The convenient calculation of some test statistics in models of discrete choice

The paper considers the use of artificial regression in calculating different types of score test when the log

A Score Test for Zero-Inflation in Correlated Count Data

To account for the preponderance of zero counts and simultaneous correlation of observations, a class of zero-inflated Poisson mixed regression models is applicable for accommodating the within-cluster dependence. In this paper, a score test for zero-inflation is developed for assessing correlated count data with excess zeros. The sampling distribution and the power of the test statistic are evaluated by simulation studies. The results show that the test statistic performs satisfactorily under a wide range of conditions. The test procedure is further illustrated using a data set on recurrent urinary tract infections. Copyright (c) 2005 John Wiley & Sons, Ltd.

Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models

We present simple matrix formulae for corrected score statistics in symmetric nonlinear regression models. The corrected score statistics follow more closely a chi (2) distribution than the classical score statistic. Our simulation results indicate that the corrected score tests display smaller size distortions than the original score test. We also compare the sizes and the powers of the corrected score tests with bootstrap-based score tests.

Improved score tests in symmetric linear regression models

The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n(-3/2)), n being the sample size. The corrections represent an improvement over the corresponding original Rao`s score statistics, which are chi-squared distributed up to errors of order O(n(-1)). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size.

Development and implementation of the population Fisher information matrix for the evaluation of population pharmacokinetic designs.

In population pharmacokinetic studies, the precision of parameter estimates is dependent on the population design. Methods based on the Fisher information matrix have been developed and extended to population studies to evaluate and optimize designs. In this paper we propose simple programming tools to evaluate population pharmacokinetic designs. This involved the development of an expression for the Fisher information matrix for nonlinear mixed-effects models, including estimation of the variance of the residual error. We implemented this expression as a generic function for two software applications: S-PLUS and MATLAB. The evaluation of population designs based on two pharmacokinetic examples from the literature is shown to illustrate the efficiency and the simplicity of this theoretic approach. Although no optimization method of the design is provided, these functions can be used to select and compare population designs among a large set of possible designs, avoiding a lot of simulations.

A score test for non-nested hypotheses with applications to discrete data models

This paper suggests that a convenient score test against non-nested alternatives can be constructed from the linear combination of the likelihood functions of the competing models. It is shown that this procedure is essentially a test for the correct specification of the conditional distribution of the variable of interest.

The sequential analysis of repeated binary responses: a score test for the case of three time points

In this paper a robust method is developed for the analysis of data consisting of repeated binary observations taken at up to three fixed time points on each subject. The primary objective is to compare outcomes at the last time point, using earlier observations to predict this for subjects with incomplete records. A score test is derived. The method is developed for application to sequential clinical trials, as at interim analyses there will be many incomplete records occurring in non-informative patterns. Motivation for the methodology comes from experience with clinical trials in stroke and head injury, and data from one such trial is used to illustrate the approach. Extensions to more than three time points and to allow for stratification are discussed. Copyright © 2005 John Wiley & Sons, Ltd.

A score test for binary data with patient non-compliance

A score test is developed for binary clinical trial data, which incorporates patient non-compliance while respecting randomization. It is assumed in this paper that compliance is all-or-nothing, in the sense that a patient either accepts all of the treatment assigned as specified in the protocol, or none of it. Direct analytic comparisons of the adjusted test statistic for both the score test and the likelihood ratio test are made with the corresponding test statistics that adhere to the intention-to-treat principle. It is shown that no gain in power is possible over the intention-to-treat analysis, by adjusting for patient non-compliance. Sample size formulae are derived and simulation studies are used to demonstrate that the sample size approximation holds. Copyright © 2003 John Wiley & Sons, Ltd.

A combined score test for binary and ordinal endpoints from clinical trials

There is growing interest, especially for trials in stroke, in combining multiple endpoints in a single clinical evaluation of an experimental treatment. The endpoints might be repeated evaluations of the same characteristic or alternative measures of progress on different scales. Often they will be binary or ordinal, and those are the cases studied here. In this paper we take a direct approach to combining the univariate score statistics for comparing treatments with respect to each endpoint. The correlations between the score statistics are derived and used to allow a valid combined score test to be applied. A sample size formula is deduced and application in sequential designs is discussed. The method is compared with an alternative approach based on generalized estimating equations in an illustrative analysis and replicated simulations, and the advantages and disadvantages of the two approaches are discussed.

Analysis of postprandial lipemia as a Cardiovascular Disease risk factor using genetic and clinical information: an Artificial Neural Network perspective

Clinical studies indicate that exaggerated postprandial lipemia is linked to the progression of atherosclerosis, leading cause of Cardiovascular Diseases (CVD). CVD is a multi-factorial disease with complex etiology and according to the literature postprandial Triglycerides (TG) can be used as an independent CVD risk factor. Aim of the current study is to construct an Artificial Neural Network (ANN) based system for the identification of the most important gene-gene and/or gene-environmental interactions that contribute to a fast or slow postprandial metabolism of TG in blood and consequently to investigate the causality of postprandial TG response. The design and development of the system is based on a dataset of 213 subjects who underwent a two meals fatty prandial protocol. For each of the subjects a total of 30 input variables corresponding to genetic variations, sex, age and fasting levels of clinical measurements were known. Those variables provide input to the system, which is based on the combined use of Parameter Decreasing Method (PDM) and an ANN. The system was able to identify the ten (10) most informative variables and achieve a mean accuracy equal to 85.21%.

