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"Covariate adjustment" in the randomized trial context refers to an estimator of the average treatment effect that adjusts for chance imbalances between study arms in baseline variables (called "covariates"). The baseline variables could include, for example, age, sex, disease severity, and biomarkers. According to two surveys of clinical trial reports, there is confusion about the statistical properties of covariate adjustment. We focus on the analysis of covariance (ANCOVA) estimator, which involves fitting a linear model for the outcome given the treatment arm and baseline variables, and trials that use simple randomization with equal probability of assignment to treatment and control. We prove the following new (to the best of our knowledge) robustness property of ANCOVA to arbitrary model misspecification: Not only is the ANCOVA point estimate consistent (as proved by Yang and Tsiatis, 2001) but so is its standard error. This implies that confidence intervals and hypothesis tests conducted as if the linear model were correct are still asymptotically valid even when the linear model is arbitrarily misspecified, for example, when the baseline variables are nonlinearly related to the outcome or there is treatment effect heterogeneity. We also give a simple, robust formula for the variance reduction (equivalently, sample size reduction) from using ANCOVA. By reanalyzing completed randomized trials for mild cognitive impairment, schizophrenia, and depression, we demonstrate how ANCOVA can achieve variance reductions of 4 to 32%., (© 2019, The International Biometric Society.)

Motivated by the analysis of complex dependent functional data such as event‐related brain potentials (ERP), this paper considers a time‐varying coefficient multivariate regression model with fixed‐time covariates for testing global hypotheses about population mean curves. Based on a reduced‐rank modeling of the time correlation of the stochastic process of pointwise test statistics, a functional generalized F‐test is proposed and its asymptotic null distribution is derived. Our analytical results show that the proposed test is more powerful than functional analysis of variance testing methods and competing signal detection procedures for dependent data. Simulation studies confirm such power gain for data with patterns of dependence similar to those observed in ERPs. The new testing procedure is illustrated with an analysis of the ERP data from a study of neural correlates of impulse control. [ABSTRACT FROM AUTHOR]

Testing homogeneity of dispersions may be of its own scientific interest as well as an important auxiliary step verifying assumptions of a main analysis. The problem is that many biological and ecological data are highly skewed and zero-inflated. Also the number of variables often exceeds the sample size. Thus data analysts often do not rely on parametric assumptions, but use a particular dissimilarity measure to calculate a matrix of pairwise differences. This matrix is then the basis for further statistical inference. Anderson (2006) proposed a distance-based test of homogeneity of multivariate dispersions for a one-way ANOVA design, for which a matrix of pairwise dissimilarities can be taken as an input. The key idea, like in Levene's test, is to replace each observation with its distance to an estimated group center. In this paper we suggest an alternative approach that is based on the means of within-group distances and does not require group centre calculations to obtain the test statistic. We show that this approach can have theoretical as well as practical advantages. A permutation procedure that gives type I error close to the prescribed value even in small samples is described., (Copyright © 2013, The International Biometric Society.)

Whenever inference for variance components is required, the choice between one-sided and two-sided tests is crucial. This choice is usually driven by whether or not negative variance components are permitted. For two-sided tests, classical inferential procedures can be followed, based on likelihood ratios, score statistics, or Wald statistics. For one-sided tests, however, one-sided test statistics need to be developed, and their null distribution derived. While this has received considerable attention in the context of the likelihood ratio test, there appears to be much confusion about the related problem for the score test. The aim of this paper is to illustrate that classical (two-sided) score test statistics, frequently advocated in practice, cannot be used in this context, but that well-chosen one-sided counterparts could be used instead. The relation with likelihood ratio tests will be established, and all results are illustrated in an analysis of continuous longitudinal data using linear mixed models.

