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PubMed2003

The use of score tests for inference on variance components.

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.

Analysis of Variance↗
PubMed2005

Lactation curves of Sarda breed goats estimated with test day models.

Test day records of milk yield (38,765), fat and protein contents (11,357) of Sarda goats (the most numerous Italian goat breed) were analysed with mixed linear models in order to estimate the effects of test date (month and year of kidding for fat and protein contents) parity, number of kids born, altitude of location of flocks (<200 m asl, 200-500 m asl, >500 m asl), flocks within altitude and lactation stage (eight days-in-milk intervals of 30 d each) on milk production. All factors considered in the models affected milk traits significantly. Milk yield was lower in first parity goats than in higher parities whereas fat and protein contents showed an opposite trend. Goats with two kids at parturition had a higher milk yield than goats with one kid and tended to have lower fat and protein percentages. Repeatability between test days within lactation was 0.34, 0.17 and 0.45 for milk yield, fat content and protein content, respectively. Lactation curves of goats farmed at different altitudes were clearly separated, especially for milk yield. Results of the present study highlight differences in milk production traits among the three subpopulations that have been previously identified within the Sarda breed on the basis of the morphological structure of animals and altitude of location of flocks.

Altitude↗
PubMed2003

Bivariate longitudinal model for the analysis of the evolution of HIV RNA and CD4 cell count in HIV infection taking into account left censoring of HIV RNA measures.

We present a bivariate linear mixed model taking into account censored measures of the response variable due to lower quantification limit of the assays. It allows an estimate of the correlation between the two response variables and takes into account this correlation for the estimation of other model parameters. This model was applied in a large cohort study (APROCO Cohort) to study the evolution under antiretroviral treatment of the two major biomarkers of the progression of Human Immunodeficiency Virus (HIV) infection: plasma HIV RNA and CD4+ T lymphocytes cell count. In a sample of 929 patients who started an highly active antiretroviral therapy, we illustrate the superiority in terms of likelihood of a bivariate model compared to two univariate models and the impact of taking into account the left-censoring of HIV-RNA. Moreover, interpretation of the model parameters allows confirmation of correlation between these two markers throughout the whole follow-up and the continuous decrease of plasma HIV RNA on average. Despite some limitations (distribution assumption, ignorance of missingness process), such a model appeared to be very useful to correctly describe the current evolution of important biomarkers in HIV infection.

CD4 Lymphocyte Count↗
PubMed2002

Prevalence of nutritional wasting in populations: building explanatory models using secondary data.

OBJECTIVE: To understand how social context affects the nutritional status of populations, as reflected by the prevalence of wasting in children under 5 years of age from Africa, Latin America, and Asia; to present a systematic way of building models for wasting prevalence, using a conceptual framework for the determinants of malnutrition; and to examine the feasibility of using readily available data collected over time to build models of wasting prevalence in populations. METHODS: Associations between prevalence of wasting and environmental variables were examined in the three regions. General linear mixed models were fitted using anthropometric survey data for countries within each region. FINDINGS: Low birth weight (LBW), measles incidence, and access to a safe water supply explained 64% of wasting variability in Asia. In Latin America, LBW and survey year explained 38%; in Africa, LBW, survey year, and adult literacy explained 7%. CONCLUSION: LBW emerged as a predictor of wasting prevalence in all three regions. Actions regarding women's rights may have an effect on the nutritional status of children since LBW seems to reflect several aspects of the conditions of women in society. Databases have to be made compatible with each other to facilitate integrated analysis for nutritional research and policy decision-making. In addition, the validity of the variables representing the conceptual framework should be improved.

Africa↗
PubMed2002

A systematic statistical linear modeling approach to oligonucleotide array experiments.