Information Matrix for Beta Distributions

2000 Mathematics Subject Classification: 33C90, 62E99.

Hypotheses Testing on a Multivariate Null Intercept Errors-in-Variables Model

Considering the Wald, score, and likelihood ratio asymptotic test statistics, we analyze a multivariate null intercept errors-in-variables regression model, where the explanatory and the response variables are subject to measurement errors, and a possible structure of dependency between the measurements taken within the same individual are incorporated, representing a longitudinal structure. This model was proposed by Aoki et al. (2003b) and analyzed under the bayesian approach. In this article, considering the classical approach, we analyze asymptotic test statistics and present a simulation study to compare the behavior of the three test statistics for different sample sizes, parameter values and nominal levels of the test. Also, closed form expressions for the score function and the Fisher information matrix are presented. We consider two real numerical illustrations, the odontological data set from Hadgu and Koch (1999), and a quality control data set.

Information processing in sleep-onset insomnia : a test of the neurocognitive model /

The present thesis study is a systematic investigation of information processing at sleep onset, using auditory event-related potentials (ERPs) as a test of the neurocognitive model of insomnia. Insomnia is an extremely prevalent disorder in society resulting in problems with daytime functioning (e.g., memory, concentration, job performance, mood, job and driving safety). Various models have been put forth in an effort to better understand the etiology and pathophysiology of this disorder. One of the newer models, the neurocognitive model of insomnia, suggests that chronic insomnia occurs through conditioned central nervous system arousal. This arousal is reflected through increased information processing which may interfere with sleep initiation or maintenance. The present thesis employed event-related potentials as a direct method to test information processing during the sleep-onset period. Thirteen poor sleepers with sleep-onset insomnia and 1 2 good sleepers participated in the present study. All poor sleepers met the diagnostic criteria for psychophysiological insomnia and had a complaint of problems with sleep initiation. All good sleepers reported no trouble sleeping and no excessive daytime sleepiness. Good and poor sleepers spent two nights at the Brock University Sleep Research Laboratory. The first night was used to screen for sleep disorders; the second night was used to investigate information processing during the sleep-onset period. Both groups underwent a repeated sleep-onsets task during which an auditory oddball paradigm was delivered. Participants signalled detection of a higher pitch target tone with a button press as they fell asleep. In addition, waking alert ERPs were recorded 1 hour before and after sleep on both Nights 1 and 2.As predicted by the neurocognitive model of insomnia, increased CNS activity was found in the poor sleepers; this was reflected by their smaller amplitude P2 component seen during wake of the sleep-onset period. Unlike the P2 component, the Nl, N350, and P300 did not vary between the groups. The smaller P2 seen in our poor sleepers indicates that they have a deficit in the sleep initiation processes. Specifically, poor sleepers do not disengage their attention from the outside environment to the same extent as good sleepers during the sleep-onset period. The lack of findings for the N350 suggest that this sleep component may be intact in those with insomnia and that it is the waking components (i.e., Nl, P2) that may be leading to the deficit in sleep initiation. Further, it may be that the mechanism responsible for the disruption of sleep initiation in the poor sleepers is most reflected by the P2 component. Future research investigating ERPs in insomnia should focus on the identification of the components most sensitive to sleep disruption. As well, methods should be developed in order to more clearly identify the various types of insomnia populations in research contexts (e.g., psychophysiological vs. sleep-state misperception) and the various individual (personality characteristics, motivation) and environmental factors (arousal-related variables) that influence particular ERP components. Insomnia has serious consequences for health, safety, and daytime functioning, thus research efforts should continue in order to help alleviate this highly prevalent condition.

Inference and local influence assessment in skew-normal null intercept measurement error model

In this article, we discuss inferential aspects of the measurement error regression models with null intercepts when the unknown quantity x (latent variable) follows a skew normal distribution. We examine first the maximum-likelihood approach to estimation via the EM algorithm by exploring statistical properties of the model considered. Then, the marginal likelihood, the score function and the observed information matrix of the observed quantities are presented allowing direct inference implementation. In order to discuss some diagnostics techniques in this type of models, we derive the appropriate matrices to assessing the local influence on the parameter estimates under different perturbation schemes. The results and methods developed in this paper are illustrated considering part of a real data set used by Hadgu and Koch [1999, Application of generalized estimating equations to a dental randomized clinical trial. Journal of Biopharmaceutical Statistics, 9, 161-178].