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PubMed2005

Multilevel mixed linear models for survival data.

For the analysis of correlated survival data mixed linear models are useful alternatives to frailty models. By their use the survival times can be directly modelled, so that the interpretation of the fixed and random effects is straightforward. However, because of intractable integration involved with the use of marginal likelihood the class of models in use has been severely restricted. Such a difficulty can be avoided by using hierarchical-likelihood, which provides a statistically efficient and fast fitting algorithm for multilevel models. The proposed method is illustrated using the chronic granulomatous disease data. A simulation study is carried out to evaluate the performance.

Case-Control Studies↗

PubMed2000

Application of log-linear models to malaria patients in Thailand.

Malaria is a common infectious disease in many tropical countries, including Thailand. The country is located geographically in a tropical zone and the transmission of malaria is particularly common in some regions, for instance in Tak province. The objective of this study is to identify risk factors causing malaria in Tak province in the rainy season by using log-linear models. Tests of independence are used (chi-square and Cramer's V-value tests) to find out the relationships between any two variables. In addition two- and three-dimensional log-linear models are used to obtain estimated parameters and expected frequencies for these models. Amongst the models fitted, the best are chosen based on the analysis of deviance. The results of this study show that most observed variables are significantly related with p-values<0.05. Causes of migration and reasons for staying overnight are highly related to personal variables. Thus, it can be concluded that two of the risk factors for malaria are causes of migration and reasons for staying overnight. Knowledge of prevention is also related to personal variables. Therefore, knowledge of prevention was concluded to be a risk factor affecting prevalence of malaria. For each set of three variables, the best model shows interaction terms of variables that have a relationship but there are no interactions of three effects in these best models.

Epidemiologic Methods↗

PubMed2005

Locomotor ecology of wild orangutans (Pongo pygmaeus abelii) in the Gunung Leuser Ecosystem, Sumatra, Indonesia: a multivariate analysis using log-linear modelling.

The large body mass and exclusively arboreal lifestyle of Sumatran orangutans identify them as a key species in understanding the dynamic between primates and their environment. Increased knowledge of primate locomotor ecology, coupled with recent developments in the standardization of positional mode classifications (Hunt et al. [1996] Primates 37:363-387), opened the way for sophisticated multivariate statistical approaches, clarifying complex associations between multiple influences on locomotion. In this study we present a log-linear modelling approach used to identify key associations between orangutan locomotion, canopy level, support use, and contextual behavior. Log-linear modelling is particularly appropriate because it is designed for categorical data, provides a systematic method for testing alternative hypotheses regarding interactions between variables, and allows interactions to be ranked numerically in terms of relative importance. Support diameter and type were found to have the strongest associations with locomotor repertoire, suggesting that orangutans have evolved distinct locomotor modes to solve a variety of complex habitat problems. However, height in the canopy and contextual behavior do not directly influence locomotion: instead, their effect is modified by support type and support diameter, respectively. Contrary to classic predictions, age-sex category has only limited influence on orangutan support use and locomotion, perhaps reflecting the presence of arboreal pathways which individuals of all age-sex categories follow. Effects are primarily related to a tendency for adult, parous females to adopt a more cautious approach to locomotion than adult males and immature subjects.

Age Factors↗

PubMed1996

Interval censored survival data: a generalized linear modelling approach.

A method is described for weak parametric modelling of arbitrarily interval censored survival data using generalized linear models. The method makes use of an associated Bernoulli model, with standard errors based on the observed information matrix. Three types of models are discussed: additive and multiplicative hazard models with piecewise constant baseline hazard, and a proportional hazards model with discrete baseline survivor function. These models may be fitted in the statistical package GLIM.

Breast Neoplasms↗

PubMed1993

Application of a hierarchical linear model to the study of adolescent deviance in an overlapping cohort design.

Hierarchical linear models provide a conceptual orientation and a flexible set of analytic techniques for studying psychological change in repeated measures studies. The researcher first formulates a model for individual change over time, with each individual's development characterized by a unique set of parameters. These parameters are then viewed as varying randomly over the population of persons. We illustrate this approach with data on attitudes toward deviance during adolescence (Raudenbush & Chan, 1992), indicating how one may assess the psychometric properties of an instrument for studying change, compare the adequacy of linear and curvilinear growth models, control for time invariant and time-varying covariates, and link overlapping cohorts of data. The results suggest that prodeviant attitudes characteristically increase during early adolescence, achieving a peak between 17 and 18 years of age. The typical trajectories for male and female adolescents have the same shape, although female adolescents tend to be less deviant than male adolescents at each age. We briefly consider the statistical power of tests of cohort differences at the points where they overlap.

