graphical diagnostics to check model misspecification for the proportional odds regression model the cumulative logit or the proportional odds regression model is commonly used to study covariate effects on ordinal responses this paper provides some graphical and numerical methods for checking the adequacy of the proportional odds regression model the methods focus on evaluating functional misspecification for specific covariate effects but misspecification of the link function can also be dealt with under the same framework for the logistic regression model with binary responses arbogast and lin statist med 2005 24 229 247 developed similar graphical and numerical methods for assessing the adequacy of the model using the cumulative sums of residuals the paper generalizes their methods to ordinal responses and illustrates them using an example from the va normative aging study simulation studies comparing the performance of the different diagnostic methods indicate that some of the graphical methods are more powerful in detecting model misspecification than the hosmer lemeshow type goodness of fit statistics for the class of models studied

performance of generalized estimating equations in practical situations moment methods for analyzing repeated binary responses have been proposed by liang and zeger 1986 biometrika 73 13 22 and extended by prentice 1988 biometrics 44 1033 1048 in their generalized estimating equations gee both liang and zeger 1986 and prentice 1988 estimate the parameters associated with the expected value of an individual s vector of binary responses as well as the correlations between pairs of binary responses in this paper we discuss one step estimators i e estimators obtained from one step of the generalized estimating equations and compare their performance to that of the fully iterated estimators in small samples in simulations we find the performance of the one step estimator to be qualitatively similar to that of the fully iterated estimator when the sample size is small and the association between binary responses is high we recommend using the one step estimator to circumvent convergence problems associated with the fully iterated gee algorithm furthermore we find the gee methods to be more efficient than ordinary logistic regression with variance correction for estimating the effect of a time varying covariate

model checking for roc regression analysis the receiver operating characteristic roc curve is a prominent tool for characterizing the accuracy of a continuous diagnostic test to account for factors that might influence the test accuracy various roc regression methods have been proposed however as in any regression analysis when the assumed models do not fit the data well these methods may render invalid and misleading results to date practical model checking techniques suitable for validating existing roc regression models are not yet available in this article we develop cumulative residual based procedures to graphically and numerically assess the goodness of fit for some commonly used roc regression models and show how specific components of these models can be examined within this framework we derive asymptotic null distributions for the residual processes and discuss resampling procedures to approximate these distributions in practice we illustrate our methods with a dataset from the cystic fibrosis registry

admissible positive systems of affine non twisted kac moody lie algebras abstract we introduce admissible positive systems and hermitian real forms of affine non twisted kac moody lie algebras and show that a real form has admissible positive system if and only if it is hermitian we use the vogan diagrams to classify the hermitian real forms and show that their symmetric spaces carry complex structures

assessing accuracy of mammography in the presence of verification bias and intrareader correlation la performance des tests diagnostiques medicaux est souvent evaluee en comparant le resultat du test au vrai etat de la maladie du patient l analyse des courbes de caracteristiques de fonctionnement roc peut etre utilisee pour resumer la precision du test cependant une telle analyse peut rencontrer plusieurs difficultes dans la pratique reelle une difficulte est la verification du biais c est a dire que l evaluation de l etat de la maladie peut etre partiellement disponible et la probabilite de determination de la maladie peut dependre aussi bien du resultat du test que des caracteristiques du sujet une deuxieme difficulte est que les tests interpretes par le meme lecteur peuvent ne pas etre independants a l aide des equations d estimation nous generalisons des methodes proposees pour prendre en compte ces problemes nous comparons la performance de differents estimateurs de la precision en utilisant les estimateurs robustes de la variance sandwich pour permettre une inference asymptotique valide nous montrons que dans le contexte d une cohorte d observation ou de bonnes informations sur les covariables sont disponibles une approche par des equations d estimations ponderees wee peut etre preferable pour sa robustesse a un modele mal specifie nous appliquons la methodologie a la mammographie comme realisee dans la communaute des radiologues

