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In many surveys and clinical trials, we obtain measurements on covariates or biomarkers that are left-censored due to the limit of detection. In such cases, it is necessary to correct for the left-censoring when studying covariate effects in regression models. The expectation-maximization (EM) algorithm is widely used for the likelihood inference in generalized linear models with censored covariates. The EM method, however, requires intensive computation involving high-dimensional integration with respect to the covariates when the dimension of the censored covariates is large. To reduce such computational difficulties, we propose and explore a Monte Carlo EM method based on the Metropolis algorithm. The finite-sample properties of the proposed estimators are studied using Monte Carlo simulations. An application is also provided using actual data obtained from a health and nutrition examination survey. Journal of Statistical Research 2021, Vol. 55, No. 2, pp. 359-375

We study robust designs for generalized linear mixed models (GLMMs) with protections against possible departures from underlying model assumptions. Among various types of model departures, an imprecision in the assumed linear predictor or the link function has a great impact on predicting the conditional mean response function in a GLMM. We develop methods for constructing adaptive sequential designs when the fitted mean response or the link function is possibly of an incorrect parametric form. We adopt the maximum likelihood method for estimating the parameters in GLMMs and investigate both I-optimal and D-optimal design criteria for the construction of robust sequential designs. To study the empirical properties of these sequential designs, we ran a series of simulations using both logistic and Poisson mixed models. As indicated in the simulation results, the I-optimal design generally outperforms the D-optimal design for all scenarios considered. Both designs are more efficient than the conventionally used uniform design and the classical D-optimal design obtained under the assumption that the fitted models are correctly specified. The proposed designs are also illustrated in an example using actual data from a dose–response experiment.

In this article, we investigate marginal models for analyzing incomplete longitudinal count data with dropouts. Specifically, we explore commonly used generalized estimating equations and weighted generalized estimating equations for fitting log-linear models to count data in the presence of monotone missing responses. A series of simulations were carried out to examine the finite-sample properties of the estimators in the presence of both correctly specified and misspecified dropout mechanisms. An application is provided using actual longitudinal survey data from the Health and Retirement Study (HRS) (HRS, 2019)

Small area estimation with categorical outcomes often requires intensive computation, as the marginal likelihood does not have a closed form in general. The likelihood analysis is further complicated by deviations in distributional assumptions often arise through outliers in the data. In this paper, the author proposes a robust method for estimating the small area parameters. Finite-sample properties of the estimators are investigated using Monte Carlo simulations. The empirical study shows that the proposed robust method is very useful for bounding the influence of outliers on the small area estimators. To approximate the mean squared errors of the estimators, a parametric bootstrap method is adopted. An application is also provided using actual data from a public health survey.

In this paper, we propose and explore a novel semiparametric approach to analyzing longitudinal count data. We address the issue of missingness in longitudinal data and propose a weighted generalized estimations equations approach to fitting marginal mean response models for count responses with dropouts. Also, we investigate a spline regression approach to approximating the curvilinear relationship between the mean response and covariates. The asymptotic properties of the proposed estimators are studied in some detail. The empirical properties of the estimators are investigated using Monte Carlo simulations. An application is also provided using actual survey data obtained from the Health and Retirement Study (HRS).

In this paper, we propose an innovative method for jointly analyzing survival data and longitudinally measured continuous and ordinal data. We use a random effects accelerated failure time model for survival outcomes, a linear mixed model for continuous longitudinal outcomes and a proportional odds mixed model for ordinal longitudinal outcomes, where these outcome processes are linked through a set of association parameters. A primary objective of this study is to examine the effects of association parameters on the estimators of joint models. The model parameters are estimated by the method of maximum likelihood. The finite-sample properties of the estimators are studied using Monte Carlo simulations. The empirical study suggests that the degree of association among the outcome processes influences the bias, efficiency, and coverage probability of the estimators. Our proposed joint model estimators are approximately unbiased and produce smaller mean squared errors as compared to the estimators obtained from separate models. This work is motivated by a large multicenter study, referred to as the Genetic and Inflammatory Markers of Sepsis (GenIMS) study. We apply our proposed method to the GenIMS data analysis.

