Simple pattern-mixture models for longitudinal data with missing observations: analysis of urinary incontinence data.

In longitudinal studies each subject is observed at several different times. Longitudinal studies are rarely balanced and complete due to occurrence of missing data. Little proposed pattern-mixture models for the analysis of incomplete multivariate normal data. Later, Little proposed an approach to modelling the drop-out mechanism based on the pattern-mixture models. We advocate the pattern-mixture models for analysing the longitudinal data with binary or Poisson responses in which the generalized estimating equations formulation of Liang and Zeger is sensible. The proposed method is illustrated with a real data set.     

Concordance correlation coefficient applied to discrete data

In any field in which decisions are subject to measurements, interchangeability between the methods used to obtain these measurements is essential. To consider methods as interchangeable, a certain degree of agreement is needed between the measurements they provide. The concordance correlation coefficient is an index that assesses the strength of agreement and it has been widely applied in situations in which measurements are made on a continuous scale. Recently the concordance correlation coefficient has been defined as a specific intraclass correlation coefficient estimated by the variance components of a Normal-Normal mixed linear model. Although this coefficient was defined for the continuous scale case, it may also be used with a discrete scale. In this case the data are often transformed and normalized, and the concordance correlation is applied. This study discusses the expression of the concordance correlation coefficient for discrete Poisson data by means of the Poisson-Normal generalized linear mixed model. The behaviour of the concordance correlation coefficient estimate is assessed by means of a simulation study, in which the estimates were compared using four models: three Normal-Normal mixed models with raw data, log-transformed data and square-root transformed data, and the Poisson-Normal generalized linear mixed model. An example is provided in which two different methods are used to measure CD34+ cells.     

Indoor air pollution and pulmonary performance: investigating errors in exposure assessment

We use pulmonary function measurements on pre-adolescent children and indoor air pollution measurements in the homes of these children to illustrate estimation techniques for linear regression models containing independent variables measured with error. In our data set, replicate measures of indoor air pollutant concentrations provide one method of estimating measurement error variances. Surrogate information in the form of cigarettes smoked is also available for the pollutant of interest. Several estimation procedures are presented, and we combine two estimators, one based on surrogate information and one based on replication information, using generalized least squares.     

Rank‐preserving regression: a more robust rank regression model against outliers

Mean‐based semi‐parametric regression models such as the popular generalized estimating equations are widely used to improve robustness of inference over parametric models. Unfortunately, such models are quite sensitive to outlying observations. The Wilcoxon‐score‐based rank regression (RR) provides more robust estimates over generalized estimating equations against outliers. However, the RR and its extensions do not sufficiently address missing data arising in longitudinal studies. In this paper, we propose a new approach to address outliers under a different framework based on the functional response models. This functional‐response‐model‐based alternative not only addresses limitations of the RR and its extensions for longitudinal data, but, with its rank‐preserving property, even provides more robust estimates than these alternatives. The proposed approach is illustrated with both real and simulated data. Copyright © 2016 John Wiley & Sons, Ltd.     

Bayesian adjustment for covariate measurement errors: A flexible parametric approach

In most epidemiological investigations, the study units are people, the outcome variable (or the response) is a health‐related event, and the explanatory variables are usually environmental and/or socio‐demographic factors. The fundamental task in such investigations is to quantify the association between the explanatory variables (covariates/exposures) and the outcome variable through a suitable regression model. The accuracy of such quantification depends on how precisely the relevant covariates are measured. In many instances, we cannot measure some of the covariates accurately. Rather, we can measure noisy (mismeasured) versions of them. In statistical terminology, mismeasurement in continuous covariates is known as measurement errors or errors‐in‐variables. Regression analyses based on mismeasured covariates lead to biased inference about the true underlying response–covariate associations. In this paper, we suggest a flexible parametric approach for avoiding this bias when estimating the response–covariate relationship through a logistic regression model. More specifically, we consider the flexible generalized skew‐normal and the flexible generalized skew‐t distributions for modeling the unobserved true exposure. For inference and computational purposes, we use Bayesian Markov chain Monte Carlo techniques. We investigate the performance of the proposed flexible parametric approach in comparison with a common flexible parametric approach through extensive simulation studies. We also compare the proposed method with the competing flexible parametric method on a real‐life data set. Though emphasis is put on the logistic regression model, the proposed method is unified and is applicable to the other generalized linear models, and to other types of non‐linear regression models as well. Copyright © 2009 John Wiley & Sons, Ltd.     