three methods for analysing correlated roc curves a comparison in real data sets from multi reader multi case studies with a factorial design this paper compares three published methods for analysing multiple correlated roc curves a method using generalized estimating equations with marginal non proportional ordinal regression models a method using jackknifed pseudovalues of summary statistics a method using a corrected f test from analysis of variance of summary statistics use of these methods is illustrated through six real data examples from studies with the common factorial design that is multiple readers interpreting images obtained with each test modality on each study subject the issue of the difference between typical summary statistics and summary statistics from typical roc curves is explored the examples also address similarities and differences among the analytical methods in particular while point estimates of differences between test modalities are similar the standard errors of these differences do not agree for all three methods a simulation study supports the standard errors provided by the generalized estimating equations with marginal non proportional ordinal regression models copyright 2003 john wiley sons ltd

a goodness of fit test for the ordered stereotype model this paper presents a new goodness of fit test for an ordered stereotype model used for an ordinal response variable the proposed test is based on the well known hosmer lemeshow test and its version for the proportional odds regression model the latter test statistic is calculated from a grouping scheme assuming that the levels of the ordinal response are equally spaced which might be not true one of the main advantages of the ordered stereotype model is that it allows us to determine a new uneven spacing of the ordinal response categories dictated by the data the proposed test takes the use of this new adjusted spacing to partition data a simulation study shows good performance of the proposed test under a variety of scenarios finally the results of the application in two examples are presented copyright 2016 john wiley sons ltd

robust estimation of area under roc curve using auxiliary variables in the presence of missing biomarker values summary in medical research the receiver operating characteristic roc curves can be used to evaluate the performance of biomarkers for diagnosing diseases or predicting the risk of developing a disease in the future the area under the roc curve roc auc as a summary measure of roc curves is widely utilized especially when comparing multiple roc curves in observational studies the estimation of the auc is often complicated by the presence of missing biomarker values which means that the existing estimators of the auc are potentially biased in this article we develop robust statistical methods for estimating the roc auc and the proposed methods use information from auxiliary variables that are potentially predictive of the missingness of the biomarkers or the missing biomarker values we are particularly interested in auxiliary variables that are predictive of the missing biomarker values in the case of missing at random mar that is missingness of biomarker values only depends on the observed data our estimators have the attractive feature of being consistent if one correctly specifies conditional on auxiliary variables and disease status either the model for the probabilities of being missing or the model for the biomarker values in the case of missing not at random mnar that is missingness may depend on the unobserved biomarker values we propose a sensitivity analysis to assess the impact of mnar on the estimation of the roc auc the asymptotic properties of the proposed estimators are studied and their finite sample behaviors are evaluated in simulation studies the methods are further illustrated using data from a study of maternal depression during pregnancy

super character theory and comparison arguments for a random walk on the upper triangular matrices abstract consider the random walk on the n n upper triangular matrices with ones on the diagonal and elements over f p where we pick a row at random and either add it or subtract it from the row directly above it the main result of this paper is to prove that the dependency of the mixing time on p is p 2 this is proven by combining super character theory and comparison theory arguments

a classification of involutive automorphisms of an affine kac moody lie algebra abstract in this thesis we classify the conjugacy classes of involutions in aut g where g is an affine kac moody lie algebra we distinguish between two kinds of involutions those which preserve the conjugacy class of a borel subalgebra and those which don t we give a complete and non redundant list of representatives of involutions of the first kind and we compute their fixed points sets we prove that any involution of the first kind has a conjugate which leaves invariant the components of the gauss decomposition g n h n we also give a complete list of representatives of the conjugacy classes of involutions of the second kind

analysis of repeated categorical data using generalized estimating equations moment methods for analysing repeated binary responses have been proposed by liang and zeger and extended by prentice and zhao and prentice in these estimating equations models are proposed for the correlation between the repeated binary responses we extend liang and zeger s method to models for the correlation between repeated nominal or ordinal categorical responses in particular when the repeated responses are binary our methods reduce to liang and zeger s method our method is illustrated with two datasets one dataset contains repeated observations of self assessment of arthritis an ordered variable with three categories collected during a randomized comparative study of alternative treatments of patients with rheumatoid arthritis the second dataset is a longitudinal study of the health effects of air pollution in which the repeated ordered multinomial response is the wheezing status no wheeze wheeze with cold wheeze apart from cold of a child at ages 9 10 11 and 12 years