Summary In a recent paper, Gaugler and Akritas (unpublished manuscript) considered testing for no main effect in a two-factor mixed effects design when the traditional assumptions do not hold. Here we extend the nonparametric modeling to the random effects design and consider the problem of testing for no interaction effect. The new models for these designs allow for dependence among the random effects, heteroscedasticity in the error and interaction terms, and do not require normality. At a more systemic level, these models differ from the classical ones in that they do not consider the random interaction term as an additional, extraneous source of variability. The proposed test procedure applies to settings where the random factor in the case of the mixed model or at least one of the random factors in the case of the random effects model has many levels. The number of replications can be small and possibly unbalanced. Moreover, the model and test procedure are general enough to accommodate data missing at random (MAR), provided the missingness mechanism is the same for each level of the random effect. The limiting distribution of the test statistic is normal. Extensive simulations indicate that our test procedure, with or without missing data, maintains the nominal Type I error rate in all simulation settings. On the contrary, the standard procedures (the F-test of PROC GLM in SAS, and the ML and REML methods of PROC MIXED in SAS), as well as the exact F-test of (1998 in Statistical Tests for Mixed Linear Models), are extremely liberal in heteroscedastic settings, while under homoscedasticity and normality, the proposed test procedure is comparable to them. An analysis of a dataset from the Mussel Watch Project is presented. [ABSTRACT FROM AUTHOR]

While the conventional Levene (Med) test is a widely used and robust test for detecting heterogeneity of variance, it does not take notice of either the linear dependencies among the residuals involved or the possibility of a mean (or median)-variance relationship. This paper explores the substantial improvements in power possible by investigating the benefits both of removing such linear dependencies (structural zeros) and of modeling (even roughly) such relationships.

This paper describes an EM algorithm for nonparametric maximum likelihood (ML) estimation in generalized linear models with variance component structure. The algorithm provides an alternative analysis to approximate MQL and PQL analyses (McGilchrist and Aisbett, 1991, Biometrical Journal 33, 131-141; Breslow and Clayton, 1993; Journal of the American Statistical Association 88, 9-25; McGilchrist, 1994, Journal of the Royal Statistical Society, Series B 56, 61-69; Goldstein, 1995, Multilevel Statistical Models) and to GEE analyses (Liang and Zeger, 1986, Biometrika 73, 13-22). The algorithm, first given by Hinde and Wood (1987, in Longitudinal Data Analysis, 110-126), is a generalization of that for random effect models for overdispersion in generalized linear models, described in Aitkin (1996, Statistics and Computing 6, 251-262). The algorithm is initially derived as a form of Gaussian quadrature assuming a normal mixing distribution, but with only slight variation it can be used for a completely unknown mixing distribution, giving a straightforward method for the fully nonparametric ML estimation of this distribution. This is of value because the ML estimates of the GLM parameters can be sensitive to the specification of a parametric form for the mixing distribution. The nonparametric analysis can be extended straightforwardly to general random parameter models, with full NPML estimation of the joint distribution of the random parameters. This can produce substantial computational saving compared with full numerical integration over a specified parametric distribution for the random parameters. A simple method is described for obtaining correct standard errors for parameter estimates when using the EM algorithm. Several examples are discussed involving simple variance component and longitudinal models, and small-area estimation.

In this paper we consider the use of within-subject coefficient of variation (WCV) for assessing the reproducibility or reliability of a measurement. Application to assessing reproducibility of biochemical markers for measuring bone turnover is described and the comparison with intraclass correlation is discussed. Both maximum likelihood and moment confidence intervals of WCV are obtained through their corresponding asymptotic distributions. Normal and log-normal cases are considered. In general, WCV is preferred when the measurement scale bears intrinsic meaning and is not subject to arbitrary shifting. The intraclass correlation may be preferred when a fixed population of subjects can be well identified.

Turkey's (1953, The Problem of Multiple Comparisons, unpublished report, Princeton University) procedure is widely used for pairwise multiple comparisons in one-way ANOVA. It provides exact simultaneous pairwise confidence intervals (SPCI) for balanced designs and conservative SPCI for unbalanced designs. In this paper, we will extend Turkey's procedure to two-way unbalanced designs. Both the exact and the conservative methods will be introduced. The application of the new procedure is illustrated with sample data from two experiments.