In many biological experiments, certain values of a biomarker are often nondetectable due to low concentrations of an analyte or the limitations of a chemical analysis device, resulting in left-censored values. There is an increasing demand for the analysis of data subject to detection limits in clinical and environmental studies. In this paper, we develop a novel statistical method for the maximum likelihood estimation in generalized linear models with covariates subject to detection limits. Simulations are carried out to study the relative performance of the proposed estimators, as compared to other existing estimators. The proposed method is also applied to a real dataset from the Maternal-Infant Research on Environmental Chemicals cohort study, where we investigate how different chemical mixtures affect the health outcomes of infants and pregnant women.

The accelerated failure time model is widely used for analyzing censored survival times often observed in clinical studies. It is well-known that the ordinary maximum likelihood estimators of the parameters in the accelerated failure time model are generally sensitive to potential outliers or small deviations from the underlying distributional assumptions. In this paper, we propose and explore a robust method for fitting the accelerated failure time model to survival data by bounding the influence of outliers in both the outcome variable and associated covariates. We also develop a sandwich-type variance-covariance function for approximating the variances of the proposed robust estimators. The finite-sample properties of the estimators are investigated based on empirical results from an extensive simulation study. An application is provided using actual data from a clinical study of primary breast cancer patients.

We discuss optimal sequential designs for analyzing longitudinal data or repeated measurements in the framework of generalized linear mixed models (GLMMs). The construction of optimal designs for GLMMs typically requires intensive computation involving irreducibly high-dimensional integrals with respect to the random effects when calculating the Fisher information. In this article, we propose a simpler method for constructing optimal sequential designs based on some “pseudo” Fisher information. We investigate the performance of the proposed designs through simulation studies. The simulation results indicate that the loss of efficiency from the pseudo-optimal design construction process is minimal as compared to the computationally intensive D-optimal design. Furthermore, the proposed design appears to be as robust as the D-optimal design when possible misspecification to the assumed random effects distribution occurs. It is concluded that the proposed approach is of practical value for designing repeated-measures experiments.

Frailty models are multiplicative hazard models for studying association between survival time and important clinical covariates. When some values of a clinical covariate are unobserved but known to be below a threshold called the limit of detection (LOD), naive approaches ignoring this problem, such as replacing the undetected value by the LOD or half of the LOD, often produce biased parameter estimate with larger mean squared error of the estimate. To address the LOD problem in a frailty model, we propose a flexible smooth nonparametric density estimator along with Simpson's numerical integration technique. This is an extension of an existing method in the likelihood framework for the estimation and inference of the model parameters. The proposed new method shows the estimators are asymptotically unbiased and gives smaller mean squared error of the estimates. Compared with the existing method, the proposed new method does not require distributional assumptions for the underlying covariates. Simulation studies were conducted to evaluate the performance of the new method in realistic scenarios. We illustrate the use of the proposed method with a data set from Genetic and Inflammatory Markers of Sepsis study in which interlekuin-10 was subject to LOD. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, the authors investigate a robust semi-parametric mixed effects model for analyzing longitudinal data with an unspecified mean response function. The robust method, developed in the framework of the maximum likelihood, is used to bound the influence of potential outliers when estimating the model parameters. The authors also present a robust test procedure for assessing the significance of a variance component in the mixed model. An application is provided using a clinical dataset from a retinopathy of prematurity study in which longitudinal measurements were obtained from premature infants treated with supplemental oxygen. The empirical properties of the proposed estimators are also studied in simulations.

We develop and study an innovative method for jointly modeling longitudinal response and time-to-event data with a covariate subject to a limit of detection. The joint model assumes a latent process based on random effects to describe the association between longitudinal and time-to-event data. We study the role of the association parameter on the regression parameters estimators. We model the longitudinal and survival outcomes using linear mixed-effects and Weibull frailty models, respectively. Because of the limit of detection, missing covariate (explanatory variable, x) values may lead to the non-ignorable missing, resulting in biased parameter estimates with poor coverage probabilities of the confidence interval. We define and estimate the probability of missing due to the limit of detection. Then we develop a novel joint density and hence the likelihood function that incorporates the effect of left-censored covariate. Monte Carlo simulations show that the estimators of the proposed method are approximately unbiased and provide expected coverage probabilities for both longitudinal and survival submodels parameters. We also present an application of the proposed method using a large clinical dataset of pneumonia patients obtained from the Genetic and Inflammatory Markers of Sepsis study.

