Rank repeated measures analysis of covariance

When analyzing a response variable at the presence of both factors and covariates, with potentially correlated responses and violated assumptions of the normal residual or the linear relationship between the response and the covariates, rank-based tests can be an option for inferential procedures instead of the parametric repeated measures analysis of covariance (ANCOVA) models. This article derives a rank-based method for multi-way ANCOVA models with correlated responses. The generalized estimating equations (GEE) technique is employed to construct the proposed rank tests. Asymptotic properties of the proposed tests are derived. Simulation studies confirmed the performance of the proposed tests.     

Stochastic analysis of covariance when the error distribution is long-tailed symmetric

In this study, we consider stochastic one-way analysis of covariance model when the distribution of the error terms is long-tailed symmetric. Estimators of the unknown model parameters are obtained by using the maximum likelihood (ML) methodology. Iteratively reweighting algorithm is used to compute the ML estimates of the parameters. We also propose new test statistic based on ML estimators for testing the linear contrasts of the treatment effects. In the simulation study, we compare the efficiencies of the traditional least-squares (LS) estimators of the model parameters with the corresponding ML estimators. We also compare the power of the test statistics based on LS and ML estimators, respectively. A real-life example is given at the end of the study.     

Generalized simultaneous confidence regions for regression coefficients and their ratios

This study constructs a simultaneous confidence region for two combinations of coefficients of linear models and their ratios based on the concept of generalized pivotal quantities. Many biological studies, such as those on genetics, assessment of drug effectiveness, and health economics, are interested in a comparison of several dose groups with a placebo group and the group ratios. The Bonferroni correction and the plug-in method based on the multivariate-t distribution have been proposed for the simultaneous region estimation. However, the two methods are asymptotic procedures, and their performance in finite sample sizes has not been thoroughly investigated. Based on the concept of generalized pivotal quantity, we propose a Bonferroni correction procedure and a generalized variable (GV) procedure to construct the simultaneous confidence regions. To address a genetic concern of the dominance ratio, we conduct a simulation study to empirically investigate the probability coverage and expected length of the methods for various combinations of sample sizes and values of the dominance ratio. The simulation results demonstrate that the simultaneous confidence region based on the GV procedure provides sufficient coverage probability and reasonable expected length. Thus, it can be recommended in practice. Numerical examples using published data sets illustrate the proposed methods.     

Bivariate distributions of some ratios of independent noncentral chi-square random variables

The bivariate distributions of three pairs of ratios of in¬dependent noncentral chi-square random variables are considered. These ratios arise in the problem of computing the joint power function of simultaneous F-tests in balanced ANOVA and ANCOVA. The distributions obtained are generalizations to the noncentral case of existing results in the literature. Of particular note is the bivariate noncentral F distribution, which generalizes a special case of Krishnaiah*s (1964,1965) bivariate central F distribution. Explicit formulae for the cdf's of these distribu¬tions are given, along with computational procedures     

Within groups analysis of covariance: multiple comparisons at specified design points using a robust measure location when there is curvature

Consider the situation where measurements are taken at two different times and let M_j(x) be some conditional robust measure of location associated with the random variable Y at time j, given that some covariate X=x. The goal is to test H₀: M₁(x)=M₂(x) for each x∈ x₁,?…?, x_K such that the probability of one or more Type I errors is less than α, where x₁,?…?, x_K are K specified values of the covariate. The paper reports simulation results comparing two methods aimed at accomplishing this goal without specifying some parametric form for the regression line. The first method is based on a simple modification of the method in Wilcox [Introduction to robust estimation and hypothesis testing. 3rd ed. San Diego, CA: Academic Press; 2012, Section 11.11.1]. The main result here is that the second method, which has never been studied, can have higher power, sometimes substantially so. Data from the Well Elderly 2 study, which motivated this paper, are used to illustrate that the alternative approach can make a practical difference. Here, the estimate of M_j(x) is based in part on either a 20% trimmed mean or the Harrell–Davis quantile estimator, but in principle the more successful method can be used with any robust location estimator.     

Testing factor–covariate interaction in rank repeated-measures analysis of covariance models

This article derives the asymptotic properties of rank-based tests for the covariate effects in rank repeated-measures analysis of covariance (ANCOVA) models (Fan and Zhang 2017 Fan, C., and D. Zhang. 2017. Rank repeated measures analysis of covariance. Communications in Statistics - Theory and Methods 46:1158–83.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) employing generalized estimating equation (GEE) techniques. One interested application of the proposed tests is to check the validity of the assumption of homogeneous covariate effects in different levels of the factors. Performance of the proposed tests has been confirmed by simulation studies and illustrated using the famous seizure count data. While the article mainly focuses on interaction tests, the scope of the proposed tests includes testing any contrast of the covariate effect such as the null of no overall covariate effect.     

Nearly optimal covariate designs—Part I

We propose to discuss at length several examples from standard text books. All of these examples deal with analysis of covariance (ANCOVA) models and related analyses of data. We intend to capitalize on our understanding of optimal covariate designs (OCDs) in different ANCOVA models and re-visit these examples with a view to suggest optimal/nearly optimal designs for estimation of the covariate parameter(s). As we will see, for some examples our task is very much routine but for others, it is indeed a highly non trivial exercise.

?We intent to cover a total of six examples—divided in two parts. This is Part I—dealing with two examples.     

Comparison of telephone RDD and online panel survey modes on CPGI scores and co-morbidities

The purpose of this study was to compare the influence of two survey modes – telephone random digit dialling (RDD) and stratified sampling of an online panel – on Canadian Problem Gambling Index (CPGI) scores and co-morbidities. An identical gambling survey was administered to 4000 South Koreans selected via random dialling of cell phone numbers and to 4330 South Korean members of an online panel. The online panelists were found to have significantly higher levels of tobacco use, drug or alcohol problems and mental health problems, higher employment status and lower happiness levels. However, even when controlling for these variables, CPGI scores for the online panel were significantly higher than those for the telephone interview. This appears to be due to higher levels of pathology among online panelists combined with potentially more valid self-reports due to enhanced anonymity.     

Some comments on a class of simultaneous inference procedures in ancova

Methods for constructing simultaneous confidence intervals for contrasts of treatment effects in analysis of covariance (ANCOVA) models are discussed and compared. A simple procedure is given by which, under a normality assumption made on the covariates, any method appropriate in an analysis of variance (ANOVA) may be applied to a corresponding ANCOVA by means of a simple adjustment of the required critical values. Some properties of this procedure are noted.     

Choice of Baselines in Clinical Trials: A Simulation Study from Statistical Power Perspective

Multiple assessments of an efficacy variable are often conducted prior to the initiation of randomized treatments in clinical trials as baseline information. Two goals are investigated in this article, where the first goal is to investigate the choice of these baselines in the analysis of covariance (ANCOVA) to increase the statistical power, and the second to investigate the magnitude of power loss when a continuous efficacy variable is dichotomized to categorical variable as commonly reported the biomedical literature. A statistical power analysis is developed with extensive simulations based on data from clinical trials in study participants with end stage renal disease (ESRD). It is found that the baseline choices primarily depend on the correlations among the baselines and the efficacy variable, with substantial gains for correlations greater than 0.6 and negligible for less than 0.2. Continuous efficacy variables always give higher statistical power in the ANCOVA modeling and dichotomizing the efficacy variable generally decreases the statistical power by 25%, which is an important practicum in designing clinical trials for study sample size and realistically budget. These findings can be easily applied in and extended to other clinical trials with similar design.