We outline and describe steps for a statistically rigorous approach to analyzing probe-level Affymetrix GeneChip data. The approach employs classical linear mixed models and operates on a gene-by-gene basis. Forgoing any attempts at gene presence or absence calls, the method simultaneously considers the data across all chips in an experiment. Primary output includes precise estimates of fold change (some as low as 1.1), their statistical significance, and measures of array and probe variability. The method can accommodate complex experiments involving many kinds of treatments and can test for their effects at the probe level. Furthermore, mismatch probe data can be incorporated in different ways or ignored altogether. Data from an ionizing radiation experiment on human cell lines illustrate the key concepts.

Cells, Cultured↗
PubMed2002

Analysis of genetic effects of major genes and polygenes on quantitative traits I. Genetic model for diploid plants and animals.

A genetic model was proposed to simultaneously investigate genetic effects of both polygenes and several single genes for quantitative traits of diploid plants and animals. Mixed linear model approaches were employed for statistical analysis. Based on two mating designs, a full diallel cross and a modified diallel cross including F(2), Monte Carlo simulations were conducted to evaluate the unbiasedness and efficiency of the estimation of generalized least squares (GLS) and ordinary least squares (OLS) for fixed effects and of minimum norm quadratic unbiased estimation (MINQUE) and Henderson III for variance components. Estimates of MINQUE (1) were unbiased and efficient in both reduced and full genetic models. Henderson III could have a large bias when used to analyze the full genetic model. Simulation results also showed that GLS and OLS were good methods to estimate fixed effects in the genetic models. Data on Drosophila melanogaster from Gilbert were used as a worked example to demonstrate the parameter estimation.

Journal Article↗
PubMed2006

Success at first insemination in Australian Angus cattle: analysis of uncertain binary responses.

Field data from Australian Angus herds were used to investigate 2 methods of analyzing uncertain binary responses for success or failure at first insemination. A linear mixed model that included herd, year, and month of mating as fixed effects; unrelated service sire, additive animal, and residual as random effects; and linear and quadratic effects of age at mating as covariates was used to analyze binary data. An average gestation length (GL) derived from artificial insemination data was used to assign an insemination date to females mated to natural service sires. Females that deviated from this average GL led to uncertain binary responses. Two analyses were carried out: 1) a threshold model fitted to uncertain binary data, ignoring uncertainty (M1); and 2) a threshold model fitted to uncertain binary data, accounting for uncertainty via fuzzy logic classification (M2). There was practically no difference between point estimates obtained from M1 and M2 for service sire and herd variance; however, when uncertain binary data were analyzed ignoring uncertainty (M1), additive variance and heritability estimates were greater than with M2. Pearson correlations indicated that no major reranking would be expected for service sire effects and animal breeding values using M1 and M2. Given the results of the current study, a threshold model contemplating uncertainty is suggested for noisy binary data to avoid bias when estimating genetic parameters.

Animals↗
PubMed2006

Structured additive regression for categorical space-time data: a mixed model approach.

Motivated by a space-time study on forest health with damage state of trees as the response, we propose a general class of structured additive regression models for categorical responses, allowing for a flexible semiparametric predictor. Nonlinear effects of continuous covariates, time trends, and interactions between continuous covariates are modeled by penalized splines. Spatial effects can be estimated based on Markov random fields, Gaussian random fields, or two-dimensional penalized splines. We present our approach from a Bayesian perspective, with inference based on a categorical linear mixed model representation. The resulting empirical Bayes method is closely related to penalized likelihood estimation in a frequentist setting. Variance components, corresponding to inverse smoothing parameters, are estimated using (approximate) restricted maximum likelihood. In simulation studies we investigate the performance of different choices for the spatial effect, compare the empirical Bayes approach to competing methodology, and study the bias of mixed model estimates. As an application we analyze data from the forest health survey.

Bayes Theorem↗
PubMed2003

Health-related quality of life among dialysis patients on three continents: the Dialysis Outcomes and Practice Patterns Study.