Variable selection for distribution‐free models for longitudinal zero‐inflated count responses

Zero‐inflated count outcomes arise quite often in research and practice. Parametric models such as the zero‐inflated Poisson and zero‐inflated negative binomial are widely used to model such responses. Like most parametric models, they are quite sensitive to departures from assumed distributions. Recently, new approaches have been proposed to provide distribution‐free, or semi‐parametric, alternatives. These methods extend the generalized estimating equations to provide robust inference for population mixtures defined by zero‐inflated count outcomes. In this paper, we propose methods to extend smoothly clipped absolute deviation (SCAD)‐based variable selection methods to these new models. Variable selection has been gaining popularity in modern clinical research studies, as determining differential treatment effects of interventions for different subgroups has become the norm, rather the exception, in the era of patent‐centered outcome research. Such moderation analysis in general creates many explanatory variables in regression analysis, and the advantages of SCAD‐based methods over their traditional counterparts render them a great choice for addressing this important and timely issues in clinical research. We illustrate the proposed approach with both simulated and real study data. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

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.     

Bivariate association analyses for the mixture of continuous and binary traits with the use of extended generalized estimating equations

Genome-wide association (GWA) study is becoming a powerful tool in deciphering genetic basis of complex human diseases/traits. Currently, the univariate analysis is the most commonly used method to identify genes associated with a certain disease/phenotype under study. A major limitation with the univariate analysis is that it may not make use of the information of multiple correlated phenotypes, which are usually measured and collected in practical studies. The multivariate analysis has proven to be a powerful approach in linkage studies of complex diseases/traits, but it has received little attention in GWA. In this study, we aim to develop a bivariate analytical method for GWA study, which can be used for a complex situation in which continuous trait and a binary trait are measured under study. Based on the modified extended generalized estimating equation (EGEE) method we proposed herein, we assessed the performance of our bivariate analyses through extensive simulations as well as real data analyses. In the study, to develop an EGEE approach for bivariate genetic analyses, we combined two different generalized linear models corresponding to phenotypic variables using a seemingly unrelated regression model. The simulation results demonstrated that our EGEE-based bivariate analytical method outperforms univariate analyses in increasing statistical power under a variety of simulation scenarios. Notably, EGEE-based bivariate analyses have consistent advantages over univariate analyses whether or not there exists a phenotypic correlation between the two traits. Our study has practical importance, as one can always use multivariate analyses as a screening tool when multiple phenotypes are available, without extra costs of statistical power and false-positive rate. Analyses on empirical GWA data further affirm the advantages of our bivariate analytical method.     

A partially linear additive model for clustered proportion data

Proportion data with support lying in the interval [0,1] are a commonplace in various domains of medicine and public health. When these data are available as clusters, it is important to correctly incorporate the within‐cluster correlation to improve the estimation efficiency while conducting regression‐based risk evaluation. Furthermore, covariates may exhibit a nonlinear relationship with the (proportion) responses while quantifying disease status. As an alternative to various existing classical methods for modeling proportion data (such as augmented Beta regression) that uses maximum likelihood, or generalized estimating equations, we develop a partially linear additive model based on the quadratic inference function. Relying on quasi‐likelihood estimation techniques and polynomial spline approximation for unknown nonparametric functions, we obtain the estimators for both parametric part and nonparametric part of our model and study their large‐sample theoretical properties. We illustrate the advantages and usefulness of our proposition over other alternatives via extensive simulation studies, and application to a real dataset from a clinical periodontal study.     

