Multiple contrast tests with repeated and multiple endpoints : with biological applications

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Multivariate Covariance Generalized Linear Models

We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a covariance link function combined with a matrix linear predictor involving known matrices. The method is motivated by three data examples that are not easily handled by existing methods. The first example concerns multivariate count data, the second involves response variables of mixed types, combined with repeated measures and longitudinal structures, and the third involves a spatio-temporal analysis of rainfall data. The models take non-normality into account in the conventional way by means of a variance function, and the mean structure is modelled by means of a link function and a linear predictor. The models are fitted using an efficient Newton scoring algorithm based on quasi-likelihood and Pearson estimating functions, using only second-moment assumptions. This provides a unified approach to a wide variety of different types of response variables and covariance structures, including multivariate extensions of repeated measures, time series, longitudinal, spatial and spatio-temporal structures.Comment: 21 pages, 5 figure

On the behavior of multiple comparison procedures in complex parametric designs

The framework for simultaneous inference by Hothorn, Bretz, and Westfall (2008) allows for a unified treatment of multiple comparisons in general parametric models where the study questions are specified as linear combinations of elemental model parameters. However, due to the asymptotic nature of the reference distribution the procedure controls the error rate across all comparisons only for sufficiently large samples. This thesis evaluates the small samples properties of simultaneous inference in complex parametric designs. These designs are necessary to address questions from applied research and include nonstandard parametric models or data in which the assumptions of classical procedures for multiple comparisons are not met. This thesis first treats multiple comparisons of samples with heterogeneous variances. Usage of a heteroscedastic consistent covariance estimation prevents an increase in the probability of false positive findings for reasonable sample sizes whereas the classical procedures show liberal or conservative behavior which persists even with increasing sample size. The focus of the second part are multiple comparisons in survival models. Multiple comparisons to a control can be performed in correlated survival data modeled by a frailty Cox model under control of the familywise error rate in sample sizes applicable for clinical trials. As a further application, multiple comparisons in survival models can be performed to investigate trends. The procedure achieves good power to detect different dose-response shapes and controls the error probability to falsely detect any trend. The third part addresses multiple comparisons in semiparametric mixed models. Simultaneous inference in the linear mixed model representation of these models yields an approach for multiple comparisons of curves of arbitrary shape. The sections on which curves differ can also be identified. For reasonably large samples the overall error rate to detect any non-existent difference is controlled. An extension allows for multiple comparisons of areas under the curve. However the resulting procedure achieves an overall error control only for sample sizes considerably larger than available in studies in which multiple AUC comparisons are usually performed. The usage of the evaluated procedures is illustrated by examples from applied research including comparisons of fatty acid contents between Bacillus simplex lineages, comparisons of experimental drugs with a control for prolongation in survival of chronic myelogeneous leukemia patients, and comparisons of curves describing a morphological structure along the spinal cord between variants of the EphA4 gene in mice

Multiple Comparisons with the Best, with Economic Applications

In this paper we discuss a statistical method called multiple comparisons with the best, or MCB. Suppose that we have N populations, and population i has parameter value θi. Let $\theta _{(N)}={\rm max}_{i=1,\ldots ,N}\theta _{i}$\nopagenumbers\end, the parameter value for the ‘best’ population. Then MCB constructs joint confidence intervals for the differences $[\theta _{(N)}-\theta _{1},\theta _{(N)}-\theta _{2},\ldots ,\theta _{(N)}-\theta _{N}]$\nopagenumbers\end. It is not assumed that it is known which population is best, and part of the problem is to say whether any population is so identified, at the given confidence level. This paper is meant to introduce MCB to economists. We discuss possible uses of MCB in economics. The application that we treat in most detail is the construction of confidence intervals for inefficiency measures from stochastic frontier models with panel data. We also consider an application to the analysis of labour market wage gaps

Extensions of multiple contrast tests

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Simultaneous inference for linear mixed model parameters with an application to small area estimation