BACKGROUND: Assessing health-related quality of life (HRQOL) can provide information on the types and degrees of burdens that afflict patients with chronic medical conditions, including end-stage renal disease (ESRD). Several studies have shown important international differences among ESRD patients treated with hemodialysis, but no studies have compared these patients' HRQOL. Our goal was to document international differences in HRQOL among dialysis patients and to identify possible explanations of those differences. METHODS: We examined data from the Dialysis Outcomes and Practice Patterns Study (DOPPS), a prospective, observational, international study of hemodialysis patients. We performed a cross-sectional analysis of DOPPS data from the United States, five countries in Europe (France, Germany, Italy, Spain, and the United Kingdom), and Japan. Linear mixed models were used to analyze differences in HRQOL, using the KDQOL-SFTM. Norm-based scores were used to minimize cultural response bias. Linear regression analysis was used to adjust for confounding factors. Other variables included demographic variables, comorbidities, primary cause of ESRD, complications of ESRD and treatment, and socioeconomic status. RESULTS: In all generic HRQOL subscales, patients on all three continents had much lower scores than their respective population norm values. Patients in the United States had the highest scores on the mental health subscale and the highest mental component summary scores. Japanese patients reported better physical functioning than did patients in the United States or Europe, but they also reported the greatest burden of kidney disease. Overall, these differences remained even after adjusting for possible confounders. CONCLUSION: On all three continents, ESRD and hemodialysis profoundly affect HRQOL. In the United States, the effects on mental health are smaller than in other countries. Japanese hemodialysis patients perceived that their kidney disease imposes a greater burden, but their physical functioning was significantly higher. Different distributions of socioeconomic factors and major comorbid conditions could explain little of this difference in physical functioning. Other possible factors, such as quality of dialysis and related health care, deserve careful study.

Cost of Illness↗
PubMed2005

Prediction of missing values in microarray and use of mixed models to evaluate the predictors.

Gene expression microarray experiments generate data sets with multiple missing expression values. In some cases, analysis of gene expression requires a complete matrix as input. Either genes with missing values can be removed, or the missing values can be replaced using prediction. We propose six imputation methods. A comparative study of the methods was performed on data from mice and data from the bacterium Enterococcus faecalis, and a linear mixed model was used to test for differences between the methods. The study showed that different methods' capability to predict is dependent on the data, hence the ideal choice of method and number of components are different for each data set. For data with correlation structure methods based on K-nearest neighbours seemed to be best, while for data without correlation structure using the average of the gene was to be preferred.

Journal Article↗
PubMed2005

Assessing uncertainty in reference intervals via tolerance intervals: application to a mixed model describing HIV infection.

We define the reference interval as the range between the 2.5th and 97.5th percentiles of a random variable. We use reference intervals to compare characteristics of a marker of disease progression between affected populations. We use a tolerance interval to assess uncertainty in the reference interval. Unlike the tolerance interval, the estimated reference interval does not contains the true reference interval with specified confidence (or credibility). The tolerance interval is easy to understand, communicate and visualize. We derive estimates of the reference interval and its tolerance interval for markers defined by features of a linear mixed model. Examples considered are reference intervals for time trends in HIV viral load, and CD4 per cent, in HIV-infected haemophiliac children and homosexual men. We estimate the intervals with likelihood methods and also develop a Bayesian model in which the parameters are estimated via Markov-chain Monte Carlo. The Bayesian formulation naturally overcomes some important limitations of the likelihood model.

Adult↗
PubMed2005

Up hill, down dale: quantitative genetics of curvaceous traits.

'Repeated' measurements for a trait and individual, taken along some continuous scale such as time, can be thought of as representing points on a curve, where both means and covariances along the trajectory can change, gradually and continually. Such traits are commonly referred to as 'function-valued' (FV) traits. This review shows that standard quantitative genetic concepts extend readily to FV traits, with individual statistics, such as estimated breeding values and selection response, replaced by corresponding curves, modelled by respective functions. Covariance functions are introduced as the FV equivalent to matrices of covariances. Considering the class of functions represented by a regression on the continuous covariable, FV traits can be analysed within the linear mixed model framework commonly employed in quantitative genetics, giving rise to the so-called random regression model. Estimation of covariance functions, either indirectly from estimated covariances or directly from the data using restricted maximum likelihood or Bayesian analysis, is considered. It is shown that direct estimation of the leading principal components of covariance functions is feasible and advantageous. Extensions to multi-dimensional analyses are discussed.