checking the cox model with cumulative sums of martingale based residuals summary this paper presents a new class of graphical and numerical methods for checking the adequacy of the cox regression model the procedures are derived from cumulative sums of martingale based residuals over follow up time and or covariate values the distributions of these stochastic processes under the assumed model can be approximated by zero mean gaussian processes each observed process can then be compared both visually and analytically with a number of simulated realizations from the approximate null distribution these comparisons enable the data analyst to assess objectively how unusual the observed residual patterns are special attention is given to checking the functional form of a covariate the form of the link function and the validity of the proportional hazards assumption an omnibus test consistent against any model misspecification is also studied the proposed techniques are illustrated with two real data sets

vogan diagrams of real forms of affine kac moody lie algebras abstract a vogan diagram is actually a dynkin diagram with some additional structure this paper develops theory of vogan diagrams for almost compact real forms of indecomposable nontwisted affine kac moody lie algebras here the equivalence classes of vogan diagrams are in one one correspondence with the isomorphism classes of almost compact real forms

pattern mixture models for multivariate incomplete data with covariates pattern mixture models stratify incomplete data by the pattern of missing values and formulate distinct models within each stratum pattern mixture models are developed for analyzing a random sample on continuous variables y 1 y 2 when values of y 2 are nonrandomly missing methods for scalar y 1 and y 2 are here generalized to vector y 1 and y 2 with additional fixed covariates x parameters in these models are identified by alternative assumptions about the missing data mechanism models may be underidentified in which case additional assumptions are needed just identified or overidentified maximum likelihood and bayesian methods are developed for the latter two situations using the em and sem algorithms direct and interactive simulation methods the methods are illustrated on a data set involving alternative dosage regimens for the treatment of schizophrenia using haloperidol and on a regression example sensitivity to alternative assumptions about the missing data mechanism is assessed and the new methods are compared with complete case analysis and maximum likelihood for a probit selection model

admissible positive systems of affine kac moody lie algebras the twisted cases abstract we introduce admissible positive systems and hermitian real forms of affine twisted kac moody lie algebras and show that a real form has admissible positive system if and only if it is hermitian we use the vogan diagrams to classify the hermitian real forms and show that their symmetric spaces carry complex structures the affine non twisted kac moody lie algebras have been treated in an earlier work and this article deals with the twisted cases

direct estimation of the area under the receiver operating characteristic curve in the presence of verification bias the area under a receiver operating characteristic roc curve auc is a commonly used index for summarizing the ability of a continuous diagnostic test to discriminate between healthy and diseased subjects if all subjects have their true disease status verified one can directly estimate the auc nonparametrically using the wilcoxon statistic in some studies verification of the true disease status is performed only for a subset of subjects possibly depending on the result of the diagnostic test and other characteristics of the subjects because estimators of the auc based only on verified subjects are typically biased it is common to estimate the auc from a bias corrected roc curve the variance of the estimator however does not have a closed form expression and thus resampling techniques are used to obtain an estimate in this paper we develop a new method for directly estimating the auc in the setting of verification bias based on u statistics and inverse probability weighting ipw closed form expressions for the estimator and its variance are derived we also show that the new estimator is equivalent to the empirical auc derived from the bias corrected roc curve arising from the ipw approach

a lack of fit test for the mean function in a generalized linear model abstract a supremum type statistic based on partial sums of residuals is proposed to test the validity of the mean function of the response variable in a generalized linear model the proposed test does not need a partition of the space of covariates to handle the case of nonreplication the new test is consistent against the alternative under which the deterministic part of the model is not the one specified in the null hypothesis the asymptotic null distribution of the test statistic can be approximated through simulations this approximation is valid even if the variance of the response variable is misspecified in the model for practical sample sizes the adequacy of this large sample approximation to the null distribution of the test statistic is carefully examined power comparisons with other lack of fit tests are also performed to show the advantage of the test in particular we find that the new procedure is rather sensitive to detect a misspecified mean function if the assumed mean functio

a new residual for ordinal outcomes we propose a new residual for regression models of ordinal outcomes defined as e sign y y where y is the observed outcome and y is a random variable from the fitted distribution this new residual is a single value per subject irrespective of the number of categories of the ordinal outcome contains directional information between the observed value and the fitted distribution and does not require the assignment of arbitrary numbers to categories we study its properties describe its connections with other residuals ranks and ridits and demonstrate its use in model diagnostics