In many biological experiments, certain values of a biomarker are often nondetectable due to low concentrations of an analyte or the limitations of a chemical analysis device, resulting in left-censored values. There is an increasing demand for the analysis of data subject to detection limits in clinical and environmental studies. In this paper, we develop a novel statistical method for the maximum likelihood estimation in generalized linear models with covariates subject to detection limits. Simulations are carried out to study the relative performance of the proposed estimators, as compared to other existing estimators. The proposed method is also applied to a real dataset from the Maternal-Infant Research on Environmental Chemicals cohort study, where we investigate how different chemical mixtures affect the health outcomes of infants and pregnant women.

This article proposes and explores a robust method for analysing longitudinal continuous responses with informative drop-outs. The robust method, developed in the framework of the maximum likelihood, is useful for bounding the influence of potential outliers when analysing the data. The asymptotic properties of the robust estimators are discussed. The empirical properties are investigated in simulations. An application is provided using longitudinal measurements on a biomarker of sepsis being studied for understanding the progression of pneumonia to severe sepsis in a group of patients. The Canadian Journal of Statistics 42: 670–695; 2014 © 2014 Statistical Society of Canada Resume Les auteurs proposent et explorent une methode d'analyse robuste pour une variable reponse longitudinale continue presentant des abandons informatifs. Developpee dans le contexte du maximum de vraisemblance, la methode robuste permet de borner l'influence des valeurs aberrantes potentielles lors de l'analyse des donnees. Les auteurs discutent les proprietes asymptotiques des estimateurs robustes et presentent des simulations afin d'en decrire les proprietes empiriques. Ils appliquent egalement leur methode a des mesures longitudinales d'un biomarqueur de la septicemie etudie afin de comprendre le developpement d'une septicemie grave a partir d'une pneumonie chez un groupe de patients. La revue canadienne de statistique 42: 1–26; 2014 © 2014 Societe statistique du Canada

Small area estimation has been extensively studied under unit level linear mixed models. In particular, empirical best linear unbiased predictors (EBLUPs) of small area means and associated estimators of mean squared prediction error (MSPE) that are unbiased to second order have been developed. However, EBLUP can be sensitive to outliers. Sinha & Rao (2009) developed a robust EBLUP method and demonstrated its advantages over the EBLUP in the presence of outliers in the random small area effects and/or unit level errors in the model. A bootstrap method for estimating MSPE of the robust EBLUP was also proposed. In this paper, we relax the assumption of linear regression for the fixed part of the model and we replace it by a weaker assumption of a semi-parametric regression. By approximating the semi-parametric mixed model by a penalized spline mixed model, we develop robust EBLUPs of small area means and bootstrap estimators of MSPE. Results of a simulation study are also presented. The Canadian Journal of Statistics 42: 126–141; 2014 © 2013 Statistical Society of Canada Resume L'estimation pour petits domaines a ete largement etudiee a l'aide de modeles lineaires mixtes au niveau des unites. Dans ce contexte, les meilleurs predicteurs lineaires sans biais empiriques (MPLSBE) pour la moyenne de petits domaines ont ete developpes, ainsi que des estimateurs sans biais au deuxieme ordre pour l'erreur quadratique moyenne de prevision (EQMP) associee. Cependant, les MPLSBE peuvent etre sensibles aux donnees aberrantes. Sinha et Rao (2009) ont elabore des MPLSBE robustes et ont demontre leurs avantages par rapport aux MPLSBE en presence de donnees aberrantes dans les effets aleatoires des petits domaines ou dans les termes d'erreur au niveau de l'unite. Ces auteurs ont aussi propose une methode bootstrap d'estimation de l'EQMP des MPLSBE robustes. Dans cet article, les auteurs assouplissent l'hypothese de regression lineaire dans la partie fixe du modele et la remplacent par une hypothese moins rigide de regression semi-parametrique. En approximant le modele mixte semi-parametrique par un modele mixte de splines penalise, ils developpent des MPLSBE robustes pour petits domaines et des estimateurs bootstrap de l'EQMP. Les resultats d'une etude de simulation sont egalement presentes. La revue canadienne de statistique 42: 126–141; 2014 © 2013 Societe statistique du Canada

