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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↗

PubMed2006

Evaluation of QT interval using a linear model in individual cynomolgus monkeys.

INTRODUCTION: The cynomolgus monkey, one of a number of primate species phylogenetically close to humans, is commonly used in cardiovascular research, but a method for determination of the RR interval-corrected QT interval in this species needs greater consideration. The objectives of this study were to determine a method for evaluating QT interval in cynomolgus monkeys individually, disregarding RR interval change artifacts, and to investigate prerequisite information for this method. METHODS: The physiological QT-RR relationship for practical evaluation of QT interval was recorded and analyzed by 24-hour telemetric ECG monitoring. A linear model for log-transformed QT and RR intervals was used to correct the QT interval from RR interval change artifacts for each animal. Sample size was also estimated based on the simulation results. RESULTS: Histograms showed that both QT and RR intervals had a right-heavy tail distribution. QT interval corrected individually by the linear model formula showed smaller within-animal variability than QTb and QTf, which were corrected by Bazett's formula and Fridericia's formula. The simulation results showed that the individual correction factor, beta(i), could be reliably estimated when at least 24 pairs of QT-RR baseline data were available. DISCUSSION: As with humans, QT interval in cynomolgus monkeys varies widely between individuals. Therefore, a method for correcting QT interval individually should be considered, whenever extensive untreated data are available.

Animals↗

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↗

PubMed2005

Bayesian analysis for generalized linear models with nonignorably missing covariates.

We propose Bayesian methods for estimating parameters in generalized linear models (GLMs) with nonignorably missing covariate data. We show that when improper uniform priors are used for the regression coefficients, phi, of the multinomial selection model for the missing data mechanism, the resulting joint posterior will always be improper if (i) all missing covariates are discrete and an intercept is included in the selection model for the missing data mechanism, or (ii) at least one of the covariates is continuous and unbounded. This impropriety will result regardless of whether proper or improper priors are specified for the regression parameters, beta, of the GLM or the parameters, alpha, of the covariate distribution. To overcome this problem, we propose a novel class of proper priors for the regression coefficients, phi, in the selection model for the missing data mechanism. These priors are robust and computationally attractive in the sense that inferences about beta are not sensitive to the choice of the hyperparameters of the prior for phi and they facilitate a Gibbs sampling scheme that leads to accelerated convergence. In addition, we extend the model assessment criterion of Chen, Dey, and Ibrahim (2004a, Biometrika 91, 45-63), called the weighted L measure, to GLMs and missing data problems as well as extend the deviance information criterion (DIC) of Spiegelhalter et al. (2002, Journal of the Royal Statistical Society B 64, 583-639) for assessing whether the missing data mechanism is ignorable or nonignorable. A novel Markov chain Monte Carlo sampling algorithm is also developed for carrying out posterior computation. Several simulations are given to investigate the performance of the proposed Bayesian criteria as well as the sensitivity of the prior specification. Real datasets from a melanoma cancer clinical trial and a liver cancer study are presented to further illustrate the proposed methods.

Bayes Theorem↗

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↗

PubMed2005

Some links between classical and modern test theory via the two-level hierarchical generalized linear model.

This article considers some links between classical test theory (CTT) and modern test theory (MTT) such as item response theory (IRT) and the Rasch model in the context of the two-level hierarchical generalized linear model (HGLM). Conceptualizing items as nested within subjects, both the CTT model and the MTT model can be reformulated as an HGLM where item difficulty parameters are represented by fixed effects and subjects' abilities are represented by random effects. In this HGLM framework, the CTT and MTT models differ only in the level 1 sampling model and the associated link function. This article also contrasts the Rasch and two-parameter IRT models by considering the property of specific objectivity in the context of CTT. It is found that the essentially tau-equivalent model exhibits specific objectivity if the data fit the model, but the congeneric measures model does not. Data from English composition scores on essay writing used by Jöreskog (1971) are reanalyzed for illustration.

Educational Measurement↗

PubMed2007

Individualizing drug dosage by using a random intercept linear model.

An algorithm for drug dosage individualization is proposed. The algorithm assumes a random intercept linear model for the log of trough-plasma-concentration-to-dosage ratio of the drug at steady-state, and aims at determining an optimum dosage for producing a trough steady-state plasma concentration within a target concentration range. The minimum number of algorithm steps necessary to find the optimum dosage is computed. Computations are illustrated for clozapine, an antipsychotic drug used to treat patients with severe schizophrenia.