Analysis of Variance↗
PubMed2005

Recipes for the linear analysis of EEG.

In this paper, we describe a simple set of "recipes" for the analysis of high spatial density EEG. We focus on a linear integration of multiple channels for extracting individual components without making any spatial or anatomical modeling assumptions, instead requiring particular statistical properties such as maximum difference, maximum power, or statistical independence. We demonstrate how corresponding algorithms, for example, linear discriminant analysis, principal component analysis and independent component analysis, can be used to remove eye-motion artifacts, extract strong evoked responses, and decompose temporally overlapping components. The general approach is shown to be consistent with the underlying physics of EEG, which specifies a linear mixing model of the underlying neural and non-neural current sources.

Algorithms↗
PubMed2006

Towards understanding of glycaemic index and glycaemic load in habitual diet: associations with measures of glycaemia in the Insulin Resistance Atherosclerosis Study.

Epidemiologic studies have applied the glycaemic index (GI) and glycaemic load (GL) to assessments of usual dietary intake. Results have been inconsistent particularly for the association of GI or GL with diabetes incidence. We aimed to advance understanding of the GI and GL as applied to food frequency questionnaires (FFQ) by evaluating GI and GL in relation to plasma measures of glycaemia. Included were 1255 adults at a baseline examination (1994-6) and 813 who returned for the 5-year follow-up examination. Usual diet, at both examinations, was assessed by a validated FFQ. GI and GL were evaluated in relation to average fasting glucose (two measures at each examination) and 2 h post-75 g glucose load plasma glucose (baseline and follow-up), and glycated haemoglobin (A1c; follow-up only); using generalized linear models. Correlation coefficients (r) for GI and GL related to measures of glycaemia, adjusted for total energy intake, ranged from -0.004 to 0.04 (all NS) for both examinations. Adjustment for potential confounders, for fasting glucose in models for 2 h glucose (to model incremental glucose) and for average fasting glucose in models for A1c (to account, in part, for overnight endogenous glucose production) also did not materially alter findings, nor did inclusion of data from both examinations together in linear mixed models. The present results call into question the utility of GI and GL to reflect glycaemic response to food adequately, when used in the context of usual diet. Further work is needed to quantify usual dietary exposures relative to glucose excursion and associated chronic glycaemia and other metabolic parameters.

Adult↗
PubMed2005

Fold-change estimation of differentially expressed genes using mixture mixed-model.

Microarray experiments produce expression measurements for thousands of genes simultaneously, though usually for a small number of RNA samples. The most common problem is the identification of genes that are differentially expressed between different groups of samples or biological conditions. As the number of genes far exceeds the number of RNA samples, the inherent multiplicity poses a severe problem in both hypothesis testing and effect estimation. While much of the recent literature is focused on the hypothesis aspects, we concentrate in this paper on effect estimation as a tool for the identification of differentially expressed genes. We propose a linear mixed model where the random effects are assumed to follow a mixture distribution, and study in detail the case of three normals, corresponding to genes that are down-, up- or non regulated. Our approach leads to a new type of non-linear shrinkage estimation, where a proportion of estimates is shrunk to zero, while the rest follows standard linear shrinkage. This allows us to estimate the log fold-change of the genes involved and to identify those that are differentially expressed within the same model framework. We investigate the operating characteristics of our method using simulation and spike-in studies, and illustrate its application to real data using a breast-cancer dataset.

Journal Article↗
PubMed2001

The relationship of a mother's working model of feeding to her feeding behaviour.