Missing data are common in many experiments, including surveys, clinical trials, epidemiological studies, and environmental studies. Unconstrained likelihood inferences for generalized linear models (GLMs) with nonignorable missing covariates have been studied extensively in the literature. However, parameter orderings or constraints may occur naturally in practice, and thus the efficiency of a statistical method may be improved by incorporating parameter constraints into the likelihood function. In this paper, we consider constrained inference for analysing GLMs with nonignorable missing covariates under linear inequality constraints on the model parameters. Specifically, constrained maximum likelihood (ML) estimation is based on the gradient projection expectation maximization approach. Further, we investigate the asymptotic null distribution of the constrained likelihood ratio test (LRT). Simulations study the empirical properties of the constrained ML estimators and LRTs, which demonstrate improved pr...

In this paper, the author investigates optimal designs for multivariate binary regression models used in many clinical experiments. As the computation of a joint likelihood for multiple binary outcomes is often tedious, the author proposes and explores a pseudo-likelihood approach for choosing an optimal design under minimal parametric assumptions. The proposed design is considered robust in the sense that it provides estimators that are almost as efficient as those obtained from D-optimal designs under correctly specified likelihood functions and it can provide more efficient estimators as compared to D-optimal designs under misspecified likelihood functions. The asymptotic relative efficiencies of the maximum pseudo-likelihood estimators with respect to the exact maximum likelihood estimators are investigated. Monte Carlo simulations are carried out to explore the finite-sample properties of the maximum pseudo-likelihood estimators obtained under the proposed design scheme. The method is also illustrated in an example using actual data from a clinical study.

Generalized linear mixed models (GLMMs) are often used for analyzing cluster correlated data, including longitudinal data and repeated measurements. Full unrestricted maximum likelihood (ML) approaches for inference on both fixed-and random-effects parameters in GLMMs have been extensively studied in the literature. However, parameter orderings or constraints may occur naturally in practice, and in such cases, the efficiency of a statistical method is improved by incorporating the parameter constraints into the ML estimation and hypothesis testing. In this paper, inference for GLMMs under linear inequality constraints is considered. The asymptotic properties of the constrained ML estimators and constrained likelihood ratio tests for GLMMs have been studied. Simulations investigated the empirical properties of the constrained ML estimators, compared to their unrestricted counterparts. An application to a recent survey on Canadian youth smoking patterns is also presented. As these survey data exhibit natural parameter orderings, a constrained GLMM has been considered for data analysis. The Canadian Journal of Statistics 40: 243–258; 2012 © 2012 Crown in the right of Canada Les modeles lineaires mixtes generalises (GLMM) sont souvent utilises pour analyser les donnees correlees en grappe, incluant les donnees longitudinales et les mesures repetees. L'approche par le maximum de vraisemblance complet non contraint pour faire de l'inference sur les parametres fixes et des effets aleatoires a ete etudiee de facon exhaustive dans la litterature. Cependant, en pratique, un ordonnancement des parametres ou des contraintes peuvent apparaitre de facon naturelle. Dans de tels cas, l'efficacite de la methode statistique est amelioree lorsque les contraintes sur les parametres sont prises en compte dans l'estimation par la methode du maximum de vraisemblance ou les tests d'hypotheses. Dans cet article, nous considerons l'inference dans les GLMM sous contraintes d'inegalites lineaires. Nous etudions les proprietes asymptotiques des estimateurs du maximum de vraisemblance contraints et des tests du rapport de vraisemblance contraints pour les GLMM. Les proprietes empiriques des estimateurs du maximum de vraisemblance contraints sont etudiees l'aide de simulations et elles sont comparees a celles des estimateurs non contraints. Nous presentons aussi une application basee une enquete recente sur le tabagisme chez les jeunes au Canada. Comme cette enquete presente un ordonnancement naturel des parametres, l'analyse des donnees est faite a l'aide des GLMM contraints. La revue canadienne de statistique 40: 243–258 2012 © 2012 Couronne du Chef du Canada

We encounter missing data in many longitudinal studies. When the missing data are nonignorable, it is important to analyze the data by incorporating the missing data mechanism into the observed data likelihood function. The classical maximum likelihood (ML) method for analyzing longitudinal missing data has been extensively studied in the literature. However, it is well-known that the ordinary ML estimators are sensitive to extreme observations or outliers in the data. In this paper, we propose and explore a robust method, which is developed in the framework of the ML method, and is useful for downweighting any influential observations in the data when estimating the model parameters. We study the empirical properties of the robust estimators in small simulations. We also illustrate the robust method using incomplete longitudinal data on CD4 counts from clinical trials of HIV-infected patients.