Algorithms↗

PubMed1993

Analyzing individual status and change with hierarchical linear models: illustration with depression in college students.

A recently developed class of multilevel or hierarchical linear models (HLM) provides an intuitive and efficient way to estimate individual growth or change curves. The approach also models the between-subjects variation of the individual change curves with treatment factors and individual attributes. Unlike other repeated measures analysis methods common in the behavioral sciences, HLM allows the fit of data with unequal numbers of repeated observations for each subject, variable timing of observations, and missing data, features which are often characteristic of data from field studies. The application of HLM for the analysis of repeated psychological measures is discussed and illustrated here with depression data for college students. Strengths and limitations of the approach are discussed.

Adaptation, Psychological↗

PubMed2007

A simple and exploratory way to determine the mean-variance relationship in generalized linear models.

This paper introduces an exploratory way to determine how variance relates to the mean in generalized linear models. This novel method employs the robust likelihood technique introduced by Royall and Tsou.A urinary data set collected by Ginsberg et al. and the fabric data set analysed by Lee and Nelder are considered to demonstrate the applicability and simplicity of the proposed technique. Application of the proposed method could easily reveal a mean-variance relationship that would generally be left unnoticed, or that would require more complex modelling to detect.

Computer Simulation↗

PubMed2004

Applications of hierarchical linear models for evaluations of health interventions: demystifying the methods and interpretations of multilevel models.

Despite the wide availability of statistical programs designed to deal with longitudinal data from a multilevel perspective, many applied researchers remain unfamiliar with the benefits of this methodology, particularly for the evaluation of interventions. The authors present an example of multilevel modeling as part of the analysis of evaluation data from an HIV intervention study. Strategies for understanding multilevel models using longitudinal (panel) data are demonstrated and discussed. The authors illustrate how multiple linear regression models provide a convenient conceptual background to understanding how hierarchical linear models can be developed and interpreted. Multilevel analysis results are compared and contrasted with typical approaches through general linear models for repeated-measures data. Analyses are presented using the SPSS and HLM 5 software.

Analysis of Variance↗

PubMed1992

On the computation of likelihood ratio and score test based confidence intervals in generalized linear models.

Numerical procedures for calculating likelihood ratio test and score test based confidence intervals in generalized linear models are considered. Newton's method appears to have better convergence properties than the secant method in the likelihood ratio test case. However, the secant method may be easier to program for models with link functions that are not natural. Similarly, the secant method is easier to implement for the computation of score test based intervals. The practical implementation of the procedures in GLIM is illustrated.

Confidence Intervals↗

PubMed2006

Power calculations for generalized linear models in observational longitudinal studies: a simulation approach in SAS.

Repeated measurements arising from longitudinal studies occur frequently in applied research. Methods to calculate power in the context of repeated measures are available for experimental settings where the covariate of interest is a discrete treatment indicator. However, no closed form expression exists to calculate power for generalized linear models with non-zero within-cluster correlation that are common in epidemiological and observational studies in which the covariate of interest varies over time and is often measured on a continuous scale, and where the researchers control for several potential confounders. We describe a Monte Carlo simulation approach conducted to calculate power, and illustrate its application in two models frequently encountered in practice, the normal linear mixed model, and the logistic regression model, both with repeated measurements and non-zero within-cluster correlation. This approach can be used to calculate the effect on power of changing various simulation conditions controlled by the researcher, such as sample size, within-cluster correlation structure, smallest meaningful difference to detect, and distributional assumptions.

Child↗

PubMed2006

Checking linearity of non-parametric component in partially linear models with an application in systemic inflammatory response syndrome study.

Two tests are proposed for checking the linearity of nonparametric function in partially linear models. The first one is based on a Crámer-von Mises statistic. This test can detect the local alternative converging to the null at the parametric rate 1/square root n. A bootstrap resample technique is provided to calculate the critical values. The second one is constructed in a penalized spline framework along with linear mixed-effects (LME) modeling. This is an extension likelihood ratio test for testing zero variance of random effects in LME models. Simulation experiments are conducted to explore the numerical performance of two tests. It is observed that two tests have good level properties, and the first test has a substantially superior power property over the second test in a variety of cases. A real data set is analysed with the proposed tests.

Humans↗