A nonparametric smoothing method for assessing GEE models with longitudinal binary data

Studies involving longitudinal binary responses are widely applied in the health and biomedical sciences research and frequently analyzed by generalized estimating equations (GEE) method. This article proposes an alternative goodness-of-fit test based on the nonparametric smoothing approach for assessing the adequacy of GEE fitted models, which can be regarded as an extension of the goodness-of-fit test of le Cessie and van Houwelingen (Biometrics 1991; 47:1267-1282). The expectation and approximate variance of the proposed test statistic are derived. The asymptotic distribution of the proposed test statistic in terms of a scaled chi-squared distribution and the power performance of the proposed test are discussed by simulation studies. The testing procedure is demonstrated by two real data. Copyright (c) 2008 John Wiley & Sons, Ltd.     

Expected estimating equation using calibration data for generalized linear models with a mixture of Berkson and classical errors in covariates

Data collected in many epidemiological or clinical research studies are often contaminated with measurement errors that may be of classical or Berkson error type. The measurement error may also be a combination of both classical and Berkson errors and failure to account for both errors could lead to unreliable inference in many situations. We consider regression analysis in generalized linear models when some covariates are prone to a mixture of Berkson and classical errors, and calibration data are available only for some subjects in a subsample. We propose an expected estimating equation approach to accommodate both errors in generalized linear regression analyses. The proposed method can consistently estimate the classical and Berkson error variances based on the available data, without knowing the mixture percentage. We investigated its finite‐sample performance numerically. Our method is illustrated by an application to real data from an HIV vaccine study. Copyright © 2013 John Wiley & Sons, Ltd.     

On performance of parametric and distribution‐free models for zero‐inflated and over‐dispersed count responses

Zero‐inflated Poisson (ZIP) and negative binomial (ZINB) models are widely used to model zero‐inflated count responses. These models extend the Poisson and negative binomial (NB) to address excessive zeros in the count response. By adding a degenerate distribution centered at 0 and interpreting it as describing a non‐risk group in the population, the ZIP (ZINB) models a two‐component population mixture. As in applications of Poisson and NB, the key difference between ZIP and ZINB is the allowance for overdispersion by the ZINB in its NB component in modeling the count response for the at‐risk group. Overdispersion arising in practice too often does not follow the NB, and applications of ZINB to such data yield invalid inference. If sources of overdispersion are known, other parametric models may be used to directly model the overdispersion. Such models too are subject to assumed distributions. Further, this approach may not be applicable if information about the sources of overdispersion is unavailable. In this paper, we propose a distribution‐free alternative and compare its performance with these popular parametric models as well as a moment‐based approach proposed by Yu et al. [Statistics in Medicine 2013; 32 : 2390–2405]. Like the generalized estimating equations, the proposed approach requires no elaborate distribution assumptions. Compared with the approach of Yu et al., it is more robust to overdispersed zero‐inflated responses. We illustrate our approach with both simulated and real study data. Copyright © 2015 John Wiley & Sons, Ltd.     

Regression modeling of combined data from multiple sample surveys

Combined data from multiple sample surveys are often used in population‐based epidemiologic studies. Combining data can be beneficial in that sampling errors are reduced and coverage biases are corrected. Also, it is often necessary in order to use information lacking in one survey but available in another. We propose an estimation equations method for generalized linear models from the combined data. The estimation procedures for logistic regression models and Poisson regression models are developed. An example of estimating the relative risk of death by smoking status is used as an illustration and a simulation study is performed to examine the performance of the method. Copyright © 2009 John Wiley & Sons, Ltd.     