We discuss the construction of D-optimal sequential designs for the analysis of longitudinal data or repeated measurements using generalized linear mixed models (GLMMs). We investigate the performance of the design through a simulation study, which indicates that the proposed design can be very successful in improving the efficiency of the ML estimators in GLMMs relative to some common competitors. Our simulations also suggest that the usual normal-theory inference procedures remain valid under the sequential sampling schemes. We also present an example using real data obtained from a clinical study.

For analyzing longitudinal binary data with nonignorable and non-monotone missing responses, a full likelihood method is complicated algebraically, and often requires intensive computation, especially when there are many follow-up times. As an alternative, a pseudo-likelihood approach has been proposed in the literature under minimal parametric assumptions. This formulation only requires specification of the marginal distributions of the responses and missing data mechanism, and uses an independence working assumption. However, this estimator can be inefficient for estimating both time-varying and time-stationary effects under moderate to strong within-subject associations among repeated responses. In this article, we propose an alternative estimator, based on a bivariate pseudo-likelihood, and demonstrate in simulations that the proposed method can be much more efficient than the previous pseudo-likelihood obtained under the assumption of independence. We illustrate the method using longitudinal data on CD4 counts from two clinical trials of HIV-infected patients.

Small area estimation has received considerable attention in recent years because of growing demand for small area statistics. Basic area-level and unit-level models have been studied in the literature to obtain empirical best linear unbiased prediction (EBLUP) estimators of small area means. Although this classical method is useful for estimating the small area means efficiently under normality assumptions, it can be highly influenced by the presence of outliers in the data. In this article, the authors investigate the robustness properties of the classical estimators and propose a resistant method for small area estimation, which is useful for downweighting any influential observations in the data when estimating the model parameters. To estimate the mean squared errors of the robust estimators of small area means, a parametric bootstrap method is adopted here, which is applicable to models with block diagonal covariance structures. Simulations are carried out to study the behaviour of the proposed robust estimators in the presence of outliers, and these estimators are also compared to the EBLUP estimators. Performance of the bootstrap mean squared error estimator is also investigated in the simulation study. The proposed robust method is also applied to some real data to estimate crop areas for counties in Iowa, using farm-interview data on crop areas and LANDSAT satellite data as auxiliary information. The Canadian Journal of Statistics 37: 381–399; 2009 © 2009 Statistical Society of Canada L'estimation de petits domaines a rec cu considerablement d'attention ces dernieres annees en raison de la demande croissante de statistiques regionales. Les modeles au niveau des domaines et des unites ont deja ete etudies dans la litterature et les meilleurs estimateurs lineaires sans biais empiriques (EBLUP) pour les petits domaines ont ete obtenus. Quoique cette methode classique est utile pour estimer les moyennes regionales de fac con efficace sous l'hypothese de normalite, ses resultats sont grandement influences par la presente de donnees aberrantes. Dans cet article, les auteurs etudient les proprietes de robustesse des estimateurs classiques et ils proposent une methode robuste pour l'estimation de petits domaines qui diminue le poids associe aux observations influentes lors de l'estimation des parametres du modele. Afin d'estimer l'erreur quadratique moyenne des estimateurs robustes des moyennes regionales, une methode d'auto-amorc cage parametrique est utilisee. Cette methode peut etre utilisee aux modeles dont la structure de covariance est bloc diagonale. Des simulations sont faites pour etudier le comportement des estimateurs robustes proposes en presence de valeurs aberrantes et aussi pour les comparer aux estimateurs EBLUP. La performance de l'estimateur “boostrap” de l'erreur quadratique moyenne est aussi etudiee dans cette etude de simulations. Cette methode robuste est appliquee a l'estimation de la superficie des cultures pour les comtes de l'Iowa en se basant sur des entrevues au niveau des fermes et en utilisant les donnees provenant du satellite LANDSAT comme information auxiliaire. La revue canadienne de statistique 37: 381–399; 2009 © 2009 Societe statistique du Canada