A considerable body of literature has arisen over the past 15 years for analyzing univariate repeated measures data. However, it is rare in applied biomedical research for interest to be restricted to a single outcome measure. In this paper, we consider the case of bivariate repeated measures. We apply a generalized estimating equations (GEE) approach to relate each set of repeated measures to important explanatory variables. We then invoke the seemingly unrelated regression paradigm to combine these GEE models into an overall analysis framework. This approach provides a great deal of flexibility in modeling the relationships to fixed and time-dependent covariates for each set of outcome variables. Estimation and hypothesis testing issues are described and the methodology is illustrated with an example.

The presence of intralitter correlation is a well known issue for analysis of the developmental toxicology data. The intralitter correlation coefficients observed in developmental toxicology data are generally different across dose groups. In this paper we use a generalized estimating equation procedure to model jointly the mean parameters and the intralitter correlation coefficients as functions of dose levels. Our procedure is similar to that used by Prentice and Zhao (1991, Biometrics 47, 825-839) for estimating the mean and variance parameters.

In order to establish bioequivalence between two formulations in a crossover trial, it is common to assume a mixed-effect analysis of variance (ANOVA) model and perform two one-sided tests. When the analysis is done on the untransformed data, the numerators of the test statistics are not, in general, treatment contrasts. Consequently, the standard errors of the numerators are difficult to compute. The usual practice is to approximate these with the standard errors of treatment contrasts (the "usual approximation"). This paper examines the goodness of this approximation. We present a few technical issues involved in analyzing the untransformed data with a mixed-effect ANOVA model, and state a parametric definition for the terminology "treatment means." The best linear unbiased estimator (BLUE) for the treatment means is derived, as well as its covariance matrix. Due to the presence of the intersubject variability, the variances and covariances of the BLUE of the treatment means are much larger than is commonly believed. A simulation study shows that these larger-than-expected variances/covariances may widen the usual approximate 90% confidence interval by as much as 10%.

The clinical trial design in which the endpoint is measured both at baseline and at the end of the study is used in a variety of situations. For two-group designs, test such as the t test or analysis of covariance are commonly used to evaluate treatment efficacy. Often such pretest-posttest trials restrict participation to subjects with a baseline measurement of the endpoint in a certain range. A range may define a disease, or it may be thought that subjects with extreme measurements are more responsive to treatment. This paper examines the effect of screening on the analysis of covariance and t-test variances relative to the population (i.e., unscreened) variances. Bivariate normal and bivariate gamma distributions are assumed for the (pretest, posttest) measurements. Because the sample size required to detect a specified difference between treatment and control is proportional to the variance, the results have direct application to setting sample size.

The matched-sample case-control study is widely used by epidemiologists to estimate the relative incidence of disease among persons exposed to different levels of one or more risk factors. An apparent limitation of such designs has been the necessity to control the effects of all potential confounding variables in the matching process. Conditional likelihood analyses based on the linear logistic equation enable one to model the effects of covariates while preserving the original matching. This paper reviews the logical basis for this methodology and illustrates its value by application to a case-control study of esophageal cancer.

In this paper the nature of the reasoning processes applied to the nature-nurture question is discussed in general and with particular reference to mental and behavioral traits. The nature of data analysis and analysis of variance is discussed. Necessarily, the nature of causation is considered. The notion that mere data analysis can establish "real" causation is attacked. Logic of quantitative genetic theory is reviewed briefly. The idea that heritability is meaningful in the human mental and behavioral arena is attacked. The conclusion is that the heredity-IQ controversy has been a "tale full of sound and fury, signifying nothing". To suppose that one can establish effects of an intervention process when it does not occur in the data is plainly ludicrous. Mere observational studies can easily lead to stupidities, and it is suggested that this has happened in the heredity-IQ arena. The idea that there are racial-genetic differences in mental abilities and behavioral traits of humans is, at best, no more than idle speculation.