Adolescent↗

PubMed1985

Confidence intervals for a variance ratio, or for heritability, in an unbalanced mixed linear model.

A procedure is presented for constructing an exact confidence interval for the ratio of the two variance components in a possibly unbalanced mixed linear model that contains a single set of m random effects. This procedure can be used in animal and plant breeding problems to obtain an exact confidence interval for a heritability. The confidence interval can be defined in terms of the output of a least squares analysis. It can be computed by a graphical or iterative technique requiring the diagonalization of an m X m matrix or, alternatively, the inversion of a number of m X m matrices. Confidence intervals that are approximate can be obtained with much less computational burden, using either of two approaches. The various confidence interval procedures can be extended to some problems in which the mixed linear model contains more than one set of random effects. Corresponding to each interval procedure is a significance test and one or more estimators.

Analysis of Variance↗

PubMed2005

Estimating time-dependent gene networks from time series microarray data by dynamic linear models with Markov switching.

In gene network estimation from time series microarray data, dynamic models such as differential equations and dynamic Bayesian networks assume that the network structure is stable through all time points, while the real network might changes its structure depending on time, affection of some shocks and so on. If the true network structure underlying the data changes at certain points, the fitting of the usual dynamic linear models fails to estimate the structure of gene network and we cannot obtain efficient information from data. To solve this problem, we propose a dynamic linear model with Markov switching for estimating time-dependent gene network structure from time series gene expression data. Using our proposed method, the network structure between genes and its change points are automatically estimated. We demonstrate the effectiveness of the proposed method through the analysis of Saccharomyces cerevisiae cell cycle time series data.

Algorithms↗

PubMed2005

Identifying differential expression in multiple SAGE libraries: an overdispersed log-linear model approach.

BACKGROUND: In testing for differential gene expression involving multiple serial analysis of gene expression (SAGE) libraries, it is critical to account for both between and within library variation. Several methods have been proposed, including the t test, tw test, and an overdispersed logistic regression approach. The merits of these tests, however, have not been fully evaluated. Questions still remain on whether further improvements can be made. RESULTS: In this article, we introduce an overdispersed log-linear model approach to analyzing SAGE; we evaluate and compare its performance with three other tests: the two-sample t test, tw test and another based on overdispersed logistic linear regression. Analysis of simulated and real datasets show that both the log-linear and logistic overdispersion methods generally perform better than the t and tw tests; the log-linear method is further found to have better performance than the logistic method, showing equal or higher statistical power over a range of parameter values and with different data distributions. CONCLUSION: Overdispersed log-linear models provide an attractive and reliable framework for analyzing SAGE experiments involving multiple libraries. For convenience, the implementation of this method is available through a user-friendly web-interface available at http://www.cbcb.duke.edu/sage.

Carcinoma, Pancreatic Ductal↗

PubMed1992

Estimating prevalence by group testing using generalized linear models.

A method is described for estimating prevalence by group testing using generalized linear models. This provides a simple way of analysing such data using widely available software. Existing methodology to correct for overdispersion using quasi-likelihoods is applied to the group testing model. The methods are illustrated by an estimation of salmonella contamination in eggs, and of yellow fever virus infection in a mosquito population.

Animals↗

PubMed1994

Directional selectivity in a nonspiking interneuron of the crayfish optic lobe: evaluation of a linear model.

1. Intracellular recordings, sine wave gratings, and paired flashes were used to characterize the directional selectivity (DS) of the peripheral neurons of the crayfish visual pathway. DS was observed in nonspiking tangential (Tan1) neurons of the distal medulla externa and it is expressed by the amplitude of the modulated synaptic potential elicited with drifting gratings. 2. The directional mechanism was characterized by variations in the grating contrast, spatial frequency, and temporal frequency. DS is both contrast and velocity dependent. 3. The velocity dependence of DS for fixed stimulus contrast can be described by a linear model including a delay and subtractive compare operation. This mechanism operates over the entire useful range of spatial and temporal frequencies. 4. The parameters of the linear model can be estimated from the spatiotemporal structure of the Tan1 cell receptive field. The receptive field exhibits a spatially asymmetric inhibitory subfield that is offset from the excitatory subfield by 3-5 degrees (1-2 ommatidia). The inhibition is delayed relative to excitation by 50-100 ms. 5. The contrast dependence of DS reflects an apparent nonlinearity in the mechanism that determines the null response amplitude. The preferred response magnitude is approximately linear with variations in contrast. 6. The nonlinearity observed in the null direction can in principle be attributed to either a tonic excitation at 0 contrast or a threshold for inhibition. There is evidence for both processes in the Tan1 cell visual response.

