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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↗

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↗

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↗

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↗

PubMed2000

Summarizing the predictive power of a generalized linear model.

This paper studies summary measures of the predictive power of a generalized linear model, paying special attention to a generalization of the multiple correlation coefficient from ordinary linear regression. The population value is the correlation between the response and its conditional expectation given the predictors, and the sample value is the correlation between the observed response and the model predicted value. We compare four estimators of the measure in terms of bias, mean squared error and behaviour in the presence of overparameterization. The sample estimator and a jack-knife estimator usually behave adequately, but a cross-validation estimator has a large negative bias with large mean squared error. One can use bootstrap methods to construct confidence intervals for the population value of the correlation measure and to estimate the degree to which a model selection procedure may provide an overly optimistic measure of the actual predictive power.

Bias↗

PubMed2000

Residuals analysis of the generalized linear models for longitudinal data.

The generalized estimation equation (GEE) method, one of the generalized linear models for longitudinal data, has been used widely in medical research. However, the related sensitivity analysis problem has not been explored intensively. One of the possible reasons for this was due to the correlated structure within the same subject. We showed that the conventional residuals plots for model diagnosis in longitudinal data could mislead a researcher into trusting the fitted model. A non-parametric method, named the Wald-Wolfowitz run test, was proposed to check the residuals plots both quantitatively and graphically. The rationale proposedin this paper is well illustrated with two real clinical studies in Taiwan.

Adult↗

PubMed1992

Log-linear modelling of pairwise interobserver agreement on a categorical scale.

This article uses log-linear models to describe pairwise agreement among several raters who classify a sample on a subjective categorical scale. The models describe agreement structure simultaneously for second-order marginal tables of a multidimensional cross-classification of ratings. Practical difficulties arise in fitting the models, because models refer to pairwise marginal tables of a very large and sparse table. A standard analysis that treats the marginal tables as independent yields consistent estimates of model parameters, but not of the covariance matrix of the estimates. We estimate the covariance matrix using the jackknife. We apply the models to describe agreement between evaluations made by seven pathologists of carcinoma in situ of the uterine cervix, using a five-level ordinal scale. Previous analyses showed differences among the pathologists in their pairwise levels of agreement, but we observe near homogeneity in the dependence structure of their ratings.

Carcinoma in Situ↗

PubMed2000

Do children with Hodgkin's disease have a better prognosis than adults? Application of a generalised linear model to a systematic review of published results.

This investigation aimed to compare survival rates in paediatric and adult Hodgkin's disease using published results. When comparing results obtained in different studies and institutions it is important to explain, estimate and allow for heterogeneity between studies. This was attempted though systematic inclusion of a large number of published results, through modelling the influence of covariates on survival using a generalised linear model, and by estimation of both the sampling errors in the extracted survival rates and the heterogeneity between studies. A significant superiority of treatment results in paediatric institutions compared with adult institutions was demonstrated, allowing for differences in patient and treatment characteristics.

Adult↗

PubMed2000

Summarizing the goodness of fit of generalized linear models for longitudinal data.

This paper extends four goodness-of-fit measures of a generalized linear model (GLM) to random effects and marginal models for longitudinal data. The four measures are the proportional reduction in entropy measure, the proportional reduction in deviance measure, the concordance correlation coefficient and the concordance index. The extended measures satisfy the basic requirements for measures of association. Two examples illustrate their use in model selection.

Adolescent↗

PubMed2000

A comparison of primary and proxy respondent reports of habitual physical activity, using kappa statistics and log-linear models.

BACKGROUND: Many epidemiological studies rely in part on proxy informants. There is little published information on the reliability of proxy-respondent reports of physical activity. METHODS: Self-reported data on vigorous and moderate physical activity, from a representative sub-sample of participants in a community-based case-control study of coronary heart disease, were compared with information collected from their next-of-kin. RESULTS: Relative to primary respondents, proxy respondents under-reported activity by approximately 10 percentage points, for both leisure and work-time activity. On a simple three point scale (inactivity/moderate activity/physical activity), 70% of primary-proxy pairs were in exact agreement with regard to leisure time activity and 67% of pairs were in exact agreement on work-time activity. The corresponding values for the weighted kappa statistic were 0.66 [95% confidence interval (CI) 0.59-0.72] and 0.62 (0.54-0.72). Log-linear modelling provided evidence for superior agreement on worktime activity when the proxy was not the primary respondent's spouse. DISCUSSION: Overall levels of primary-proxy respondent agreement on physical activity seem somewhat lower than has been reported for smoking and alcohol-drinking frequency. There seems little reason to prefer spouse proxies when endeavouring to elicit information on work-time physical activity. Log-linear modelling provides an efficient means of exploring covariate effects in observer-agreement studies.

Adult↗

PubMed1989

Log-linear models for the analysis of matched cohort studies.

The application of conditional logistic regression to the analysis of matched case-control studies has now become quite customary. In addition, it is well known that software designed to fit linear logistic and log-linear models can be used in these analyses. The application of conditional logistic regression to cohort designs is described, and an approach is developed that adapts the linear logistic and log-linear models for the analysis of prospectively collected data. Specific situations discussed include matched pairs, 2:1 matching, and studies in which some subjects are pair matched and others matched 2:1. The methods are illustrated with numeric examples.

Case-Control Studies↗

PubMed1990

Application of log-linear model in inference on karyotypic evolution in chronic myelocytic leukemia.

Relationships among additional chromosome abnormalities in chronic myelocytic leukemia (CML) with translocation 9;22 [Philadelphia chromosome (Ph1)-positive CML] were analyzed by log-linear models on 709 karyotypes reported in the literature. Additional abnormalities, such as the gain of chromosome 8 (+8), gain of Philadelphia chromosome (+Ph1), isochromosome of the long arm (q) of chromosome 17 [i(17q)], and the gain of chromosome 19 (+19), were frequently observed. A four-way 2 x 2 x 2 x 2 contingency table was considered with respect to the appearance of these four abnormalities, then the hierarchical log-linear models having at least four main effects were fitted to the observed contingency table. Akaike's information criteria of the models reflected the fitness of the model very well. Parameter estimates of the interaction terms indicated that the combinations of two abnormalities, '+8 and +19', '+Ph1 and +19', and '+8 and i(17q)' were positively associated, while '+Ph1 and i(17q)', and '+19 and i(17q)' were negatively associated. Based on the results of the data analysis, an inference was made on the route of karyotypic evolution in Ph1-positive CML; it statistically supports the hypothesis presented by Heim and Mitelman.

Aneuploidy↗