Interindividual differences in the dynamics of the homeostatic process are trait-like and distinct for sleep versus wakefulness

The sleep homeostatic Process S reflects the build-up of sleep pressure during waking and its dissipation during sleep. Process S is modelled as a saturating exponential function during waking and a decreasing exponential function during sleep. Slow wave activity is a physiological marker for non-rapid eye movement (non-REM) sleep intensity and serves as an index of Process S. There is considerable interindividual variability in the sleep homeostatic responses to sleep and sleep deprivation. The aim of this study was to investigate whether interindividual differences in Process S are trait-like. Polysomnographic recordings of 8 nights (12-h sleep opportunities, 22:00-10:00 hours) interspersed with three 36-h periods of sustained wakefulness were performed in 11 healthy young adults. Empirical mean slow wave activity per non-REM sleep episode at episode mid-points were used for parameter estimation. Parameters of Process S were estimated using different combinations of consecutive sleep recordings, resulting in two to three sets of parameters per subject. Intraclass correlation coefficients were calculated to assess whether the parameters were stable across the study protocol and they showed trait-like variability among individuals. We found that the group-average time constants of the build-up and dissipation of Process S were 19.2 and 2.7 h, respectively. Intraclass correlation coefficients ranged from 0.48 to 0.56, which reflects moderate trait variability. The time constants of the build-up and dissipation varied independently among subjects, indicating two distinct traits. We conclude that interindividual differences in the parameters of the dynamics of the sleep homeostatic Process S are trait-like.

Estimates of heritability and genetic correlations for milk coagulation properties and individual laboratory cheese yield in Sarda ewes

Objective of this study was to estimate genetic parameters of milk coagulation properties (MCPs) and individual laboratory cheese yield (ILCY) in a sample of 1018 Sarda breed ewes farmed in 47 flocks. Rennet coagulation time (RCT), curd-firming time (k 20) and curd firmness (a 30) were measured using Formagraph instrument, whereas ILCY were determined by a micromanufacturing protocol. About 10% of the milk samples did not coagulate within 30 min and 13% had zero value for k 20. The average ILCY was 36%. (Co)variance components of considered traits were estimated by fitting both single- and multiple-trait animal models. Flock-test date explained from 13% to 28% of the phenotypic variance for MCPs and 26% for ILCY, respectively. The largest value of heritability was estimated for RCT (0.23±0.10), whereas it was about 0.15 for the other traits. Negative genetic correlations between RCT and a 30 (-0.80±0.12), a 30 and k 20 (-0.91±0.09), and a 30 and ILCY (-0.67±0.08) were observed. Interesting genetic correlations between MCPs and milk composition (r G>0.40) were estimated for pH, NaCl and casein. Results of the present study suggest to use only one out of three MCPs to measure milk renneting ability, due to high genetic correlations among them. Moreover, negative correlations between ILCY and MCPs suggest that great care should be taken when using these methods to estimate cheese yield from small milk samples.

Genetic parameters for growth characteristics of free-range chickens under univariate random regression models

Repeated measures from the same individual have been analyzed by using repeatability and finite dimension models under univariate or multivariate analyses. However, in the last decade, the use of random regression models for genetic studies with longitudinal data have become more common. Thus, the aim of this research was to estimate genetic parameters for body weight of four experimental chicken lines by using univariate random regression models. Body weight data from hatching to 84 days of age (n = 34,730) from four experimental free-range chicken lines (7P, Caipirão da ESALQ, Caipirinha da ESALQ and Carijó Barbado) were used. The analysis model included the fixed effects of contemporary group (gender and rearing system), fixed regression coefficients for age at measurement, and random regression coefficients for permanent environmental effects and additive genetic effects. Heterogeneous variances for residual effects were considered, and one residual variance was assigned for each of six subclasses of age at measurement. Random regression curves were modeled by using Legendre polynomials of the second and third orders, with the best model chosen based on the Akaike Information Criterion, Bayesian Information Criterion, and restricted maximum likelihood. Multivariate analyses under the same animal mixed model were also performed for the validation of the random regression models. The Legendre polynomials of second order were better for describing the growth curves of the lines studied. Moderate to high heritabilities (h(2) = 0.15 to 0.98) were estimated for body weight between one and 84 days of age, suggesting that selection for body weight at all ages can be used as a selection criteria. Genetic correlations among body weight records obtained through multivariate analyses ranged from 0.18 to 0.96, 0.12 to 0.89, 0.06 to 0.96, and 0.28 to 0.96 in 7P, Caipirão da ESALQ, Caipirinha da ESALQ, and Carijó Barbado chicken lines, respectively. Results indicate that genetic gain for body weight can be achieved by selection. Also, selection for body weight at 42 days of age can be maintained as a selection criterion.