Techniques that describe the use of covariance when heterogeneity of slopes exists are severely limited. Although a few procedures for model selection have been recommended, none, except the hierarchical approach, is straightforward and usable with present computer programs. The hierarchical subset selection procedure presented in this paper is based on the proposition that heterogeneity may be present only for certain terms in the model. After hierarchical selection, those terms which do not involve heterogeneity are interpreted as in the usual analysis for covariance. The interpretations of those terms which do involve heterogeneity are modified with respect to significance tests performed at various values of the covariate. The hierarchical subset selection method allows one to investigate heterogeneity of slopes in covariance models as functions of the classification variables present in the design.

The rank transformation refers to the replacement of data by their ranks, with a subsequent analysis using the usual normal theory procedure, but calculated on the ranks rather than on the data. Rank transformation procedures have previously been shown by the authors to have properties of robustness and power in both regression and analysis of variance. It seems natural to consider the use of the rank transformation in analysis of covariance, which is a combination of regression and analysis of variance. In this paper the rank transformation approach to analysis of covariance is presented and examined. Comparisons are made with the rank transformation procedure given by Quade (1967, Journal of the American Statistical Association 62, 1187-1200), and some 'standard' data sets are used to compare the results of these two procedures. A Monte Carlo simulation study examines the behavior of these methods under the null hypothesis and under alternative hypotheses, with both normal and nonnormal distributions. All results are compared with the usual analysis of covariance procedure on the basis of robustness and power.

Researchers often use a two‐step process to analyze multivariate data. First, dimensionality is reduced using a technique such as principal component analysis, followed by a group comparison using a t‐test or analysis of variance. Although this practice is often discouraged, the statistical properties of this procedure are not well understood, starting with the hypothesis being tested. We suggest that this approach might be considering two distinct hypotheses, one of which is a global test of no differences in the mean vectors, and the other being a focused test of a specific linear combination where the coefficients have been estimated from the data. We study the asymptotic properties of the two‐sample t‐statistic for these two scenarios, assuming a nonsparse setting. We show that the size of the global test agrees with the presumed level but that the test has poor power. In contrast, the size of the focused test can be arbitrarily distorted with certain mean and covariance structures. A simple method is provided to correct the size of the focused test. Data analyses and simulations are used to illustrate the results. Recommendations on the use of this two‐step method and the related use of principal components for prediction are provided. [ABSTRACT FROM AUTHOR]

The field of neuroimaging dedicated to mapping connections in the brain is increasingly being recognized as key for understanding neurodevelopment and pathology. Networks of these connections are quantitatively represented using complex structures, including matrices, functions, and graphs, which require specialized statistical techniques for estimation and inference about developmental and disorder‐related changes. Unfortunately, classical statistical testing procedures are not well suited to high‐dimensional testing problems. In the context of global or regional tests for differences in neuroimaging data, traditional analysis of variance (ANOVA) is not directly applicable without first summarizing the data into univariate or low‐dimensional features, a process that might mask the salient features of high‐dimensional distributions. In this work, we consider a general framework for two‐sample testing of complex structures by studying generalized within‐group and between‐group variances based on distances between complex and potentially high‐dimensional observations. We derive an asymptotic approximation to the null distribution of the ANOVA test statistic, and conduct simulation studies with scalar and graph outcomes to study finite sample properties of the test. Finally, we apply our test to our motivating study of structural connectivity in autism spectrum disorder. [ABSTRACT FROM AUTHOR]

Summary: In stepped wedge cluster randomized trials, intact clusters of individuals switch from control to intervention from a randomly assigned period onwards. Such trials are becoming increasingly popular in health services research. When a closed cohort is recruited from each cluster for longitudinal follow‐up, proper sample size calculation should account for three distinct types of intraclass correlations: the within‐period, the inter‐period, and the within‐individual correlations. Setting the latter two correlation parameters to be equal accommodates cross‐sectional designs. We propose sample size procedures for continuous and binary responses within the framework of generalized estimating equations that employ a block exchangeable within‐cluster correlation structure defined from the distinct correlation types. For continuous responses, we show that the intraclass correlations affect power only through two eigenvalues of the correlation matrix. We demonstrate that analytical power agrees well with simulated power for as few as eight clusters, when data are analyzed using bias‐corrected estimating equations for the correlation parameters concurrently with a bias‐corrected sandwich variance estimator. [ABSTRACT FROM AUTHOR]

