Semiparametric regression for periodic longitudinal hormone data from multiple menstrual cycles

We consider semiparametric regression for periodic longitudinal data. Parametric fixed effects are used to model the covariate effects and a periodic nonparametric smooth function is used to model the time effect. The within-subject correlation is modeled using subject-specific random effects and a random stochastic process with a periodic variance function. We use maximum penalized likelihood to estimate the regression coefficients and the periodic nonparametric time function, whose estimator is shown to be a periodic cubic smoothing spline. We use restricted maximum likelihood to simultaneously estimate the smoothing parameter and the variance components. We show that all model parameters can be easily obtained by fitting a linear mixed model. A common problem in the analysis of longitudinal data is to compare the time profiles of two groups, e.g., between treatment and placebo. We develop a scaled chi-squared test for the equality of two nonparametric time functions. The proposed model and the test are illustrated by analyzing hormone data collected during two consecutive menstrual cycles and their performance is evaluated through simulations.     

Fitting conditional survival models to meta-analytic data by using a transformation toward mixed-effects models

Summary .   Frailty models are widely used to model clustered survival data. Classical ways to fit frailty models are likelihood-based. We propose an alternative approach in which the original problem of "fitting a frailty model" is reformulated into the problem of "fitting a linear mixed model" using model transformation. We show that the transformation idea also works for multivariate proportional odds models and for multivariate additive risks models. It therefore bridges segregated methodologies as it provides a general way to fit conditional models for multivariate survival data by using mixed models methodology. To study the specific features of the proposed method we focus on frailty models. Based on a simulation study, we show that the proposed method provides a good and simple alternative for fitting frailty models for data sets with a sufficiently large number of clusters and moderate to large sample sizes within covariate-level subgroups in the clusters. The proposed method is applied to data from 27 randomized trials in advanced colorectal cancer, which are available through the Meta-Analysis Group in Cancer.     

Efficient estimation for patient-specific rates of disease progression using nonnormal linear mixed models

Summary .  This article presents a new class of nonnormal linear mixed models that provide an efficient estimation of subject-specific disease progression in the analysis of longitudinal data from the Modification of Diet in Renal Disease (MDRD) trial. This new analysis addresses the previously reported finding that the distribution of the random effect characterizing disease progression is negatively skewed. We assume a log-gamma distribution for the random effects and provide the maximum likelihood inference for the proposed nonnormal linear mixed model. We derive the predictive distribution of patient-specific disease progression rates, which demonstrates rather different individual progression profiles from those obtained from the normal linear mixed model analysis. To validate the adequacy of the log-gamma assumption versus the usual normality assumption for the random effects, we propose a lack-of-fit test that clearly indicates a better fit for the log-gamma modeling in the analysis of the MDRD data. The full maximum likelihood inference is also advantageous in dealing with the missing at random (MAR) type of dropouts encountered in the MDRD data.     

Biometrical modeling of twin and family data using standard mixed model software

Summary .   Biometrical genetic modeling of twin or other family data can be used to decompose the variance of an observed response or 'phenotype' into genetic and environmental components. Convenient parameterizations requiring few random effects are proposed, which allow such models to be estimated using widely available software for linear mixed models (continuous phenotypes) or generalized linear mixed models (categorical phenotypes). We illustrate the proposed approach by modeling family data on the continuous phenotype birth weight and twin data on the dichotomous phenotype depression. The example data sets and commands for Stata and R/S-PLUS are available at the Biometrics website.     

Diagnosis of random-effect model misspecification in generalized linear mixed models for binary response

Summary .  Generalized linear mixed models (GLMMs) are widely used in the analysis of clustered data. However, the validity of likelihood-based inference in such analyses can be greatly affected by the assumed model for the random effects. We propose a diagnostic method for random-effect model misspecification in GLMMs for clustered binary response. We provide a theoretical justification of the proposed method and investigate its finite sample performance via simulation. The proposed method is applied to data from a longitudinal respiratory infection study.     