Genetic Architecture of Domestication-Related Traits in Maize

Strong directional selection occurred during the domestication of maize from its wild ancestor teosinte, reducing its genetic diversity, particularly at genes controlling domestication-related traits. Nevertheless, variability for some domestication-related traits is maintained in maize. The genetic basis of this could be sequence variation at the same key genes controlling maize-teosinte differentiation (due to lack of fixation or arising as new mutations after domestication), distinct loci with large effects, or polygenic background variation. Previous studies permit annotation of maize genome regions associated with the major differences between maize and teosinte or that exhibit population genetic signals of selection during either domestication or postdomestication improvement. Genome-wide association studies and genetic variance partitioning analyses were performed in two diverse maize inbred line panels to compare the phenotypic effects and variances of sequence polymorphisms in regions involved in domestication and improvement to the rest of the genome. Additive polygenic models explained most of the genotypic variation for domestication-related traits; no large-effect loci were detected for any trait. Most trait variance was associated with background genomic regions lacking previous evidence for involvement in domestication. Improvement sweep regions were associated with more trait variation than expected based on the proportion of the genome they represent. Selection during domestication eliminated large-effect genetic variants that would revert maize toward a teosinte type. Small-effect polygenic variants (enriched in the improvement sweep regions of the genome) are responsible for most of the standing variation for domestication-related traits in maize.

Association Tests for Rare Variants

Over the past few years, interest in the identification of rare variants that influence human phenotype has led to the development of many statistical methods for testing for association between sets of rare variants and binary or quantitative traits. Here, I review some of the most important ideas that underlie these methods and the most relevant issues when choosing a method for analysis. In addition to the tests for association, I review crucial issues in performing a rare variant study, from experimental design to interpretation and validation. I also discuss the many challenges of these studies, some of their limitations, and future research directions.

Spatial variation in adult sex ratio across multiple scales in the invasive golden apple snail, Pomacea canaliculata

Adult sex ratio (ASR) has critical effects on behavior and life history and has implications for population demography, including the invasiveness of introduced species. ASR exhibits immense variation in nature, yet the scale dependence of this variation is rarely analyzed. In this study, using the generalized multilevel models, we investigated the variation in ASR across multiple nested spatial scales and analyzed the underlying causes for an invasive species, the golden apple snail Pomacea canaliculata. We partitioned the variance in ASR to describe the variations at different scales and then included the explanatory variables at the individual and group levels to analyze the potential causes driving the variation in ASR. We firstly determined there is a significant female‐biased ASR for this species when accounting for the spatial and temporal autocorrelations of sampling. We found that, counter to nearly equal distributed variation at plot, habitat and region levels, ASR showed little variation at the town level. Temperature and precipitation at the region level were significantly positively associated with ASR, whereas the individual weight, the density characteristic, and sampling time were not significant factors influencing ASR. Our study suggests that offspring sex ratio of this species may shape the general pattern of ASR in the population level while the environmental variables at the region level translate the unbiased offspring sex ratio to the female‐biased ASR. Future research should consider the implications of climate warming on the female‐biased ASR of this invasive species and thus on invasion pattern.

The Quantitative-MFG Test: A Linear Mixed Effect Model to Detect Maternal-Offspring Gene Interactions

Maternal-offspring gene interactions, aka maternal-fetal genotype (MFG) incompatibilities, are neglected in complex diseases and quantitative trait studies. They are implicated in birth to adult onset diseases but there are limited ways to investigate their influence on quantitative traits. We present the quantitative-MFG (QMFG) test, a linear mixed model where maternal and offspring genotypes are fixed effects and residual correlations between family members are random effects. The QMFG handles families of any size, common or general scenarios of MFG incompatibility, and additional covariates. We develop likelihood ratio tests (LRTs) and rapid score tests and show they provide correct inference. In addition, the LRT's alternative model provides unbiased parameter estimates. We show that testing the association of SNPs by fitting a standard model, which only considers the offspring genotypes, has very low power or can lead to incorrect conclusions. We also show that offspring genetic effects are missed if the MFG modeling assumptions are too restrictive. With genome-wide association study data from the San Antonio Family Heart Study, we demonstrate that the QMFG score test is an effective and rapid screening tool. The QMFG test therefore has important potential to identify pathways of complex diseases for which the genetic etiology remains to be discovered.

Direct and social genetic effects on body weight at 270 days and carcass and ham quality traits in heavy pigs