In this article we propose an accelerated intensity frailty (AIF) model for recurrent events data and derive a test for the variance of frailty. In addition, we develop a kernel-smoothing-based EM algorithm for estimating regression coefficients and the baseline intensity function. The variance of the resulting estimator for regression parameters is obtained by a numerical differentiation method. Simulation studies are conducted to evaluate the finite sample performance of the proposed estimator under practical settings and demonstrate the efficiency gain over the Gehan rank estimator based on the AFT model for counting process (Lin et al., 1998). Our method is further illustrated with an application to a bladder tumor recurrence data. [ABSTRACT FROM AUTHOR]

This article presents an Analysis of Variance model for functional data that explicitly incorporates phase variability through a time-warping component, allowing for a unified approach to estimation and inference in presence of amplitude and time variability. The focus is on single-random-factor models but the approach can be easily generalized to more complex ANOVA models. The behavior of the estimators is studied by simulation, and an application to the analysis of growth curves of flour beetles is presented. Although the model assumes a smooth latent process behind the observed trajectories, smootheness of the observed data is not required; the method can be applied to irregular time grids, which are common in longitudinal studies. [ABSTRACT FROM AUTHOR]

Spatial-clustered data refer to high-dimensional correlated measurements collected from units or subjects that are spatially clustered. Such data arise frequently from studies in social and health sciences. We propose a unified modeling framework, termed as GeoCopula, to characterize both large-scale variation, and small-scale variation for various data types, including continuous data, binary data, and count data as special cases. To overcome challenges in the estimation and inference for the model parameters, we propose an efficient composite likelihood approach in that the estimation efficiency is resulted from a construction of over-identified joint composite estimating equations. Consequently, the statistical theory for the proposed estimation is developed by extending the classical theory of the generalized method of moments. A clear advantage of the proposed estimation method is the computation feasibility. We conduct several simulation studies to assess the performance of the proposed models and estimation methods for both Gaussian and binary spatial-clustered data. Results show a clear improvement on estimation efficiency over the conventional composite likelihood method. An illustrative data example is included to motivate and demonstrate the proposed method. [ABSTRACT FROM AUTHOR]

Changes in human microbiome are associated with many human diseases. Next generation sequencing technologies make it possible to quantify the microbial composition without the need for laboratory cultivation. One important problem of microbiome data analysis is to identify the environmental/biological covariates that are associated with different bacterial taxa. Taxa count data in microbiome studies are often over-dispersed and include many zeros. To account for such an over-dispersion, we propose to use an additive logistic normal multinomial regression model to associate the covariates to bacterial composition. The model can naturally account for sampling variabilities and zero observations and also allow for a flexible covariance structure among the bacterial taxa. In order to select the relevant covariates and to estimate the corresponding regression coefficients, we propose a group [ABSTRACT FROM AUTHOR]

Functional principal components (FPC) analysis is widely used to decompose and express functional observations. Curve estimates implicitly condition on basis functions and other quantities derived from FPC decompositions; however these objects are unknown in practice. In this article, we propose a method for obtaining correct curve estimates by accounting for uncertainty in FPC decompositions. Additionally, pointwise and simultaneous confidence intervals that account for both model- and decomposition-based variability are constructed. Standard mixed model representations of functional expansions are used to construct curve estimates and variances conditional on a specific decomposition. Iterated expectation and variance formulas combine model-based conditional estimates across the distribution of decompositions. A bootstrap procedure is implemented to understand the uncertainty in principal component decomposition quantities. Our method compares favorably to competing approaches in simulation studies that include both densely and sparsely observed functions. We apply our method to sparse observations of CD4 cell counts and to dense white-matter tract profiles. Code for the analyses and simulations is publicly available, and our method is implemented in the R package refund on CRAN. [ABSTRACT FROM AUTHOR]