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

methods for conducting sensitivity analysis of trials with potentially nonignorable competing causes of censoring we consider inference for the treatment arm mean difference of an outcome that would have been measured at the end of a randomized follow up study if during the course of the study patients had not initiated a nonrandomized therapy or dropped out we argue that the treatment arm mean difference is not identified unless unverifiable assumptions are made we describe identifying assumptions that are tantamount to postulating relationships between the components of a pattern mixture model but that can also be interpreted as imposing restrictions on the cause specific censoring probabilities of a selection model we then argue that although sufficient for identification these assumptions are insufficient for inference due to the curse of dimensionality we propose reducing dimensionality by specifying semiparametric cause specific selection models these models are useful for conducting a sensitivity analysis to examine how inference for the treatment arm mean difference changes as one varies the magnitude of the cause specific selection bias over a plausible range we provide methodology for conducting such sensitivity analysis and illustrate our methods with an analysis of data from the aids clinical trial group actg study 002

semiparametric regression for repeated outcomes with nonignorable nonresponse abstract we consider inference about the parameter indexing the conditional mean of a vector of correlated outcomes given a vector of explanatory variables when some of the outcomes are missing in a subsample of the study and the probability of response depends on both observed and unobserved data values that is nonresponse is nonignorable we propose a class of augmented inverse probability of response weighted estimators that are consistent and asymptotically normal can for estimating when the response probabilities can be parametrically modeled and a can estimator exists the proposed estimators do not require full specification of a parametric likelihood and their computation does not require numerical integration our estimators can be viewed as an extension of generalized estimating equation estimators that allows for nonignorable nonresponse we show that our class essentially consists of all can estimators of we also show that the asymptotic variance of the optimal estimator in our

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

on the statistical analysis of roc curves we introduce a new accuracy index for receiver operating characteristic roc curves namely the partial area under the binormal roc graph over any specified region of interest we propose a simple but general procedure based on a conventional analysis of variance for comparing accuracy indices derived from two or more different modalities the proposed method is related to and compared with existing methodology and is illustrated by results from an experiment on optimization of density and contrast yielded by multiform photographic images used for scintigraphy

model checking techniques for stratified case control studies we present graphical and numerical methods for assessing the adequacy of the logistic regression model for stratified case control data the proposed methods are derived from the cumulative sum of residuals over the covariate or linear predictor under the assumed model the cumulative residual process converges weakly to a zero mean gaussian process whose distribution can be approximated via monte carlo simulation the observed cumulative residual pattern can then be compared both visually and analytically to a number of simulated realizations from the approximate null distribution these comparisons enable one to examine the functional form of each covariate the logistic link function as well as the overall model adequacy simulation studies demonstrate that the proposed methods perform well in practical settings illustration with an oesophageal cancer study is provided

analysis of semi parametric regression models with non ignorable non response in this article we consider the problem of making inferences about the parameter 0 indexing the conditional mean of an outcome given a vector of regressors when a subset of the variables outcome or covariates are missing for some study subjects and the probability of non response depends upon both observed and unobserved data values that is non response is non ignorable we propose a new class of inverse probability of censoring weighted estimators that are consistent and asymptotically normal can for estimating 0 when the non response probabilities can be parametrically modelled and a can estimator exists the proposed estimators do not require full specification of the likelihood and their computation does not require numerical integration we show that the asymptotic variance of the optimal estimator in our class attains the semi parametric variance bound for the model in some models no can estimator of 0 exists we provide a general algorithm for determining when can estimators of 0 exist our results follow after specializing a general representation described in the article for the efficient score and the influence function of regular asymptotically linear estimators in an arbitrary semi parametric model with non ignorable non response in which the probability of observing complete data is bounded away from zero and the non response probabilities can be parametrically modelled 1997 by john wiley sons ltd