Acetylcholine↗

PubMed1986

Bivariate linear models in neurobiology: problems of concept and methodology.

Bivariate linear models, used to describe morphological and functional characteristics between two sets of observations, are examined both in concept and in application. This paper focuses on the underlying assumptions and statistics of the method most frequently used: ordinary linear regression, principal axis and standard major axis. It is shown how the choice of method should depend on: the purpose of the analysis and the a priori assumptions regarding the residual variance. It appears that none of the methods has a universal application. Differences among the models discussed are illustrated by a bivariate morphometric analysis of cerebrocortical regions in primates.

Animals↗

PubMed1997

Predictive variable selection for the multivariate linear model.

We develop a predictive Bayesian approach to variable selection in the multivariate linear model. A criterion derived from the Bayesian predictive density is proposed and a calibration is provided for it. Reference and informative priors are discussed, and an automated method that focuses on the response variable is proposed for specifying informative priors for the regression parameters. Relationships between the proposed criterion and other several well-known criteria are examined. Illustrative examples involving real data are given to demonstrate the methodology.

Asbestos↗

PubMed2005

Orphan comparisons and indirect meta-analysis: a case study on antidepressant efficacy in dysthymia comparing tricyclic antidepressants, selective serotonin reuptake inhibitors, and monoamine oxidase inhibitors by using general linear models.

Direct comparisons of the efficacy of competing interventions are not always available in the literature. This situation leads to the presence of clinically relevant "orphan comparisons" of therapeutic interventions which have never been compared head-to-head. To overcome this limitation, simple methods for indirect meta-analysis have been suggested. Nevertheless, their results are prone to bias when more than 1 indirect comparison is tested because of the likely duplication of data for some comparisons. In contrast, general linear models can be used to extend simple indirect meta-analysis beyond 1 indirect comparison by fitting to incomplete data using maximum likelihood within the framework of multitreatment comparisons. This study presents a tutorial application of general linear models to the comparative efficacy of several antidepressants in dysthymia (tricyclic antidepressants, selective serotonin reuptake inhibitors, and monoamine oxidase inhibitors. Working with previously published data comparing the efficacy of antidepressants with placebo, it is shown that tricyclic antidepressants and selective serotonin reuptake inhibitors present similar efficacy (odds ratio = 1.19, P = 0.37; relative risk = 1.10, P = 0.24; risk difference = 0.03, P = 0.53), whereas monoamine oxidase inhibitors outperform both tricyclic antidepressants and selective serotonin reuptake inhibitors, at least for some effect scales (odds ratio = 1.57, P = 0.05; relative risk = 1.25, P = 0.05; risk difference = 0.09, P = 0.08). This finding, which is an instance of a relevant orphan comparison and could not be obtained otherwise, could motivate the conduct of clinical trials or focused systematic reviews to support or refute its importance through appropriate head-to-head comparisons.

Antidepressive Agents, Tricyclic↗

PubMed2005

Application of log-linear models to cancer patients: a case study of data from the National Cancer Institute.

Cancer is a noninfectious disease which is on the increase throughout the world and has become a serious problem for public health in many countries, including Thailand. In Thailand, cancer has risen significantly to become a leading cause of death and most patients are admitted to the National Cancer Institute. The objective of this study is to identify the associated factors between personal, cancer/clinical variables of cancer patients using log-linear models. Tests of independence are used (chi-square and Cramer's V-value tests) to find out the relationships between any two variables. In addition two- and three-dimensional log-linear models are used to obtain estimated parameters and expected frequencies for these models. Amongst the models fitted, the best are chosen based on the analysis of deviance. The results of this study show that most paired variables of personal, cancer/clinical variables are significantly related at p-value <0.05. For both male and female patients, the variable site of the cancer is highly related to marital status, diagnostic evidence and treatment, which provide the highest Cramer's V value. Moreover, the site of cancer also affects the method of diagnostic evidence and treatment. Since the site of cancer in each sex is different, prevention for various sites of cancer should be considered for each specific sex. In addition, for male and female patients, treatment is related to the site of cancer. Consequently, physicians may consider these factors before selecting the appropriate method of treatment.