The aims of this study were to estimate covariance components for BW at 270 d (BW270) and carcass and ham quality traits in heavy pigs using models accounting for social effects and to compare the ability of such models to fit the data relative to models ignoring social interactions. Phenotypic records were from 9,871 pigs sired by 293 purebred boars mated to 456 crossbred sows. Piglets were born and reared at the same farm and randomly assigned at 60 d of age to groups (6.1 pigs per group on average) housed in finishing pens, each having an area of 6 m(2). The average additive genetic relationship among group mates was 0.11. Pigs were slaughtered at 277 ± 3 d of age and 169.7 ± 13.9 kg BW in groups of nearly 70 animals each. Four univariate animal models were compared: a basic model (M1) including only direct additive genetic effects, a model (M2) with nonheritable social group (pen) effects in addition to effects in M1, a model (M3) accounting for litter effects in addition to M2, and a model (M4) accounting for social genetic effects in addition to effects in M3. Restricted maximum likelihood estimates of covariance components were obtained for BW270; carcass backfat depth; carcass lean meat content (CLM); iodine number (IOD); and linoleic acid content (LIA) of raw ham subcutaneous fat; subcutaneous fat depth in the proximity of semimembranosus muscle (SFD1) and quadriceps femoris muscle (SFD2); and linear scores for ham round shape (RS), subcutaneous fat (SF), and marbling. Likelihood ratio tests indicated that, for all traits, M2 fit the data better than M1 and that M3 was superior to M2 except for SFD1 and SFD2. Model M4 was significantly better than M3 for BW270 (P < 0.001) and CLM, IOD, RS, and SF (P < 0.05). The contribution of social genetic effects to the total heritable variance was large for CLM and BW270, ranging from 33.2 to 35%, whereas the one for ham quality traits ranged from 6.8 (RS) to 11.2% (SF). Direct and social genetic effects on BW270 were uncorrelated, whereas there was a negative genetic covariance between direct and social effects on CLM, IOD, RS, and SF, which reduced the total heritable variance. This variance, measured relative to phenotypic variance, ranged from 21 (CLM) to 54% (BW270). Results indicate that social genetic effects affect variation in traits relevant for heavy pigs used in dry-cured hams manufacturing. Such effects should be exploited and taken into account in design of breeding programs for heavy pigs.

Functional-mixed effects models for candidate genetic mapping in imaging genetic studies

The aim of this paper is to develop a functional-mixed effects modeling (FMEM) framework for the joint analysis of high-dimensional imaging data in a large number of locations (called voxels) of a three-dimensional volume with a set of genetic markers and clinical covariates. Our FMEM is extremely useful for efficiently carrying out the candidate gene approaches in imaging genetic studies. FMEM consists of two novel components including a mixed effects model for modeling nonlinear genetic effects on imaging phenotypes by introducing the genetic random effects at each voxel and a jumping surface model for modeling the variance components of the genetic random effects and fixed effects as piecewise smooth functions of the voxels. Moreover, FMEM naturally accommodates the correlation structure of the genetic markers at each voxel, while the jumping surface model explicitly incorporates the intrinsically spatial smoothness of the imaging data. We propose a novel two-stage adaptive smoothing procedure to spatially estimate the piecewise smooth functions, particularly the irregular functional genetic variance components, while preserving their edges among different piecewise-smooth regions. We develop weighted likelihood ratio tests and derive their exact approximations to test the effect of the genetic markers across voxels. Simulation studies show that FMEM significantly outperforms voxel-wise approaches in terms of higher sensitivity and specificity to identify regions of interest for carrying out candidate genetic mapping in imaging genetic studies. Finally, FMEM is used to identify brain regions affected by three candidate genes including CR1, CD2AP, and PICALM, thereby hoping to shed light on the pathological interactions between these candidate genes and brain structure and function.

Analytical strategies for discovery and replication of genetic effects in pharmacogenomic studies

In the past decade, the pharmaceutical industry and biomedical research sector have devoted considerable resources to pharmacogenomics (PGx) with the hope that understanding genetic variation in patients would deliver on the promise of personalized medicine. With the advent of new technologies and the improved collection of DNA samples, the roadblock to advancements in PGx discovery is no longer the lack of high-density genetic information captured on patient populations, but rather the development, adaptation, and tailoring of analytical strategies to effectively harness this wealth of information. The current analytical paradigm in PGx considers the single-nucleotide polymorphism (SNP) as the genomic feature of interest and performs single SNP association tests to discover PGx effects – ie, genetic effects impacting drug response. While it can be straightforward to process single SNP results and to consider how this information may be extended for use in downstream patient stratification, the rate of replication for single SNP associations has been low and the desired success of producing clinically and commercially viable biomarkers has not been realized. This may be due to the fact that single SNP association testing is suboptimal given the complexities of PGx discovery in the clinical trial setting, including: 1) relatively small sample sizes; 2) diverse clinical cohorts within and across trials due to genetic ancestry (potentially impacting the ability to replicate findings); and 3) the potential polygenic nature of a drug response. Subsequently, a shift in the current paradigm is proposed: to consider the gene as the genomic feature of interest in PGx discovery. The proof-of-concept study presented in this manuscript demonstrates that genomic region-based association testing has the potential to improve the power of detecting single SNP or complex PGx effects in the discovery stage (by leveraging the underlying genetic architecture and reducing the multiplicity burden), and it can also improve power in the replication stage.