Variable Selection for Semiparametric Mixed Models in Longitudinal Studies

Summary .  We propose a double-penalized likelihood approach for simultaneous model selection and estimation in semiparametric mixed models for longitudinal data. Two types of penalties are jointly imposed on the ordinary log-likelihood: the roughness penalty on the nonparametric baseline function and a nonconcave shrinkage penalty on linear coefficients to achieve model sparsity. Compared to existing estimation equation based approaches, our procedure provides valid inference for data with missing at random, and will be more efficient if the specified model is correct. Another advantage of the new procedure is its easy computation for both regression components and variance parameters. We show that the double-penalized problem can be conveniently reformulated into a linear mixed model framework, so that existing software can be directly used to implement our method. For the purpose of model inference, we derive both frequentist and Bayesian variance estimation for estimated parametric and nonparametric components. Simulation is used to evaluate and compare the performance of our method to the existing ones. We then apply the new method to a real data set from a lactation study.     

A joint model for longitudinal measurements and survival data in the presence of multiple failure types

Summary .   In this article we study a joint model for longitudinal measurements and competing risks survival data. Our joint model provides a flexible approach to handle possible nonignorable missing data in the longitudinal measurements due to dropout. It is also an extension of previous joint models with a single failure type, offering a possible way to model informatively censored events as a competing risk. Our model consists of a linear mixed effects submodel for the longitudinal outcome and a proportional cause-specific hazards frailty submodel ( Prentice et al., 1978 , Biometrics 34, 541–554) for the competing risks survival data, linked together by some latent random effects. We propose to obtain the maximum likelihood estimates of the parameters by an expectation maximization (EM) algorithm and estimate their standard errors using a profile likelihood method. The developed method works well in our simulation studies and is applied to a clinical trial for the scleroderma lung disease.     

Joint regression analysis of correlated data using Gaussian copulas

Summary .  This article concerns a new joint modeling approach for correlated data analysis. Utilizing Gaussian copulas, we present a unified and flexible machinery to integrate separate one-dimensional generalized linear models (GLMs) into a joint regression analysis of continuous, discrete, and mixed correlated outcomes. This essentially leads to a multivariate analogue of the univariate GLM theory and hence an efficiency gain in the estimation of regression coefficients. The availability of joint probability models enables us to develop a full maximum likelihood inference. Numerical illustrations are focused on regression models for discrete correlated data, including multidimensional logistic regression models and a joint model for mixed normal and binary outcomes. In the simulation studies, the proposed copula-based joint model is compared to the popular generalized estimating equations, which is a moment-based estimating equation method to join univariate GLMs. Two real-world data examples are used in the illustration.     

Generalized linear mixed models with varying coefficients for longitudinal data

The routinely assumed parametric functional form in the linear predictor of a generalized linear mixed model for longitudinal data may be too restrictive to represent true underlying covariate effects. We relax this assumption by representing these covariate effects by smooth but otherwise arbitrary functions of time, with random effects used to model the correlation induced by among-subject and within-subject variation. Due to the usually intractable integration involved in evaluating the quasi-likelihood function, the double penalized quasi-likelihood (DPQL) approach of Lin and Zhang (1999, Journal of the Royal Statistical Society, Series B61, 381-400) is used to estimate the varying coefficients and the variance components simultaneously by representing a nonparametric function by a linear combination of fixed effects and random effects. A scaled chi-squared test based on the mixed model representation of the proposed model is developed to test whether an underlying varying coefficient is a polynomial of certain degree. We evaluate the performance of the procedures through simulation studies and illustrate their application with Indonesian children infectious disease data.     

Gamma generalized linear models for pharmacokinetic data

Summary .   This article considers the modeling of single-dose pharmacokinetic data. Traditionally, so-called compartmental models have been used to analyze such data. Unfortunately, the mean function of such models are sums of exponentials for which inference and computation may not be straightforward. We present an alternative to these models based on generalized linear models, for which desirable statistical properties exist, with a logarithmic link and gamma distribution. The latter has a constant coefficient of variation, which is often appropriate for pharmacokinetic data. Inference is convenient from either a likelihood or a Bayesian perspective. We consider models for both single and multiple individuals, the latter via generalized linear mixed models. For single individuals, Bayesian computation may be carried out with recourse to simulation. We describe a rejection algorithm that, unlike Markov chain Monte Carlo, produces independent samples from the posterior and allows straightforward calculation of Bayes factors for model comparison. We also illustrate how prior distributions may be specified in terms of model-free pharmacokinetic parameters of interest. The methods are applied to data from 12 individuals following administration of the antiasthmatic agent theophylline.     