Epidemiologic Methods↗

PubMed2001

Closed-form approximations to the REML estimator of a variance ratio (or heritability) in a mixed linear model.

In this article, we estimate heritability or intraclass correlation in a mixed linear model having two sources of variation. In most applications, the commonly used restricted maximum likelihood (REML) estimator can only be obtained via an iterative approach. In some cases, the algorithm used to compute REML estimates may be slow or may even fail to converge. We develop a set of closed-form approximations to the REML estimator, and the performance of these estimators is compared with that of the REML estimator. We provide guidelines regarding how to choose the estimator that best approximates the REML estimator. Examples presented in the article suggest that the closed-form estimators compete with and, in some cases, outperform the REML estimator.

Algorithms↗

PubMed1999

Use of the generalised linear model with Poisson distribution to compare caries indices.

In dental epidemiological studies, an analysis of variance assuming a normal distribution is commonly used to compare caries indices, which are often not normally distributed. As these indices represent discontinuous data, it would be preferable to use the negative binomial or the Poisson distribution. In this study, in order to compare the DMFS indices of adults working in the confectionery manufacturing industry in France, the results of the generalised linear model obtained using the normal and the Poisson distribution with identity or log built-in link function were compared. The negative binomial distribution was not used because it is very often unavailable in the most used statistical software. Analysis of the caries indices showed that the use of the normal distribution could lead to an incorrect interpretation of the data. Therefore it is concluded that the generalised linear model with Poisson distribution and over dispersion is to be preferred when comparing caries levels.

Adult↗

PubMed2004

Modelling land use change with generalized linear models--a multi-model analysis of change between 1860 and 2000 in Gallatin Valley, Montana.

This paper develops an approach to modelling land use change that links model selection and multi-model inference with empirical models and GIS. Land use change is frequently studied, and understanding gained, through a process of modelling that is an empirical analysis of documented changes in land cover or land use patterns. The approach here is based on analysis and comparison of multiple models of land use patterns using model selection and multi-model inference. The approach is illustrated with a case study of rural housing as it has developed for part of Gallatin County, Montana, USA. A GIS contains the location of rural housing on a yearly basis from 1860 to 2000. The database also documents a variety of environmental and socio-economic conditions. A general model of settlement development describes the evolution of drivers of land use change and their impacts in the region. This model is used to develop a series of different models reflecting drivers of change at different periods in the history of the study area. These period specific models represent a series of multiple working hypotheses describing (a) the effects of spatial variables as a representation of social, economic and environmental drivers of land use change, and (b) temporal changes in the effects of the spatial variables as the drivers of change evolve over time. Logistic regression is used to calibrate and interpret these models and the models are then compared and evaluated with model selection techniques. Results show that different models are 'best' for the different periods. The different models for different periods demonstrate that models are not invariant over time which presents challenges for validation and testing of empirical models. The research demonstrates (i) model selection as a mechanism for rating among many plausible models that describe land cover or land use patterns, (ii) inference from a set of models rather than from a single model, (iii) that models can be developed based on hypothesised relationships based on consideration of underlying and proximate causes of change, and (iv) that models are not invariant over time.

Agriculture↗

PubMed2006

Regional admixture mapping and structured association testing: conceptual unification and an extensible general linear model.

Individual genetic admixture estimates, determined both across the genome and at specific genomic regions, have been proposed for use in identifying specific genomic regions harboring loci influencing phenotypes in regional admixture mapping (RAM). Estimates of individual ancestry can be used in structured association tests (SAT) to reduce confounding induced by various forms of population substructure. Although presented as two distinct approaches, we provide a conceptual framework in which both RAM and SAT are special cases of a more general linear model. We clarify which variables are sufficient to condition upon in order to prevent spurious associations and also provide a simple closed form "semiparametric" method of evaluating the reliability of individual admixture estimates. An estimate of the reliability of individual admixture estimates is required to make an inherent errors-in-variables problem tractable. Casting RAM and SAT methods as a general linear model offers enormous flexibility enabling application to a rich set of phenotypes, populations, covariates, and situations, including interaction terms and multilocus models. This approach should allow far wider use of RAM and SAT, often using standard software, in addressing admixture as either a confounder of association studies or a tool for finding loci influencing complex phenotypes in species as diverse as plants, humans, and nonhuman animals.

Computer Simulation↗