nonparametric multiple imputation for receiver operating characteristics analysis when some biomarker values are missing at random the receiver operating characteristics roc curve is a widely used tool for evaluating discriminative and diagnostic power of a biomarker when the biomarker value is missing for some observations the roc analysis based solely on complete cases loses efficiency because of the reduced sample size and more importantly it is subject to potential bias in this paper we investigate nonparametric multiple imputation methods for roc analysis when some biomarker values are missing at random and there are auxiliary variables that are fully observed and predictive of biomarker values and or missingness of biomarker values although a direct application of standard nonparametric imputation is robust to model misspecification its finite sample performance suffers from curse of dimensionality as the number of auxiliary variables increases to address this problem we propose new nonparametric imputation methods which achieve dimension reduction through the use of one or two working models namely models for prediction and propensity scores the proposed imputation methods provide a platform for a full range of roc analysis and hence are more flexible than existing methods that primarily focus on estimating the area under the roc curve we conduct simulation studies to evaluate the finite sample performance of the proposed methods and find that the proposed methods are robust to various types of model misidentification and outperform the standard nonparametric approach even when the number of auxiliary variables is moderate we further illustrate the proposed methods by using an observational study of maternal depression during pregnancy copyright 2011 john wiley sons ltd

effect of verification bias on positive and negative predictive values the pairing of sensitivity and specificity expresses the efficacy of a test and positive and negative predictive values measure the accuracy of a diagnostic test when applied to a particular patient to calculate these measures one has to know the true disease status of each patient in practice however some patients may not be selected for verification of disease status it has been shown that the estimated sensitivity and specificity may be biased if one includes in the study sample only the patients with verified disease statuses this paper concerns the properties of the estimators of positive and negative predictive values using only patients with verified disease statuses first i show that these estimators are unbiased and provide consistent estimators for the variances of these estimators under the assumption that the probability of selecting a patient for a disease verification procedure does not depend directly on the true disease status of the patient then i use the ml method to study the sensitivity of the naive estimators to the departure from the conditional independence assumption

doubly robust estimation of the area under the receiver operating characteristic curve in the presence of verification bias the area under the receiver operating characteristic curve auc is a popular summary measure of the efficacy of a medical diagnostic test to discriminate between healthy and diseased subjects a frequently encountered problem in studies that evaluate a new diagnostic test is that not all patients undergo disease verification because the verification test is expensive invasive or both furthermore the decision to send patients to verification often depends on the new test and on other predictors of true disease status in such cases usual estimators of the auc based on verified patients only are biased in this article we develop estimators of the auc of markers measured on any scale that adjust for selection to verification these estimators adjust for measured patient covariates and diagnostic test results and also for an assumed degree of residual selection bias they can then be used in a sensitivity analysis to examine how the auc estimates change when different plausible degrees of residual asso

extended vogan diagrams an extended vogan diagram is an extended dynkin diagram with a diagram involution such that the vertices fixed by the involution can be painted or unpainted every extended vogan diagram represents an almost compact real form of some affine kac moody lie algebra two diagrams may represent isomorphic algebras and in this case we say that the diagrams are equivalent in this paper we classify the equivalence classes of extended vogan diagrams and provide a complete list of all diagrams within each class it gives a combinatorial classification of the isomorphic classes of almost compact real forms of the affine kac moody lie algebras

u processes rates of convergence on introduit un nouveau processus stochastique une collection de statistiques u indicees par une famille de noyaux symetriques on obtient des conditions pour la convergence presque sure uniforme d une suite de tels processus

semiparametric estimation of the covariate specific roc curve in presence of ignorable verification bias covariate specific roc curves are often used to evaluate the classification accuracy of a medical diagnostic test or a biomarker when the accuracy of the test is associated with certain covariates in many large scale screening tests the gold standard is subject to missingness due to high cost or harmfulness to the patient in this paper we propose a semiparametric estimation of the covariate specific roc curves with a partial missing gold standard a location scale model is constructed for the test result to model the covariates effect but the residual distributions are left unspecified thus the baseline and link functions of the roc curve both have flexible shapes with the gold standard missing at random mar assumption we consider weighted estimating equations for the location scale parameters and weighted kernel estimating equations for the residual distributions three roc curve estimators are proposed and compared namely imputation based inverse probability weighted and doubly robust estimators we derive the asymptotic normality of the estimated roc curve as well as the analytical form the standard error estimator the proposed method is motivated and applied to the data in an alzheimer s disease research