Genome‐wide association studies identify susceptibility loci affecting respiratory disease in Chinese Erhualian pigs under natural conditions

Prevalence of swine respiratory disease causes poor growth performance in and serious economic losses to the swine industry. In this study, a categorical trait of enzootic pneumonia‐like (EPL) score representing the infection gradient of a respiratory disease, more likely enzootic pneumonia, was recorded in a herd of 332 Chinese Erhualian pigs. According to their EPL scores and the disease effect on weight gains, these pigs were grouped into controls (EPL score ≤ 1) and cases (EPL score > 1). The weight gain of the case group reduced significantly at days 180, 210, 240 and 300 as compared to the control group. The heritability of EPL score was estimated to be 0.24 based on the pedigree information using a linear mixed model. All 332 Erhualian pigs and their nine sire parents were genotyped with Illumina Porcine 60K SNP chips. Two genome‐wide association studies were performed under a generalized linear mixed model and a case–control model respectively. In total, five loci surpassed the suggestive significance level (P = 2.98 × 10^?5) on chromosomes 2, 8, 12 and 14. CXCL6, CXCL8, KIT and CTBP2 were highlighted as candidate genes that might play important roles in determining resistance/susceptibility to swine EP‐like respiratory disease. The findings advance understanding of the genetic basis of resistance/susceptibility to respiratory disease in pigs.     

Genome‐wide association analysis identifies quantitative trait loci for growth in a Landrace purebred population

Growth‐related traits are complex and economically important in the livestock industry. The aim of this study was to identify quantitative trait loci (QTL) and the associated positional candidate genes affecting growth in pigs. A genome‐wide association study (GWAS) was performed using the porcine single‐nucleotide polymorphism (SNP) 60K bead chip. A mixed‐effects model and linear regression approach were used for the GWAS. The data used in the study included 490 purebred Landrace pigs. All experimental animals were genotyped with 39 438 SNPs located throughout the pig autosomes. We identified a strong association between a SNP marker on chromosome 16 and body weight at 71 days of age (ALGA0092396, P = 5.35 × 10^?9, Bonferroni adjusted P < 0.05). The SNP marker was located near the genomic region containing IRX4, which encodes iroquois homeobox 4. This SNP marker could be useful in the selective breeding program after validating its effect on other populations.     

Spectral analysis of distributions: finding periodic components in eukaryotic enzyme length data

We introduce the spectral analysis of distributions (SAD), a method for detecting and evaluating possible periodicity in experimental data distributions (histograms) of arbitrary shape. SAD determines whether a given empirical distribution contains a periodic component. We also propose a system of probabilistic mixture distributions to model a histogram consisting of a smooth background together with peaks at periodic intervals, with each peak corresponding to a fixed number of subunits added together. This mixture distribution model allows us to estimate the parameters of the data and to test the statistical significance of the estimated peaks. The analysis is applied to the length distribution of eukaryotic enzymes.     

Linear Equality Constraints in the General Linear Mixed Model

Scientists may wish to analyze correlated outcome data with constraints among the responses. For example, piecewise linear regression in a longitudinal data analysis can require use of a general linear mixed model combined with linear parameter constraints. Although well developed for standard univariate models, there are no general results that allow a data analyst to specify a mixed model equation in conjunction with a set of constraints on the parameters. We resolve the difficulty by precisely describing conditions that allow specifying linear parameter constraints that insure the validity of estimates and tests in a general linear mixed model. The recommended approach requires only straightforward and noniterative calculations to implement. We illustrate the convenience and advantages of the methods with a comparison of cognitive developmental patterns in a study of individuals from infancy to early adulthood for children from low-income families.     

Glucose biosensor based on nano-SiO2 and "unprotected" Pt nanoclusters

The “unprotected” Pt nanoclusters (average size 2 nm) mixed with the nanoscale SiO₂ particles (average size 13 nm) were used as a glucose oxidase immobilization carrier to fabricate the amperometric glucose biosensor. The bioactivity of glucose oxidase (GOx) immobilized on the composite was maintained and the as-prepared biosensor demonstrated high sensitivity (3.85 μA mM⁻¹) and good stability in glucose solution. The Pt–SiO₂ biosensor showed a detection limit of 1.5 μM with a linear range from 0.27 to 4.08 mM. In addition, the biosensor can be operated under wide pH range (pH 4.9–7.5) without great changes in its sensitivity. Cyclic voltammetry measurements showed a mixed controlled electrode reaction.     