We examine a generalized F-test of a nonparametric function through penalized splines and a linear mixed effects model representation. With a mixed effects model representation of penalized splines, we imbed the test of an unspecified function into a test of some fixed effects and a variance component in a linear mixed effects model with nuisance variance components under the null. The procedure can be used to test a nonparametric function or varying-coefficient with clustered data, compare two spline functions, test the significance of an unspecified function in an additive model with multiple components, and test a row or a column effect in a two-way analysis of variance model. Through a spectral decomposition of the residual sum of squares, we provide a fast algorithm for computing the null distribution of the test, which significantly improves the computational efficiency over bootstrap. The spectral representation reveals a connection between the likelihood ratio test (LRT) in a multiple variance components model and a single component model. We examine our methods through simulations, where we show that the power of the generalized F-test may be higher than the LRT, depending on the hypothesis of interest and the true model under the alternative. We apply these methods to compute the genome-wide critical value and p-value of a genetic association test in a genome-wide association study (GWAS), where the usual bootstrap is computationally intensive (up to 108 simulations) and asymptotic approximation may be unreliable and conservative. [ABSTRACT FROM AUTHOR]

Rank-based inference is widely used because of its robustness. This article provides optimal rank-based estimating functions in analysis of clustered data with random cluster effects. The extensive simulation studies carried out to evaluate the performance of the proposed method demonstrate that it is robust to outliers and is highly efficient given the existence of strong cluster correlations. The performance of the proposed method is satisfactory even when the correlation structure is misspecified, or when heteroscedasticity in variance is present. Finally, a real dataset is analyzed for illustration. [ABSTRACT FROM AUTHOR]

In some survival analysis of medical studies, there are often long-term survivors who can be considered as permanently cured. The goals in these studies are to estimate the noncured probability of the whole population and the hazard rate of the susceptible subpopulation. When covariates are present as often happens in practice, to understand covariate effects on the noncured probability and hazard rate is of equal importance. The existing methods are limited to parametric and semiparametric models. We propose a two-component mixture cure rate model with nonparametric forms for both the cure probability and the hazard rate function. Identifiability of the model is guaranteed by an additive assumption that allows no time-covariate interactions in the logarithm of hazard rate. Estimation is carried out by an expectation-maximization algorithm on maximizing a penalized likelihood. For inferential purpose, we apply the Louis formula to obtain point-wise confidence intervals for noncured probability and hazard rate. Asymptotic convergence rates of our function estimates are established. We then evaluate the proposed method by extensive simulations. We analyze the survival data from a melanoma study and find interesting patterns for this study. [ABSTRACT FROM AUTHOR]

In this article, we investigate clustering methods for multilevel functional data, which consist of repeated random functions observed for a large number of units (e.g., genes) at multiple subunits (e.g., bacteria types). To describe the within- and between variability induced by the hierarchical structure in the data, we take a multilevel functional principal component analysis (MFPCA) approach. We develop and compare a hard clustering method applied to the scores derived from the MFPCA and a soft clustering method using an MFPCA decomposition. In a simulation study, we assess the estimation accuracy of the clustering membership and the cluster patterns under a series of settings: small versus moderate number of time points; various noise levels; and varying number of subunits per unit. We demonstrate the applicability of the clustering analysis to a real data set consisting of expression profiles from genes activated by immunity system cells. Prevalent response patterns are identified by clustering the expression profiles using our multilevel clustering analysis. [ABSTRACT FROM AUTHOR]