Combining family- and population-based imputation data for association analysis of rare and common variants in large pedigrees

In the last two decades, complex traits have become the main focus of genetic studies. The hypothesis that both rare and common variants are associated with complex traits is increasingly being discussed. Family-based association studies using relatively large pedigrees are suitable for both rare and common variant identification. Because of the high cost of sequencing technologies, imputation methods are important for increasing the amount of information at low cost. A recent family-based imputation method, Genotype Imputation Given Inheritance (GIGI), is able to handle large pedigrees and accurately impute rare variants, but does less well for common variants where population-based methods perform better. Here, we propose a flexible approach to combine imputation data from both family- and population-based methods. We also extend the Sequence Kernel Association Test for Rare and Common variants (SKAT-RC), originally proposed for data from unrelated subjects, to family data in order to make use of such imputed data. We call this extension "famSKAT-RC." We compare the performance of famSKAT-RC and several other existing burden and kernel association tests. In simulated pedigree sequence data, our results show an increase of imputation accuracy from use of our combining approach. Also, they show an increase of power of the association tests with this approach over the use of either family- or population-based imputation methods alone, in the context of rare and common variants. Moreover, our results show better performance of famSKAT-RC compared to the other considered tests, in most scenarios investigated here.

Plasma lipidome is independently associated with variability in metabolic syndrome in Mexican American families

Plasma lipidome is now increasingly recognized as a potentially important marker of chronic diseases, but the exact extent of its contribution to the interindividual phenotypic variability in family studies is unknown. Here, we used the rich data from the ongoing San Antonio Family Heart Study (SAFHS) and developed a novel statistical approach to quantify the independent and additive value of the plasma lipidome in explaining metabolic syndrome (MS) variability in Mexican American families recruited in the SAFHS. Our analytical approach included two preprocessing steps: principal components analysis of the high-resolution plasma lipidomics data and construction of a subject-subject lipidomic similarity matrix. We then used the Sequential Oligogenic Linkage Analysis Routines software to model the complex family relationships, lipidomic similarities, and other important covariates in a variance components framework. Our results suggested that even after accounting for the shared genetic influences, indicators of lipemic status (total serum cholesterol, TGs, and HDL cholesterol), and obesity, the plasma lipidome independently explained 22% of variability in the homeostatic model of assessment-insulin resistance trait and 16% to 22% variability in glucose, insulin, and waist circumference. Our results demonstrate that plasma lipidomic studies can additively contribute to an understanding of the interindividual variability in MS.

Heritability of phenotypes associated with glucose homeostasis and adiposity in a rural area of Brazil

We aimed to estimate the heritability and genetic correlation between glucose homeostasis and adiposity traits in a population in a rural community in Brazil. The Jequitinhonha Community Family Study cohort consists of subjects aged ≥18 years residing in rural areas in Brazil. The data on the following traits were assembled for 280 individuals (51.7% women): body mass index (BMI), body fat percentage, waist and mid-upper arm circumferences, triceps skinfold, conicity index, insulin, glucose, high-density lipoprotein cholesterol (HDLc), triglycerides and C-reactive protein. Extended pedigrees were constructed up to the third generation of individuals using the data management software PEDSYS. The heritability and genetic correlations were estimated using a variance component method. The age- and sex-adjusted heritability values estimated for insulin (h(2) = 52%), glucose (h(2) = 51%), HDLc (h(2) = 58%), and waist circumference (WC; h(2) = 49%) were high. Significantly adjusted genetic correlations were observed between insulin paired with each of the following phenotypes; (BMI; ρg = 0.48), WC (ρg = 0.47) and HDLc (ρg = -0.47). The homeostasis model assessment of insulin resistance (HOMA-IR) was genetically correlated with BMI (ρg = 0.53) and HDLc (ρg = -0.58). The adjusted genetic correlations between traits were consistently higher compared with the environmental correlations. In conclusion, glucose metabolism and adiposity traits are highly heritable and share common genetic effects with body adiposity traits.

Sampling theory and automated simulations for vertical sections, applied to human brain

In recent years, there have been substantial developments in both magnetic resonance imaging techniques and automatic image analysis software. The purpose of this paper is to develop stereological image sampling theory (i.e. unbiased sampling rules) that can be used by image analysts for estimating geometric quantities such as surface area and volume, and to illustrate its implementation. The methods will ideally be applied automatically on segmented, properly sampled 2D images - although convenient manual application is always an option - and they are of wide applicability in many disciplines. In particular, the vertical sections design to estimate surface area is described in detail and applied to estimate the area of the pial surface and of the boundary between cortex and underlying white matter (i.e. subcortical surface area). For completeness, cortical volume and mean cortical thickness are also estimated. The aforementioned surfaces were triangulated in 3D with the aid of FreeSurfer software, which provided accurate surface area measures that served as gold standards. Furthermore, a software was developed to produce digitized trace curves of the triangulated target surfaces automatically from virtual sections. From such traces, a new method (called the 'lambda method') is presented to estimate surface area automatically. In addition, with the new software, intersections could be counted automatically between the relevant surface traces and a cycloid test grid for the classical design. This capability, together with the aforementioned gold standard, enabled us to thoroughly check the performance and the variability of the different estimators by Monte Carlo simulations for studying the human brain. In particular, new methods are offered to split the total error variance into the orientations, sectioning and cycloid components. The latter prediction was hitherto unavailable--one is proposed here and checked by way of simulations on a given set of digitized vertical sections with automatically superimposed cycloid grids of three different sizes. Concrete and detailed recommendations are given to implement the methods.