Aberrant crypt foci and semiparametric modeling of correlated binary data

Summary .   Motivated by the spatial modeling of aberrant crypt foci (ACF) in colon carcinogenesis, we consider binary data with probabilities modeled as the sum of a nonparametric mean plus a latent Gaussian spatial process that accounts for short-range dependencies. The mean is modeled in a general way using regression splines. The mean function can be viewed as a fixed effect and is estimated with a penalty for regularization. With the latent process viewed as another random effect, the model becomes a generalized linear mixed model. In our motivating data set and other applications, the sample size is too large to easily accommodate maximum likelihood or restricted maximum likelihood estimation (REML), so pairwise likelihood, a special case of composite likelihood, is used instead. We develop an asymptotic theory for models that are sufficiently general to be used in a wide variety of applications, including, but not limited to, the problem that motivated this work. The splines have penalty parameters that must converge to zero asymptotically: we derive theory for this along with a data-driven method for selecting the penalty parameter, a method that is shown in simulations to improve greatly upon standard devices, such as likelihood crossvalidation. Finally, we apply the methods to the data from our experiment ACF. We discover an unexpected location for peak formation of ACF.     

Recombination between the linear plasmid pPZG101 and the linear chromosome of Streptomyces rimosus can lead to exchange of ends

The 387 kb linear plasmid pPZG101 of Streptomyces rimosus R6 can integrate into the chromosome or form a prime plasmid carrying the oxytetracycline biosynthesis cluster. The integration of plasmid pPZG101 into the linear chromosome of S. rimosus R6-501 in mutant MV25 was shown to be due to a single cross-over at a 4 bp common sequence. pPZG101 had integrated into a 250 kb DNA sequence that was reiterated at a low level. This sequence includes the oxytetracycline biosynthesis cluster, so that homologous recombination generated a mixed population carrying different copy numbers of the region. The 1 Mb linear plasmid pPZG103 in mutant MV17 had also arisen from a cross-over between pPZG101 and the chromosome, so that one end of pPZG103 consists of c . 850 kb of chromosomal sequence including the oxytetracycline biosynthesis cluster. The plasmid pPZG101 was shown to consist of a unique central region of about 30 kb flanked by terminal inverted repeats of about 180 kb. Analysis of a presumed ancestor plasmid pPZG102 suggested that the long terminal repeats had arisen by a recombination event during the strain development programme.     

利用混合模型分析地域对国内马尾松生物量的影响

开展全国森林生物量监测和评估,建立适合较大区域范围的通用性立木生物量模型是一项重要的基础工作,而分析森林生物量受不同地域的影响并保证不同尺度范围森林生物量估计值的可靠性,是必须面临的问题。以南方马尾松(Pinus massoniana)地上生物量数据为例,介绍了如何利用混合模型理论来分析地域对马尾松地上生物量的影响以及利用混合模型构建全国通用性立木生物量模型,为得到不同区域尺度范围内可靠的森林生物量评价和估计提供了有效途径。结果表明,混合模型不仅提高了模型的精度和通用性,并且模型中每个参数都有特定的数学含义,通过这些参数很容易分析出随机因子对生物量的影响程度。因此混合模型方法具有较大的灵活性和适应性,可推广到其它通用性模型(如材积方程)的建立。     

Association Models for Clustered Data with Binary and Continuous Responses

Summary .  We consider analysis of clustered data with mixed bivariate responses, i.e., where each member of the cluster has a binary and a continuous outcome. We propose a new bivariate random effects model that induces associations among the binary outcomes within a cluster, among the continuous outcomes within a cluster, between a binary outcome and a continuous outcome from different subjects within a cluster, as well as the direct association between the binary and continuous outcomes within the same subject. For the ease of interpretations of the regression effects, the marginal model of the binary response probability integrated over the random effects preserves the logistic form and the marginal expectation of the continuous response preserves the linear form. We implement maximum likelihood estimation of our model parameters using standard software such as PROC NLMIXED of SAS . Our simulation study demonstrates the robustness of our method with respect to the misspecification of the regression model as well as the random effects model. We illustrate our methodology by analyzing a developmental toxicity study of ethylene glycol in mice.