We propose a novel class of models for functional data exhibiting skewness or other shape characteristics that vary with spatial or temporal location. We use copulas so that the marginal distributions and the dependence structure can be modeled independently. Dependence is modeled with a Gaussian or t-copula, so that there is an underlying latent Gaussian process. We model the marginal distributions using the skew t family. The mean, variance, and shape parameters are modeled nonparametrically as functions of location. A computationally tractable inferential framework for estimating heterogeneous asymmetric or heavy-tailed marginal distributions is introduced. This framework provides a new set of tools for increasingly complex data collected in medical and public health studies. Our methods were motivated by and are illustrated with a state-of-the-art study of neuronal tracts in multiple sclerosis patients and healthy controls. Using the tools we have developed, we were able to find those locations along the tract most affected by the disease. However, our methods are general and highly relevant to many functional data sets. In addition to the application to one-dimensional tract profiles illustrated here, higher-dimensional extensions of the methodology could have direct applications to other biological data including functional and structural magnetic resonance imaging (MRI). [ABSTRACT FROM AUTHOR]

Summary Despite recent flourish of proposals on variable selection, genome-wide multiple loci mapping remains to be challenging. The majority of existing variable selection methods impose a model, and often the homoscedastic linear model, prior to selection. However, the true association between the phenotypical trait and the genetic markers is rarely known a priori, and the presence of epistatic interactions makes the association more complex than a linear relation. Model-free variable selection offers a useful alternative in this context, but the fact that the number of markers p often far exceeds the number of experimental units n renders all the existing model-free solutions that require n > p inapplicable. In this article, we examine a number of model-free variable selection methods for small- n-large- p regressions in the context of genome-wide multiple loci mapping. We propose and advocate a multivariate group-wise adaptive penalization solution, which requires no model prespecification and thus works for complex trait-marker association, and handles one variable at a time so that works for n < p. Effectiveness of the new method is demonstrated through both intensive simulations and a comprehensive real data analysis across 6100 gene expression traits. [ABSTRACT FROM AUTHOR]

Summary We consider the problem of high-dimensional regression under nonconstant error variances. Despite being a common phenomenon in biological applications, heteroscedasticity has, so far, been largely ignored in high-dimensional analysis of genomic data sets. We propose a new methodology that allows nonconstant error variances for high-dimensional estimation and model selection. Our method incorporates heteroscedasticity by simultaneously modeling both the mean and variance components via a novel doubly regularized approach. Extensive Monte Carlo simulations indicate that our proposed procedure can result in better estimation and variable selection than existing methods when heteroscedasticity arises from the presence of predictors explaining error variances and outliers. Further, we demonstrate the presence of heteroscedasticity in and apply our method to an expression quantitative trait loci (eQTLs) study of 112 yeast segregants. The new procedure can automatically account for heteroscedasticity in identifying the eQTLs that are associated with gene expression variations and lead to smaller prediction errors. These results demonstrate the importance of considering heteroscedasticity in eQTL data analysis. [ABSTRACT FROM AUTHOR]

Summary We propose a new criterion for confounder selection when the underlying causal structure is unknown and only limited knowledge is available. We assume all covariates being considered are pretreatment variables and that for each covariate it is known (i) whether the covariate is a cause of treatment, and (ii) whether the covariate is a cause of the outcome. The causal relationships the covariates have with one another is assumed unknown. We propose that control be made for any covariate that is either a cause of treatment or of the outcome or both. We show that irrespective of the actual underlying causal structure, if any subset of the observed covariates suffices to control for confounding then the set of covariates chosen by our criterion will also suffice. We show that other, commonly used, criteria for confounding control do not have this property. We use formal theory concerning causal diagrams to prove our result but the application of the result does not rely on familiarity with causal diagrams. An investigator simply need ask, 'Is the covariate a cause of the treatment?' and 'Is the covariate a cause of the outcome?' If the answer to either question is 'yes' then the covariate is included for confounder control. We discuss some additional covariate selection results that preserve unconfoundedness and that may be of interest when used with our criterion. [ABSTRACT FROM AUTHOR]