Characterizing behavioural 'characters': an evolutionary framework

Biologists often study phenotypic evolution assuming that phenotypes consist of a set of quasi-independent units that have been shaped by selection to accomplish a particular function. In the evolutionary literature, such quasi-independent functional units are called 'evolutionary characters', and a framework based on evolutionary principles has been developed to characterize them. This framework mainly focuses on 'fixed' characters, i.e. those that vary exclusively between individuals. In this paper, we introduce multi-level variation and thereby expand the framework to labile characters, focusing on behaviour as a worked example. We first propose a concept of 'behavioural characters' based on the original evolutionary character concept. We then detail how integration of variation between individuals (cf. 'personality') and within individuals (cf. 'individual plasticity') into the framework gives rise to a whole suite of novel testable predictions about the evolutionary character concept. We further propose a corresponding statistical methodology to test whether observed behaviours should be considered expressions of a hypothesized evolutionary character. We illustrate the application of our framework by characterizing the behavioural character 'aggressiveness' in wild great tits, Parus major.

A semiparametric recurrent events model with time-varying coefficients

We consider a recurrent events model with time-varying coefficients motivated by two clinical applications. We use a random effects (Gaussian frailty) model to describe the intensity of recurrent events. The model can accommodate both time-varying and time-constant coefficients. We use the penalized spline method to estimate the time-varying coefficients. We use Laplace approximation to evaluate the penalized likelihood without a closed form. We estimate the smoothing parameters in a similar way to variance components. We conduct simulations to evaluate the performance of the estimates for both time-varying and time-independent coefficients. We apply this method to analyze two data sets: a stroke study and a child wheeze study.

Partitioning sexual selection into its mating success and fertilization success components

Postcopulatory sexual selection due to sperm competition and/or cryptic female choice has been documented in a diversity of taxonomic groups and is considered a pivotal component of sexual selection. Despite this apparent importance, the relative contribution of postcopulatory fertilization success to overall sexual selection has not yet been measured in any species. Here, we used a laboratory-adapted population of the promiscuous fruit fly Drosophila melanogaster to partition the variance in male reproductive success into mating success (a major component of precopulatory sexual selection) and fertilization success (a major component of postcopulatory sexual selection). We found that fertilization success contributed nearly as strongly as mating success to a male's net performance in sexual selection, but that most of this postcopulatory component was attributable to variation in male mating order (the tendency to be the last male to mate a female). After adjusting for mating order, only ≈2% of the residual variation in male reproductive success was attributable to differential fertilization success. We found no correlation between male mating success and fertilization success in this system. Unlike natural populations of Drosophila, our laboratory population is adapted to a semelparous lifecycle, so our findings will be most applicable to other promiscuous species with strong sperm precedence and one short breeding period per year or lifetime. In these species, fertilization success may have as much influence on male reproductive success as mating success, but the timing of mating (mating order) may be the predominant factor contributing to variation in fertilization success.

Assessing variance components in multilevel linear models using approximate Bayes factors: A case study of ethnic disparities in birthweight

Racial/ethnic disparities in birthweight are a large source of differential morbidity and mortality worldwide and have remained largely unexplained in epidemiologic models. We assess the impact of maternal ancestry and census tract residence on infant birth weights in New York City and the modifying effects of race and nativity by incorporating random effects in a multilevel linear model. Evaluating the significance of these predictors involves the test of whether the variances of the random effects are equal to zero. This is problematic because the null hypothesis lies on the boundary of the parameter space. We generalize an approach for assessing random effects in the two-level linear model to a broader class of multilevel linear models by scaling the random effects to the residual variance and introducing parameters that control the relative contribution of the random effects. After integrating over the random effects and variance components, the resulting integrals needed to calculate the Bayes factor can be efficiently approximated with Laplace's method.

Confidence interval estimation for the Bland-Altman limits of agreement with multiple observations per individual

The limits of agreement (LoA) method proposed by Bland and Altman has become a standard for assessing agreement between different methods measuring the same quantity. Virtually, all method comparison studies have reported only point estimates of LoA due largely to the lack of simple confidence interval procedures. In this article, we address confidence interval estimation for LoA when multiple measurements per individual are available. Separate procedures are proposed for situations when the underlying true value of the measured quantity is assumed changing and when it is perceived as stable. A fixed number of replicates per individual is not needed for the procedures to work. As shown by the worked examples, the construction of these confidence intervals requires only quantiles from the standard normal and chi-square distributions. Simulation results show the proposed procedures perform well. A SAS macro implementing the methods is available on the publisher's website.