Estimation of average treatment effects among multiple treatment groups by using an ensemble approach

In observational studies, generalized propensity score (GPS)–based statistical methods, such as inverse probability weighting (IPW) and doubly robust (DR) method, have been proposed to estimate the average treatment effect (ATE) among multiple treatment groups. In this article, we investigate the GPS-based statistical methods to estimate treatment effects from two aspects. The first aspect of our investigation is to obtain an optimal GPS estimation method among four competing GPS estimation methods by using a rank aggregation approach. We further examine whether the optimal GPS-based IPW and DR methods would improve the performance for estimating ATE. It is well known that the DR method is consistent if either the GPS or the outcome models are correctly specified. The second aspect of our investigation is to examine whether the DR method could be improved if we ensemble outcome models. To that end, bootstrap method and rank aggregation method are used to obtain the ensemble optimal outcome model from several competing outcome models, and the resulting outcome model is incorporated into the DR method, resulting in an ensemble DR (enDR) method. Extensive simulation results indicate that the enDR method provides the best performance in estimating the ATE regardless of the method used for estimating GPS. We illustrate our methods using the MarketScan healthcare insurance claims database to examine the treatment effects among three different bones and substitutes used for spinal fusion surgeries. We draw conclusions based on the estimates from the enDR method coupled with the optimal GPS estimation method.     

Leveraging prognostic baseline variables to gain precision in randomized trials

We focus on estimating the average treatment effect in a randomized trial. If baseline variables are correlated with the outcome, then appropriately adjusting for these variables can improve precision. An example is the analysis of covariance (ANCOVA) estimator, which applies when the outcome is continuous, the quantity of interest is the difference in mean outcomes comparing treatment versus control, and a linear model with only main effects is used. ANCOVA is guaranteed to be at least as precise as the standard unadjusted estimator, asymptotically, under no parametric model assumptions and also is locally semiparametric efficient. Recently, several estimators have been developed that extend these desirable properties to more general settings that allow any real‐valued outcome (e.g., binary or count), contrasts other than the difference in mean outcomes (such as the relative risk), and estimators based on a large class of generalized linear models (including logistic regression). To the best of our knowledge, we give the first simulation study in the context of randomized trials that compares these estimators. Furthermore, our simulations are not based on parametric models; instead, our simulations are based on resampling data from completed randomized trials in stroke and HIV in order to assess estimator performance in realistic scenarios. We provide practical guidance on when these estimators are likely to provide substantial precision gains and describe a quick assessment method that allows clinical investigators to determine whether these estimators could be useful in their specific trial contexts. Copyright © 2015 John Wiley & Sons, Ltd.     

Inferences on the common coefficient of variation

The coefficient of variation is often used as a measure of precision and reproducibility of data in medical and biological science. This paper considers the problem of making inference about the common population coefficient of variation when it is a priori suspected that several independent samples are from populations with a common coefficient of variation. The procedures for confidence interval estimation and hypothesis testing are developed based on the concepts of generalized variables. The coverage properties of the proposed confidence intervals and type-I errors of the proposed tests are evaluated by simulation. The proposed methods are illustrated by a real life example.     

Measures of agreement for vectorcardiography data

In this paper, nonparametric methods are proposed for quantifying agreement and disagreement between different measurement methods when the results of the measurements are rotation matrices. First, the expected squared distance between two matrices is used to quantify the measurement agreement. Two choices of such distance are considered—the Frobenius distance and geodesic distance. Second, the notion of ‘concordance correlation coefficient’, a commonly used measure of agreement, is extended to the space of rotation matrices. Such generalized concordance coefficient can be treated as a normalized expected squared distance. Since no two measurement systems can be expected to be in perfect agreement, it becomes necessary to define a notion of practical agreement. We define such a notion. Moreover, for both proposed methods, the percentile bootstrap procedure is implemented to provide a confidence interval to help make a decision concerning practical agreement/disagreement in real‐life applications. The methodology is illustrated using two data sets, one based on an application involving vectorcardiography data (Biometrika 1972; 59 :665–676) and the other based on a synthetic data set. Copyright © 2009 John Wiley & Sons, Ltd.