AIMS OF THE STUDY: This study aimed to examine the difference the attunement of a mother's working model of feeding to her infant makes for her positive feeding affect and behaviour, accounting for infant and mother conditions. BACKGROUND/RATIONALE: The concept of a mother's working model of feeding is derived from attachment theory. Caregiving, including feeding, is a component of this theory. The conditions that may influence the attunement of a mother's working model of feeding to her infant include infant birth maturity status (premature, full-term), age at assessment, and robustness, indexed by weight-for-age z score (WAZ). Mother conditions include symptoms of depression and feeding practice (breast feeding or exclusive bottle feeding). DESIGN/METHODS: Participants in this longitudinal study were 99 mothers and their infants (47 full-term, 52 premature, very low birth weight). After written informed consent was given, home assessments were made when infants were approximately 1, 4, 8 and 12 months old (adjusted age for premature infants). Working model attunement was assessed with a video-assisted interview. A mother's positive affect and behaviour, including sensitivity and responsiveness, were rated from videotaped feeding interaction. RESULTS/FINDINGS: Repeated measures analysis with a general linear mixed model showed a significant positive relationship with positive affect and behaviour for both working model attunement and the WAZ score and a significant negative relationship for symptoms of depression. Neither birth maturity status, infant age, nor feeding practice had a significant effect on mother's positive affect and behaviour during feeding. CONCLUSIONS: Nurses' efforts to enhance the attunement of a mother's working model of feeding may help mothers feed with greater positive affect and behaviour. Further study of how the attunement of a mother's feeding expectations and intentions are related to her symptoms of depression and with what she makes of the infant's growth and well-being is needed. The theoretical model needs testing with infants from the entire premature population.

Adult↗
PubMed2004

Spatio-temporal modeling of benthic biological species.

The spatial and temporal distribution of the number of benthic species located in an important area under ecological stress (Puerto CALICA, Quintana Roo, Mexico) is analyzed by means of Gaussian Spatial Linear Mixed Models. Following a model-based approach we derive spatial predictions taking into account temporal variations between May 1996 and June 1999. The proposed models were evaluated in terms of their ability to detect the underlying spatial structure for further interpolation. Uncertainty in the prediction could be evaluated by using the Bayesian paradigm. The results can be used as a guide for further environmental management policies in the region.

Animals↗
PubMed1999

A GEE moving average analysis of the relationship between air pollution and mortality for asthma in Barcelona, Spain.

Several studies have assessed the association between air pollution and hospital admissions or emergency room visits for asthma. Because of both the presence of missing data and the small number of observations, the relationship between air pollution and mortality for respiratory causes has been rarely analysed, and when it has, the results are very inconclusive or even inconsistent. The objective of this study is to assess the relation between levels of air pollutants (black smoke, sulphur dioxide, nitrogen dioxide and ozone), meteorological variables (24th average temperature and relative humidity) and daily mortality for asthma (ICD-9 493, 2 to 45 years old) in Barcelona, Spain, during the period 1986-1989. Since the range of daily mortality for asthma (2 to 45 years old) during the period 1986-1989 was 0-1), we have preferred to consider this variable as dichotomous. First, the relationship between air pollutants, meteorological variables and daily mortality (controlled for the occurrence of asthma epidemics) was estimated using logistic regression models. As was expected, the residuals from this regression were autocorrelated, showing a complex moving average (MA) structure. If covariates were not time dependent the so-called generalized linear mixed models, could be applied. In our case the covariates vary. As a consequence the likelihood is numerically intractable because it involves the evaluation of n-fold integral. An alternative method that avoids these numerical problems is the generalized estimating equations method (GEE). It is a multivariate analogue of quasi-likelihood estimation. In the absence of a likelihood function the parameters can be estimated by solving a multivariate analogue of the quasi score function. We have modified the GEE method in this paper, allowing for a different structure in the error covariance matrix (MA). Both air pollutants and meteorological variables are related with the occurrence of a death for asthma. In this sense, nitrogen dioxide, NO(2) (ss=0.037, p<0. 05), ozone, O(3) (ss=0.021, p<0.06) and high temperature (the ss's were in the range (0.098-0.182), p<0.05) increased the probability of dying for asthma in Barcelona during the period 1986-1989.

Adolescent↗