Fixed effects and variance components estimation in three-level meta-analysis

Meta-analytic methods have been widely applied to education, medicine, and the social sciences. Much of meta-analytic data are hierarchically structured because effect size estimates are nested within studies, and in turn, studies can be nested within level-3 units such as laboratories or investigators, and so forth. Thus, multilevel models are a natural framework for analyzing meta-analytic data. This paper discusses the application of a Fisher scoring method in two-level and three-level meta-analysis that takes into account random variation at the second and third levels. The usefulness of the model is demonstrated using data that provide information about school calendar types. sas proc mixed and hlm can be used to compute the estimates of fixed effects and variance components. Copyright © 2011 John Wiley & Sons, Ltd.

The Neuro/PsyGRID calibration experiment: identifying sources of variance and bias in multicenter MRI studies

Calibration experiments precede multicenter trials to identify potential sources of variance and bias. In support of future imaging studies of mental health disorders and their treatment, the Neuro/PsyGRID consortium commissioned a calibration experiment to acquire functional and structural MRI from twelve healthy volunteers attending five centers on two occasions. Measures were derived of task activation from a working memory paradigm, fractal scaling (Hurst exponent) from resting fMRI, and grey matter distributions from T(1) -weighted sequences. At each intracerebral voxel a fixed-effects analysis of variance estimated components of variance corresponding to factors of center, subject, occasion, and within-occasion order, and interactions of center-by-occasion, subject-by-occasion, and center-by-subject, the latter (since there is no intervention) a surrogate of the expected variance of the treatment effect standard error across centers. A rank order test of between-center differences was indicative of crossover or noncrossover subject-by-center interactions. In general, factors of center, subject and error variance constituted >90% of the total variance, whereas occasion, order, and all interactions were generally <5%. Subject was the primary source of variance (70%-80%) for grey-matter, with error variance the dominant component for fMRI-derived measures. Spatially, variance was broadly homogenous with the exception of fractal scaling measures which delineated white matter, related to the flip angle of the EPI sequence. Maps of P values for the associated F-tests were also derived. Rank tests were highly significant indicating the order of measures across centers was preserved. In summary, center effects should be modeled at the voxel-level using existing and long-standing statistical recommendations.

Matched ascertainment of informative families for complex genetic modelling

Family data are used extensively in quantitative genetic studies to disentangle the genetic and environmental contributions to various diseases. Many family studies based their analysis on population-based registers containing a large number of individuals composed of small family units. For binary trait analyses, exact marginal likelihood is a common approach, but, due to the computational demand of the enormous data sets, it allows only a limited number of effects in the model. This makes it particularly difficult to perform joint estimation of variance components for a binary trait and the potential confounders. We have developed a data-reduction method of ascertaining informative families from population-based family registers. We propose a scheme where the ascertained families match the full cohort with respect to some relevant statistics, such as the risk to relatives of an affected individual. The ascertainment-adjusted analysis, which we implement using a pseudo-likelihood approach, is shown to be efficient relative to the analysis of the whole cohort and robust to mis-specification of the random effect distribution.

Bayesian inference in semiparametric mixed models for longitudinal data

We consider Bayesian inference in semiparametric mixed models (SPMMs) for longitudinal data. SPMMs are a class of models that use a nonparametric function to model a time effect, a parametric function to model other covariate effects, and parametric or nonparametric random effects to account for the within-subject correlation. We model the nonparametric function using a Bayesian formulation of a cubic smoothing spline, and the random effect distribution using a normal distribution and alternatively a nonparametric Dirichlet process (DP) prior. When the random effect distribution is assumed to be normal, we propose a uniform shrinkage prior (USP) for the variance components and the smoothing parameter. When the random effect distribution is modeled nonparametrically, we use a DP prior with a normal base measure and propose a USP for the hyperparameters of the DP base measure. We argue that the commonly assumed DP prior implies a nonzero mean of the random effect distribution, even when a base measure with mean zero is specified. This implies weak identifiability for the fixed effects, and can therefore lead to biased estimators and poor inference for the regression coefficients and the spline estimator of the nonparametric function. We propose an adjustment using a postprocessing technique. We show that under mild conditions the posterior is proper under the proposed USP, a flat prior for the fixed effect parameters, and an improper prior for the residual variance. We illustrate the proposed approach using a longitudinal hormone dataset, and carry out extensive simulation studies to compare its finite sample performance with existing methods.

Spatial Linear Mixed Models with Covariate Measurement Errors

Spatial data with covariate measurement errors have been commonly observed in public health studies. Existing work mainly concentrates on parameter estimation using Gibbs sampling, and no work has been conducted to understand and quantify the theoretical impact of ignoring measurement error on spatial data analysis in the form of the asymptotic biases in regression coefficients and variance components when measurement error is ignored. Plausible implementations, from frequentist perspectives, of maximum likelihood estimation in spatial covariate measurement error models are also elusive. In this paper, we propose a new class of linear mixed models for spatial data in the presence of covariate measurement errors. We show that the naive estimators of the regression coefficients are attenuated while the naive estimators of the variance components are inflated, if measurement error is ignored. We further develop a structural modeling approach to obtaining the maximum likelihood estimator by accounting for the measurement error. We study the large sample properties of the proposed maximum likelihood estimator, and propose an EM algorithm to draw inference. All the asymptotic properties are shown under the increasing-domain asymptotic framework. We illustrate the method by analyzing the Scottish lip cancer data, and evaluate its performance through a simulation study, all of which elucidate the importance of adjusting for covariate measurement errors.