In many applications of generalized linear mixed models to clustered correlated or longitudinal data, often we are interested in testing whether a random effects variance component is zero. The usual asymptotic mixture of chi-square distributions of the score statistic for testing constrained variance components does not necessarily hold. In this article, the author proposes and explores a parametric bootstrap test that appears to be valid based on its estimated level of significance under the null hypothesis. Results from a simulation study indicate that the bootstrap test has a level much closer to the nominal one while the asymptotic test is conservative, and is more powerful than the usual asymptotic score test based on a mixture of chi-squares. The proposed bootstrap test is illustrated using two sets of real-life data obtained from clinical trials. The Canadian Journal of Statistics © 2009 Statistical Society of Canada Dans plusieurs applications des modeles lineaires mixtes generalises aux donnees correlees en grappe ou aux donnees longitudinales, nous sommes souvent interesses a voir si la composante de la variance reliee aux effets aleatoires est nulle ou non. La distribution asymptotique standard, correspondant a un melange de distributions du khi carre, des statistiques de type score utilisee pour tester la composante de la variance contrainte n'est pas necessairement valide. Dans cet article, l'auteur propose et etudie un test de reechantillonnage parametrique qui semble etre valide si nous nous basons sur son niveau de confiance sous l'hypothese nulle. Des simulations indiquent que le test de reechanillonnage a un niveau plus pres de la valeur nominale tandis que le test asymptotique est conservateur. De plus, il est plus puissant que celui base sur le melange de distributions du khi carre. L'utilisation de ce test de reechantillonnage est illustree a l'aide de deux jeux de donnees provenant d'essais cliniques. La revue canadienne de statistique © 2009 Societe statistique du Canada

The EM algorithm is often used for finding the maximum likelihood estimates in generalized linear models with incomplete data. In this article, the author presents a robust method in the framework of the maximum likelihood estimation for fitting generalized linear models when nonignorable covariates are missing. His robust approach is useful for downweighting any influential observations when estimating the model parameters. To avoid computational problems involving irreducibly high-dimensional integrals, he adopts a Metropolis-Hastings algorithm based on a Markov chain sampling method. He carries out simulations to investigate the behaviour of the robust estimates in the presence of outliers and missing co variates; furthermore, he compares these estimates to the classical maximum likelihood estimates. Finally, he illustrates his approach using data on the occurrence of delirium in patients operated on for abdominal aortic aneurysm.

In this paper, we propose and explore a semiparametric approach to analyzing longitudinal binary data often observed in clinical studies. We applied second-order GEE approach to analyze longitudinal binary responses based on a partially linear single-index model. We use a local polynomial smoothing technique to estimate the single-index. We study the empirical properties of the proposed estimators using simulations. The empirical results demonstrate that if the true underlying model is partially linear, then our proposed method generally provides unbiased and efficient estimators. The proposed method is also applied to some real data sets obtained from longitudinal studies.

The author develops a robust quasi-likelihood method, which appears to be useful for down-weighting any influential data points when estimating the model parameters. He illustrates the computational issues of the method in an example. He uses simulations to study the behaviour of the robust estimates when data are contaminated with outliers, and he compares these estimates to those obtained by the ordinary quasi-likelihood method. Inference robuste pour des modeles de donnees longitudinales lineaires generalises L'auteur developpe une methode de quasi-vraisemblance robuste qui semble utile pour reduire l'impact des points influents sur l'estimation des parametres d'un modele. Il illustre les questions de calcul liees a la methode a l'aide d'un exemple. Il a recours a des simulations pour etudier le comportement des estimations robustes lorsque les donnees sont contaminees par des valeurs aberrantes et il compare ces estimations a celles obtenues par la methode de quasi-vraisemblance ordinaire.

The method of maximum likelihood (ML) is widely used for analyzing generalized linear mixed models (GLMM's). A full maximum likelihood analysis requires numerical integration techniques for calculation of the log-likelihood, and to avoid the computational problems involving irreducibly high-dimensional integrals, several maximum likelihood algorithms have been proposed in the literature to estimate the model parameters by approximating the log-likelihood function. Although these likelihood algorithms are useful for fitting the GLMM's efficiently under strict model assumptions, they can be highly influenced by the presence of unusual data points. In this article, the author develops a technique for finding robust maximum likelihood (RML) estimates of the model parameters in GLMM's, which appears to be useful in downweighting the influential data points when estimating the parameters. The asymptotic properties of the robust estimators are investigated under some regularity conditions. Small simulations are ...