goodness of fit methods for generalized linear mixed models we develop graphical and numerical methods for checking the adequacy of generalized linear mixed models glmms these methods are based on the cumulative sums of residuals over covariates or predicted values of the response variable under the assumed model the asymptotic distributions of these stochastic processes can be approximated by certain zero mean gaussian processes whose realizations can be generated through monte carlo simulation each observed process can then be compared both visually and analytically to a number of realizations simulated from the null distribution these comparisons enable one to assess objectively whether the observed residual patterns reflect model misspecification or random variation the proposed methods are particularly useful for checking the functional form of a covariate or the link function extensive simulation studies show that the proposed goodness of fit tests have proper sizes and are sensitive to model misspecification applications to two medical studies lead to improved models

a class of pattern mixture models for normal incomplete data summary likelihood based methods are developed for analyzing a random sample on two continuous variables when values of one of the variables are missing normal maximum likelihood estimates when values are missing completely at random were derived by anderson 1957 they are also maximum likelihood providing the missing data mechanism is ignorable in rubin s 1976 sense that the mechanism depends only on observed data a new class of pattern mixture models little 1993 is described for the situation where missingness is assumed to depend on an arbitrary unspecified function of a linear combination of the two variables maximum likelihood for models in this class is straightforward and yields the estimates of anderson 1957 when missingness depends solely on the completely observed variable and the estimates of brown 1990 when missingness depends solely on the incompletely observed variable another choice of linear combination yields estimates from complete case analysis large sample and bayesian methods are described for this model the data do not supply information about the ratio of the coefficients of the linear combination that controls missingness if this ratio is not welldetermined based on prior knowledge a prior distribution can be specified and bayesian inference is then readily accomplished alternatively sensitivity of inferences can be displayed for a variety of choices of the ratio

smooth semiparametric receiver operating characteristic curves for continuous diagnostic tests we propose a semiparametric kernel distribution function estimator based on which a new smooth semiparametric estimator of the receiver operating characteristic roc curve is constructed we derive the asymptotic bias and variance of the newly proposed distribution function estimator and show that it is more efficient than the traditional non parametric kernel distribution estimator we also derive the asymptotic bias and variance of our new roc curve estimator and show that it is more efficient than the smooth non parametric roc curve estimator proposed by zou et al stat med 1997 16 2143 2156 and lloyd j am stat assoc 1998 93 1356 1364 for our proposed estimators we derive data based methods for bandwidth selection in addition we present some results on the analysis of two real data sets finally a simulation study is presented to show that our estimators are better than the non parametric counterparts in terms of bias standard error and mean square error

residuals and diagnostics for ordinal regression models a surrogate approach ordinal outcomes are common in scientific research and everyday practice and we often rely on regression models to make inference a long standing problem with such regression analyses is the lack

covariate adjustment in estimating the area under roc curve with partially missing gold standard in roc analysis covariate adjustment is advocated when the covariates impact the magnitude or accuracy of the test under study meanwhile for many large scale screening tests the true condition status may be subject to missingness because it is expensive and or invasive to ascertain the disease status the complete case analysis may end up with a biased inference also known as verification bias to address the issue of covariate adjustment with verification bias in roc analysis we propose several estimators for the area under the covariate specific and covariate adjusted roc curves aucx and aauc the aucx is directly modeled in the form of binary regression and the estimating equations are based on the u statistics the aauc is estimated from the weighted average of aucx over the covariate distribution of the diseased subjects we employ reweighting and imputation techniques to overcome the verification bias problem our proposed estimators are initially derived assuming that the true disease status is missing at random mar and then with some modification the estimators can be extended to the not missing at random nmar situation the asymptotic distributions are derived for the proposed estimators the finite sample performance is evaluated by a series of simulation studies our method is applied to a data set in alzheimer s disease research

invariants of real forms of affine kac moody lie algebras abstract the theory of vogan diagrams which are dynkin diagrams with an overlay of certain additional information allows one to give a rapid classification of finite dimensional real semisimple lie algebras and to make use of this classification in practice this paper develops a corresponding theory of vogan diagrams for almost compact real forms of indecomposable nontwisted affine kac moody lie algebras in this case also the equivalence classes of vogan diagrams correspond to the isomorphism classes of almost compact real forms although the real forms of such algebras had already been classified the theory of vogan diagrams introduces invariants for such algebras and makes it possible to locate a given real form within the classification