Summary Gap time hazard estimation is of particular interest in recurrent event data. This article proposes a fully nonparametric approach for estimating the gap time hazard. Smoothing spline analysis of variance (ANOVA) decompositions are used to model the log gap time hazard as a joint function of gap time and covariates, and general frailty is introduced to account for between-subject heterogeneity and within-subject correlation. We estimate the nonparametric gap time hazard function and parameters in the frailty distribution using a combination of the Newton-Raphson procedure, the stochastic approximation algorithm (SAA), and the Markov chain Monte Carlo (MCMC) method. The convergence of the algorithm is guaranteed by decreasing the step size of parameter update and/or increasing the MCMC sample size along iterations. Model selection procedure is also developed to identify negligible components in a functional ANOVA decomposition of the log gap time hazard. We evaluate the proposed methods with simulation studies and illustrate its use through the analysis of bladder tumor data. [ABSTRACT FROM AUTHOR]

Summary Measurement errors in covariates may result in biased estimates in regression analysis. Most methods to correct this bias assume nondifferential measurement errors-i.e., that measurement errors are independent of the response variable. However, in regression models for zero-truncated count data, the number of error-prone covariate measurements for a given observational unit can equal its response count, implying a situation of differential measurement errors. To address this challenge, we develop a modified conditional score approach to achieve consistent estimation. The proposed method represents a novel technique, with efficiency gains achieved by augmenting random errors, and performs well in a simulation study. The method is demonstrated in an ecology application. [ABSTRACT FROM AUTHOR]

Summary This article is concerned with variance estimation for statistics that are computed from single recurrent event processes. Such statistics are important in diagnosis for each individual recurrent event process. The proposed method only assumes a semiparametric form for the first-order structure of the processes but not for the second-order (i.e., dependence) structure. The new variance estimator is shown to be consistent for the target parameter under very mild conditions. The estimator can be used in many applications in semiparametric rate regression analysis of recurrent event data such as outlier detection, residual diagnosis, as well as robust regression. A simulation study and application to two real data examples are used to demonstrate the use of the proposed method. [ABSTRACT FROM AUTHOR]

It is of great practical interest to simultaneously identify the important predictors that correspond to both the fixed and random effects components in a linear mixed-effects (LME) model. Typical approaches perform selection separately on each of the fixed and random effect components. However, changing the structure of one set of effects can lead to different choices of variables for the other set of effects. We propose simultaneous selection of the fixed and random factors in an LME model using a modified Cholesky decomposition. Our method is based on a penalized joint log likelihood with an adaptive penalty for the selection and estimation of both the fixed and random effects. It performs model selection by allowing fixed effects or standard deviations of random effects to be exactly zero. A constrained expectation-maximization algorithm is then used to obtain the final estimates. It is further shown that the proposed penalized estimator enjoys the Oracle property, in that, asymptotically it performs as well as if the true model was known beforehand. We demonstrate the performance of our method based on a simulation study and a real data example. [ABSTRACT FROM AUTHOR]

The classical concordance correlation coefficient (CCC) to measure agreement among a set of observers assumes data to be distributed as normal and a linear relationship between the mean and the subject and observer effects. Here, the CCC is generalized to afford any distribution from the exponential family by means of the generalized linear mixed models (GLMMs) theory and applied to the case of overdispersed count data. An example of CD34+ cell count data is provided to show the applicability of the procedure. In the latter case, different CCCs are defined and applied to the data by changing the GLMM that fits the data. A simulation study is carried out to explore the behavior of the procedure with a small and moderate sample size. [ABSTRACT FROM AUTHOR]

In a microarray experiment, one experimental design is used to obtain expression measures for all genes. One popular analysis method involves fitting the same linear mixed model for each gene, obtaining gene-specific p-values for tests of interest involving fixed effects, and then choosing a threshold for significance that is intended to control false discovery rate (FDR) at a desired level. When one or more random factors have zero variance components for some genes, the standard practice of fitting the same full linear mixed model for all genes can result in failure to control FDR. We propose a new method that combines results from the fit of full and selected linear mixed models to identify differentially expressed genes and provide FDR control at target levels when the true underlying random effects structure varies across genes. [ABSTRACT FROM AUTHOR]