Generalized M (or GM) estimation has been extended to the case of a nonlinear regression model with autoregressive and heteroscedastic errors. The robustness properties of the GM estimators have been investigated based on the time-series analog of Hampel's influence function. The asymptotic properties of these estimators have been studied in some detail.

Despite recent therapeutic advances, multiple myeloma (MM) remains largely incurable. Herein we report results of a phase I/II trial to evaluate the safety and activity of autologous T-cells engineered to express an affinity-enhanced T-cell receptor (TCR) recognizing a naturally processed peptide shared by the cancer-testis antigens NY-ESO-1 and LAGE-1. Twenty patients with antigen-positive MM received an average 2.4×109 engineered T cells two days after autologous stem cell transplant (ASCT). Infusions were well-tolerated without clinically apparent cytokine release syndrome, despite high IL-6 levels. Engineered T-cells expanded, persisted, trafficked to marrow and exhibited a cytotoxic phenotype. Persistence of engineered T cells in blood was inversely associated with NY-ESO-1 levels in the marrow. Disease progression was associated with loss of T cell persistence or antigen escape, consistent with the expected mechanism of action of the transferred T cells. Encouraging clinical responses were observed in 16 of 20 patients (80%) with advanced disease, with a median progression free survival of 19.1 months. NY-ESO-1/LAGE-1 TCR-engineered T-cells were safe, trafficked to marrow and showed extended persistence that correlated with clinical activity against antigen-positive myeloma.

This article proposes and explores a robust approach to identifying differential circulating miRNAs in the plasma of patients with breast cancer. The proposed approach, developed in the framework of the M-estimation, is used to provide protection against potential outliers in miRNA expression data. As the study involves multiple comparisonswith a large number of circulating miRNAs, robust multiple tests are adopted at a given level of false discovery rate (FDR). Also, due to the uncertainties in the underlying distributions of the miRNA expression data sets, the p-values of the multiple tests are approximated using a permutation method. The empirical properties of the proposed robust tests are studied in simulations. An application is provided using miRNA expression data from a breast cancer study.

The authors introduce the formal notion of an approximately specified nonlinear regression model and investigate sequential design methodologies when the fitted model is possibly of an incorrect parametric form. They present small-sample simulation studies which indicate that their new designs can be very successful, relative to some common competitors, in reducing mean squared error due to model misspecifi-cation and to heteroscedastic variation. Their simulations also suggest that standard normal-theory inference procedures remain approximately valid under the sequential sampling schemes. The methods are illustrated both by simulation and in an example using data from an experiment described in the chemical engineering literature. Les auteurs definissent formellement le concept de modele de regression non lineaire approxima-tif et proposentdes plans d'experience sequentiels pour les situations o4uG la forme parametrique du modele ajuste est inexacte. Ils presentent une etude de simulation qui montre que, pour de petits echantillons, leurs nouveaux plans sont largement preferables aux plans usuels en terme de reduction de I'erreur quadratique moyenne associee a rinadequation du modele et a l'heteroscedasticite. Leurs simulations montrent aussi que les procedures d'inference classiques associees au paradigme normal restent valables, a peu de choses pres, pour ces plans expeimentaux se'quentiels. La methodologie proposde est illustree par voie de simulation et au moyen d'une application concrete tiree de la pratique du genie chimique.

The authors consider the construction of weights for Generalised M-estimation. Such weights, when combined with appropriate score functions, afford protection from biases arising through incorrectly specified response functions, as well as from natural variation. The authors obtain minimax fixed weights of the Mallows type under the assumption that the density of the independent variables is correctly specified, and they obtain adaptive weights when this assumption is relaxed. A simulation study indicates that one can expect appreciable gains in precision when the latter weights are used and the various sources of model uncertainty are present.