Joint models for a primary endpoint and multiple longitudinal covariate processes

Joint models are formulated to investigate the association between a primary endpoint and features of multiple longitudinal processes. In particular, the subject-specific random effects in a multivariate linear random-effects model for multiple longitudinal processes are predictors in a generalized linear model for primary endpoints. Li, Zhang, and Davidian (2004, Biometrics60, 1-7) proposed an estimation procedure that makes no distributional assumption on the random effects but assumes independent within-subject measurement errors in the longitudinal covariate process. Based on an asymptotic bias analysis, we found that their estimators can be biased when random effects do not fully explain the within-subject correlations among longitudinal covariate measurements. Specifically, the existing procedure is fairly sensitive to the independent measurement error assumption. To overcome this limitation, we propose new estimation procedures that require neither a distributional or covariance structural assumption on covariate random effects nor an independence assumption on within-subject measurement errors. These new procedures are more flexible, readily cover scenarios that have multivariate longitudinal covariate processes, and can be implemented using available software. Through simulations and an analysis of data from a hypertension study, we evaluate and illustrate the numerical performances of the new estimators.

Intra-plant variation in nectar sugar composition in two Aquilegia species (Ranunculaceae): contrasting patterns under field and glasshouse conditions

BACKGROUND AND AIMS

Intra-specific variation in nectar chemistry under natural conditions has been only rarely explored, yet it is an essential aspect of our understanding of how pollinator-mediated selection might act on nectar traits. This paper examines intra-specific variation in nectar sugar composition in field and glasshouse plants of the bumblebee-pollinated perennial herbs Aquilegia vulgaris subsp. vulgaris and Aquilegia pyrenaica subsp. cazorlensis (Ranunculaceae). The aims of the study are to assess the generality of extreme intra-plant variation in nectar sugar composition recently reported for other species in the field, and gaining insight on the possible mechanisms involved.

METHODS

The proportions of glucose, fructose and sucrose in single-nectary nectar samples collected from field and glasshouse plants were determined using high performance liquid chromatography. A hierarchical variance partition was used to dissect total variance into components due to variation among plants, flowers within plants, and nectaries within flowers.

KEY RESULTS

Nectar of the two species was mostly sucrose-dominated, but composition varied widely in the field, ranging from sucrose-only to fructose-dominated. Most intra-specific variance was due to differences among nectaries of the same flower, and flowers of the same plant. The high intra-plant variation in sugar composition exhibited by field plants vanished in the glasshouse, where nectar composition emerged as a remarkably constant feature across plants, flowers and nectaries.

CONCLUSIONS

In addition to corroborating the results of previous studies documenting extreme intra-plant variation in nectar sugar composition in the field, this study suggests that such variation may ultimately be caused by biotic factors operating on the nectar in the field but not in the glasshouse. Pollinator visitation and pollinator-borne yeasts are suggested as likely causal agents.

Within-home versus between-home variability of house dust endotoxin in a birth cohort

Endotoxin exposure has been proposed as an environmental determinant of allergen responses in children. To better understand the implications of using a single measurement of house dust endotoxin to characterize exposure in the first year of life, we evaluated room-specific within-home and between-home variability in dust endotoxin obtained from 470 households in Boston, Massachusetts. Homes were sampled up to two times over 5-11 months. We analyzed 1,287 dust samples from the kitchen, family room, and baby's bedroom for endotoxin. We fit a mixed-effects model to estimate mean levels and the variation of endotoxin between homes, between rooms, and between sampling times. Endotoxin ranged from 2 to 1,945 units per milligram of dust. Levels were highest during summer and lowest in the winter. Mean endotoxin levels varied significantly from room to room. Cross-sectionally, endotoxin was moderately correlated between family room and bedroom floor (r = 0.30), between family room and kitchen (r = 0.32), and between kitchen and bedroom (r = 0.42). Adjusting for season, the correlation of endotoxin levels within homes over time was 0.65 for both the bedroom and kitchen and 0.54 for the family room. The temporal within-home variance of endotoxin was lowest for bedroom floor samples and highest for kitchen samples. Between-home variance was lowest in the family room and highest for kitchen samples. Adjusting for season, within-home variation was less than between-home variation for all three rooms. These results suggest that room-to-room and home-to-home differences in endotoxin influence the total variability more than factors affecting endotoxin levels within a room over time.

