋转组合设计方法研究了提取温度、提取时间、乙醇浓度、料液比对桑枝总黄酮提取得率的影响,运用DPS软件对最佳工艺进行优化和验证。结果显示：试验范围内各因子对桑枝总黄酮提取率作用影响大小依次为提取温度〉料液比〉乙醇浓度〉提取时间;最佳提取参数为温度80℃,提取时间3．5h,乙醇浓度60％,料液比1：40部。因此,所建立数学回归模型在试验范围内能较准确的预测桑枝总黄酮的提取率．预测值与实测值相吻合,证明最佳工艺条件切实可行。     

Regression modeling of semicompeting risks data

Semicompeting risks data are often encountered in clinical trials with intermediate endpoints subject to dependent censoring from informative dropout. Unlike with competing risks data, dropout may not be dependently censored by the intermediate event. There has recently been increased attention to these data, in particular inferences about the marginal distribution of the intermediate event without covariates. In this article, we incorporate covariates and formulate their effects on the survival function of the intermediate event via a functional regression model. To accommodate informative censoring, a time-dependent copula model is proposed in the observable region of the data which is more flexible than standard parametric copula models for the dependence between the events. The model permits estimation of the marginal distribution under weaker assumptions than in previous work on competing risks data. New nonparametric estimators for the marginal and dependence models are derived from nonlinear estimating equations and are shown to be uniformly consistent and to converge weakly to Gaussian processes. Graphical model checking techniques are presented for the assumed models. Nonparametric tests are developed accordingly, as are inferences for parametric submodels for the time-varying covariate effects and copula parameters. A novel time-varying sensitivity analysis is developed using the estimation procedures. Simulations and an AIDS data analysis demonstrate the practical utility of the methodology.     

Semiparametric regression of multidimensional genetic pathway data: least-squares kernel machines and linear mixed models

We consider a semiparametric regression model that relates a normal outcome to covariates and a genetic pathway, where the covariate effects are modeled parametrically and the pathway effect of multiple gene expressions is modeled parametrically or nonparametrically using least-squares kernel machines (LSKMs). This unified framework allows a flexible function for the joint effect of multiple genes within a pathway by specifying a kernel function and allows for the possibility that each gene expression effect might be nonlinear and the genes within the same pathway are likely to interact with each other in a complicated way. This semiparametric model also makes it possible to test for the overall genetic pathway effect. We show that the LSKM semiparametric regression can be formulated using a linear mixed model. Estimation and inference hence can proceed within the linear mixed model framework using standard mixed model software. Both the regression coefficients of the covariate effects and the LSKM estimator of the genetic pathway effect can be obtained using the best linear unbiased predictor in the corresponding linear mixed model formulation. The smoothing parameter and the kernel parameter can be estimated as variance components using restricted maximum likelihood. A score test is developed to test for the genetic pathway effect. Model/variable selection within the LSKM framework is discussed. The methods are illustrated using a prostate cancer data set and evaluated using simulations.     

Joint modeling of progression of HIV resistance mutations measured with uncertainty and failure time data

Development of HIV resistance mutations is a major cause for failure of antiretroviral treatment. This article proposes a method for jointly modeling the processes of viral genetic changes and treatment failure. Because the viral genome is measured with uncertainty, a hidden Markov model is used to fit the viral genetic process. The uncertain viral genotype is included as a time-dependent covariate in a Cox model for failure time, and an expectation-maximization algorithm is used to estimate the model parameters. This model allows simultaneous evaluation of the sequencing uncertainty and the effect of resistance mutation on the risk of virological and immunological failures. Various model checking tests are provided to assess the appropriateness of the model. Simulation studies are performed to investigate the finite-sample properties of the proposed methods, which are then applied to data collected in three phase II clinical trials testing antiretroviral treatments containing the drug efavirenz.     

Testing a Partial Ordering of Population Means with Application to Inference about Growth Habits of Cowpea Genotypes

Using general results available in the literature, we derive the likelihood ratio test for a particular partial ordering of means that naturally arises in a biological context. We then show that the conceptual and computational complexity of the derivation can be substantially reduced by equivalently deriving the test using the intersection-union principle for decomposing a complex null hypothesis into elemental forms. A Monte Carlo algorithm for obtaining the p-value of the test is proposed. The test procedure is illustrated with a data set of the competitive ability of several cowpea genotypes, where previous experiments have indicated the proposed partial order of the means. A simulation study is used to examine the power of the test.     

Semiparametric Bayesian analysis of case-control data under conditional gene-environment independence

In case-control studies of gene-environment association with disease, when genetic and environmental exposures can be assumed to be independent in the underlying population, one may exploit the independence in order to derive more efficient estimation techniques than the traditional logistic regression analysis (Chatterjee and Carroll, 2005, Biometrika92, 399-418). However, covariates that stratify the population, such as age, ethnicity and alike, could potentially lead to nonindependence. In this article, we provide a novel semiparametric Bayesian approach to model stratification effects under the assumption of gene-environment independence in the control population. We illustrate the methods by applying them to data from a population-based case-control study on ovarian cancer conducted in Israel. A simulation study is conducted to compare our method with other popular choices. The results reflect that the semiparametric Bayesian model allows incorporation of key scientific evidence in the form of a prior and offers a flexible, robust alternative when standard parametric model assumptions do not hold.     

Testing goodness-of-fit in logistic case-control studies

We present a goodness-of-fit test for the logistic regressionmodel under case-control sampling. The test statistic is constructedvia a discrepancy between two competing kernel density estimatorsof the underlying conditional distributions given case-controlstatus. The proposed goodness-of-fit test is shown to comparevery favourably with previously proposed tests for case-controlsampling in terms of power. The test statistic can be easilycomputed as a quadratic form in the residuals from a prospectivelogistic regression maximum likelihood fit. In addition, theproposed test is affine invariant and has an alternative representationin terms of empirical characteristic functions.     

A Hybrid Pairwise Likelihood Method

A modification to the pairwise likelihood method is proposed,which aims to improve the estimation of the marginal distributionparameters. This is achieved by replacing the pairwise likelihoodscore equations, for estimating such parameters, by the optimallinear combinations of the marginal score functions. A furtheradvantage of the proposed estimator of marginal parameters,over pairwise likelihood, is that it is robust to misspecificationof the bivariate distributions as long as the univariate marginaldistributions are correctly specified. While alternating logisticregression can be seen as a special case of the proposed method,it is shown that an existing generalization of alternating logisticregression applicable to ordinal data is not the same as andis inferior to the proposed method because it replaces certainconditional densities by pseudodensities that assume workingindependence. The fitting of the multivariate negative binomialdistribution is another scenario involving intractable likelihoodthat calls for the use of pairwise likelihood methods, and thesuperiority of the modified method is demonstrated in a simulationstudy. Two examples, based on the analyses of salamander matingand patient-controlled analgesia data, demonstrate the usefulnessof the proposed method. The possibility of combining optimallythe pairwise, rather than marginal, scores is also consideredand its difficulty and potential are discussed.