generalized estimating equations for ordinal categorical data arbitrary patterns of missing responses and missingness in a key covariate summary we propose methods for regression analysis of repeatedly measured ordinal categorical data when there is nonmonotone missingness in these responses and when a key covariate is missing depending on observables the methods use ordinal regression models in conjunction with generalized estimating equations gees we extend the gee methodology to accommodate arbitrary patterns of missingness in the responses when this missingness is independent of the unobserved responses we further extend the methodology to provide correction for possible bias when missingness in knowledge of a key covariate may depend on observables the approach is illustrated with the analysis of data from a study in diagnostic oncology in which multiple correlated receiver operating characteristic curves are estimated and corrected for possible verification bias when the true disease status is missing depending on observables

a goodness of fit test for the proportional odds regression model we examine goodness of fit tests for the proportional odds logistic regression model the most commonly used regression model for an ordinal response variable we derive a test statistic based on the hosmer lemeshow test for binary logistic regression using a simulation study we investigate the distribution and power properties of this test and compare these with those of three other goodness of fit tests the new test has lower power than the existing tests however it was able to detect a greater number of the different types of lack of fit considered in this study moreover the test allows for the results to be summarized in a contingency table of observed and estimated frequencies which is a useful supplementary tool to assess model fit we illustrate the ability of the tests to detect lack of fit using a study of aftercare decisions for psychiatrically hospitalized adolescents the test proposed in this paper is similar to a recently developed goodness of fit test for multinomial logistic regression a unified approach for testing goodness of fit is now available for binary multinomial and ordinal logistic regression models copyright 2012 john wiley sons ltd

regression models for convex roc curves the performance of a diagnostic test is summarized by its receiver operating characteristic roc curve under quite natural assumptions about the latent variable underlying the test the roc curve is convex empirical data on a test s performance often comes in the form of observed true positive and false positive relative frequencies under varying conditions this paper describes a family of regression models for analyzing such data the underlying roc curves are specified by a quality parameter delta and a shape parameter mu and are guaranteed to be convex provided delta 1 both the position along the roc curve and the quality parameter delta are modeled linearly with covariates at the level of the individual the shape parameter mu enters the model through the link functions log p mu log 1 p mu of a binomial regression and is estimated either by search or from an appropriate constructed variate one simple application is to the meta analysis of independent studies of the same diagnostic test illustrated on some data of moses shapiro and littenberg 1993 a second application to so called vigilance data is given where roc curves differ across subjects and modeling of the position along the roc curve is of primary interest

bayesian roc curve estimation under verification bias receiver operating characteristic roc curve has been widely used in medical science for its ability to measure the accuracy of diagnostic tests under the gold standard however in a complicated medical practice a gold standard test can be invasive expensive and its result may not always be available for all the subjects under study thus a gold standard test is implemented only when it is necessary and possible this leads to the so called verification bias meaning that subjects with verified disease status also called label are not selected in a completely random fashion in this paper we propose a new bayesian approach for estimating an roc curve based on continuous data following the popular semiparametric binormal model in the presence of verification bias by using a rank based likelihood and following gibbs sampling techniques we compute the posterior distribution of the binormal parameters intercept and slope as well as the area under the curve by imputing the missing labels within markov chain monte carlo iterations consistency of the resulting posterior under mild conditions is also established we compare the new method with other comparable methods and conclude that our estimator performs well in terms of accuracy copyright 2014 john wiley sons ltd

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

inference in randomized studies with informative censoring and discrete time to event endpoints summary in this article we present a method for estimating and comparing the treatment specific distributions of a discrete time to event variable from right censored data our method allows for 1 adjustment for informative censoring due to measured prognostic factors for time to event and censoring and 2 quantification of the sensitivity of the inference to residual dependence between time to event and censoring due to unmeasured factors we develop our approach in the context of a randomized trial for the treatment of chronic schizophrenia we perform a simulation study to assess the practical performance of our methodology