Binary logistic and Poisson mixed models are used to analyse over/under-dispersed proportion and count data, respectively. It is, however, well known that a full likelihood analysis for such mixed models is hampered by the need for numerical integrations. To overcome such integration problems, recently Sutradhar and Qu (On Approximate Likelihood Inference in Poisson Mixed Model. The Canadian Journal of Statistics 1998, 26, 169–186) has introduced a small variance component (for random effects) based likelihood approximation (LA) approach to estimate the parameters of the Poisson mixed models and have shown that their LA approach performs better as compared to other leading approaches. More recently, Sutradhar and Das (A Higher-Order Approximation to the Likelihood Inference in the Poisson Mixed Model. Statistics and Probability Letters 2001, 52, 59–67) further improved the LA approach of Sutradhar and Qu to accommodate larger values of the variance component. These likelihood approximation techni...

In biomedical and epidemiological studies, often outcomes obtained are of mixed discrete and continuous in nature. Furthermore, due to some technical inconvenience or else, continuous responses are censored and also a few covariates cease to be observed completely. In this paper, we develop a model to tackle these complex situations. Our methodology is developed in a more general framework and provides a full-scale robust analysis of such complex models. The proposed robust maximum likelihood estimators of the model parameters are resistant to potential outliers in the data. We discuss the asymptotic properties of the robust estimators. To avoid computational difficulties involving irreducibly high-dimensional integrals, we propose a Monte Carlo method based on the Metropolis algorithm for approximating the robust maximum likelihood estimators. We study the empirical properties of these estimators in simulations. We also illustrate the proposed robust method using clustered data on blood sugar content from a clinical trial of individuals who were investigated for diabetes.

Problem statement: Modeling survival data with a set of covariates usually assumes that the values of the covariates are fully observed. However, in a variety of applications, some values of a covariate may be left-censored due to inadequate instrument sensitivity to quantify the biospecimen. When data are left-censored, the true values are missing but are known to be smaller than the detection limit. The most commonly used ad-hoc method to deal with nondetect values is to substitute the nondetect values by the detection limit. Such ad-hoc analysis of survival data with an explanatory variable subject to left-censoring may provide biased and inefficient estimators of hazard ratios and survivor functions. Method: We consider a parametric proportional hazards model to analyze time-to-event data. We propose a likelihood method for the estimation and inference of model parameters. In this likelihood approach, instead of replacing the nondetect values by the detection limit, we adopt a numerical integration technique to evaluate the observed data likelihood in the presence of a left-censored covariate. Monte Carlo simulations were used to demonstrate various properties of the proposed regression estimators including the consistency and efficiency. Results: The simulation study shows that the proposed likelihood approach provides approximately unbiased estimators of the model parameters. The proposed method also provides estimators that are more efficient than those obtained under the ad-hoc method. Also, unlike the ad-hoc estimators, the coverage probabilities of the proposed estimators are at their nominal level. Analysis of a large cohort study, genetic and inflammatory marker of sepsis study, shows discernibly different results based on the proposed method. Conclusion: Naive use of detection limit in a parametric survival model may provide biased and inefficient estimators of hazard ratios and survivor functions. The proposed likelihood approach provides approximately unbiased and efficient estimators of hazard ratios and survivor functions.

In the analysis of recurrent event data, frailties are commonly used to model the dependence structure among repeated event times within an individual. Often it is of interest to test whether the variance component in a frailty model is zero. It is well-known that the usual asymptotic mixtures of chi-square distributions of the score statistics for testing constrained variance components do not necessarily hold. In this paper, we propose and explore a stochastic permutation score test based on randomly permuting the indices associated with the individuals of a survival model. An empirical study suggests that the proposed score test has approximately the correct level of significance and is more powerful than the asymptotic score test based on the mixture of chi-square distributions. The proposed test is illustrated using two sets of actual recurrence failure time data obtained from clinical experiments.

We revisit a proposal, for robust sequential design in the presence of uncertainty about the regression response, previously made by these authors. We obtain conditions under which a sequence of designs for nonlinear regression models leads to asymptotically normally distributed estimates. The results are illustrated in a simulation study. We conclude that estimates computed after the experiment has been carried out sequentially may, in only moderately sized samples, be safely used to make standard normal-theory inferences, ignoring the dependencies arising from the sequential nature of the sampling. The quality of the normal approximation deteriorates somewhat when the random errors are heteroscedastic.