Phenotypic plasticity of growth trajectory and ontogenic allometry in response to density for eucalyptus hybrid clones and families

BACKGROUND

and Aims Response to density is a crucial aspect of the ecology of trees in forests and plantations. Few studies have investigated the genetics of plasticity in response to density for growth traits such as height and circumference through development.

METHODS

Two experiments were carried out in the field, the first with full-sib families of Eucalyptus urophylla x E. grandis hybrids, and the second with clones of E. tereticornis x E. grandis hybrids planted across a range of densities (625, 1111 and 2500 trees ha-1). Height, circumference and stem taper were measured through development in both experiments. Variance components were estimated and a repeated measure approach for plasticity and three different methods were used to compare the variance-covariance matrix across densities.

KEY RESULTS

Genetic variance was significantly different from zero but the density x genotype interaction was significant only for clone experiments at the adult stage. Significant plasticity for three traits in both experiments was found. In the clone experiments, a significant clone x time x density interaction was found, suggesting that plasticity for growth and stem form is under genetic control. In both experiments, density did not affect environmental correlation, which remained high throughout tree development. The impact of density on genetic correlation was marked in the clone experiment, with a reduced value at lower density, but was not observed in the family trial. The differences between clones and family are mainly explained by the distribution of genetic variation within and among genotypes.

CONCLUSIONS

The results suggest that plasticity for growth traits and form of tropical Eucalyptus species is under genetic control and that the environment changes genetic co-variation through ontogeny. The findings confirm that a tree population with a narrow genetic basis (represented by clones) is sensitive to a changing environment, whereas a population with a broader genetic basis (full-sib family here) exhibits a more stable reaction.

Estimation of quantitative genetic parameters

This paper gives a short review of the development of genetic parameter estimation over the last 40 years. This shows the development of more statistically and computationally efficient methods that allow the fitting of more biologically appropriate models. Methods have evolved from direct methods based on covariances between relatives to methods based on individual animal models. Maximum-likelihood methods have a natural interpretation in terms of best linear unbiased predictors. Improvements in iterative schemes to give estimates are discussed. As an example, a recent estimation of genetic parameters for a British population of dairy cattle is discussed. The development makes a connection to relevant work by Bill Hill.

Statistical Interpretation of Key Comparison Reference Value and Degrees of Equivalence

Key comparisons carried out by the Consultative Committees (CCs) of the International Committee of Weights and Measures (CIPM) or the Bureau International des Poids et Mesures (BIPM) are referred to as CIPM key comparisons. The outputs of a statistical analysis of the data from a CIPM key comparison are the key comparison reference value, the degrees of equivalence, and their associated uncertainties. The BIPM publications do not discuss statistical interpretation of these outputs. We discuss their interpretation under the following three statistical models: nonexistent laboratory-effects model, random laboratory-effects model, and systematic laboratory-effects model.

Alternative implementations of Monte Carlo EM algorithms for likelihood inferences

Two methods of computing Monte Carlo estimators of variance components using restricted maximum likelihood via the expectation-maximisation algorithm are reviewed. A third approach is suggested and the performance of the methods is compared using simulated data.

Within- and between-subject variations in pharmacokinetic parameters of ethanol by analysis of breath, venous blood and urine

AIMS

To evaluate the prerequisites for using ethanol dilution to estimate total body water, we studied the within- and between-subject variation in the parameter estimates of a two-compartment model for ethanol pharmacokinetics with parallel Michaelis-Menten and first-order renal elimination. Because sampling of breath might be preferable in some clinical situations the parameter estimates derived from breath and venous blood were compared.

METHODS

On two occasions, ethanol 0.4 g kg-1 was given by intravenous infusion to 16 volunteers after they had fasted overnight. The proposed model was fitted by means of nonlinear regression to concentration-time data measured in the breath, venous blood and urine during 360 min. The model contained six parameters: Vmax and Km (Michaelis-Menten elimination constants), CLd (intercompartmental distribution parameter), VC and VT (volumes of the central and tissue compartment, respectively) and CLR (renal clearance). The volume of distribution, Vss, was calculated as the sum of VC and VT.

RESULTS

The mean +/- total s.d. of the parameter estimates derived from blood data were Vmax 95 +/- 25 mg min-1, Km 27 +/- 19 mg l-1, CLd 809 +/- 232 ml min-1, VC 14.5 +/- 4.3 l, VT 21. 2 +/- 4.4 l, CLR 3.6 +/- 2.0 ml min-1 and Vss 35.8 +/- 4.3 l. The variation within subjects amounted to 3%, 9%, 21%, 21%, 17%, 26% and 2%, respectively, of the total variation. Breath samples were associated with a similar or lower variation than blood, both within and between subjects. About 1.5% of the infused ethanol was recovered in the urine.

CONCLUSIONS

The low within-subject variation of the key parameter Vss (only 2%) suggests that ethanol dilution analysed by the pharmacokinetic model applied here may be used as an index of the total body water. Breath samples yielded at least as good reproducibility in the model parameters as venous blood.