Open access financiado por Universite de Geneve (article funding)European Regional Development Fund[Abstract]: Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever clustered, hierarchical or longitudinal data are investigated. Nonetheless, statistical tools for valid simultaneous inference for mixed parameters are rare. This is surprising because one often faces inferential problems beyond the pointwise examination of fixed or mixed parameters. For example, there is an interest in a comparative analysis of cluster-level parameters or subject-specific estimates in studies with repeated measurements. We discuss methods for simultaneous inference assuming a linear mixed model. Specifically, we develop simultaneous prediction intervals as well as multiple testing procedures for mixed parameters. They are useful for joint considerations or comparisons of cluster-level parameters. We employ a consistent bootstrap approximation of the distribution of max-type statistic to construct our tools. The numerical performance of the developed methodology is studied in simulation experiments and illustrated in a data example on household incomes in small areas.Swiss National Science Foundation; 200021-192345,Swiss National Science Foundation; P2GEP2_195898Xunta de Galicia; ED431C 2020/14Ministerio de Ciencia e Innovación; PID2020-113578RB-I00Galician Innovation Agency/ Ministerio de Economía, empleo e industria; COV20/00604Xunta de Galicia; ED431G2019/0

A Groupwise Approach for Inferring Heterogeneous Treatment Effects in Causal Inference

There is a growing literature in nonparametric estimation of the conditional average treatment effect given a specific value of covariates. However, this estimate is often difficult to interpret if covariates are high dimensional and in practice, effect heterogeneity is discussed in terms of subgroups of individuals with similar attributes. The paper propose to study treatment heterogeneity under the groupwise framework. Our method is simple, only based on linear regression and sample splitting, and is semiparametrically efficient under assumptions. We also discuss ways to conduct multiple testing. We conclude by reanalyzing a get-out-the-vote experiment during the 2014 U.S. midterm elections.Comment: 65 pages including supplementary materials, 9 figures, 5 table

Temporal Characteristics of Monoptic, Dichoptic and Half-Binocular Collinear Lateral Masking of Contrast Detection

Purpose: The temporal characteristics of dichoptic contrast integration across space in primary visual cortex are relatively unknown. This study investigated the effect of varying interstimulus interval (ISI) and flank duration on contrast detection threshold (CDT) of a sinusoid target under monoptic, dichoptic and half-binocular viewing. Methods: Eleven subjects with normal vision participated for a mean of 25 hours each. In the main experiment, target and flanks were 3 cpd vertical sinusoids with 6 lambda (sigma = 1.5 lambda) center-to-center vertical separation. Flank contrast was normalized to 3X flank CDT. Flanks were presented at 4 durations (67-500ms) and ISIs were presented at 8 durations (0-2500ms) resulting in 0-3000ms stimulus onset asynchronies (SOA). Target presentations were 250ms to dominant eye using a mirror haploscope and septum. Flanks were presented to dominant (monoptic and half-binocular) and non-dominant eyes (dichoptic and half-binocular). Forward masking was used throughout with a 1-FC detection paradigm and 7-level MOCS. Each target CDT was the product of approximately 700 trials. Results: As expected, simultaneous presentation resulted in CDT facilitation (monoptic = 19%± 3.86% (SE), dichoptic = 13.9%± 4.00%, half-binocular = 18.0%± 4.20%). For all viewing conditions, relative facilitation decreased as SOA increased up to 1000ms. Unexpectedly, dichoptic flanks produced significant CDT suppression (p \u3c 0.05) at 500-1000ms SOAs that was maximal at the 1000ms SOA (9.9%± 5.1%). All viewing conditions approached no effect at the longest SOAs (1500-3000ms). Flank duration had a significantly greater contribution to the overall effect than ISI for monoptic (p \u3c 0.01) and half-binocular (p \u3c 0.05) viewing. Discussion: The collinear CDT facilitation produced by intra-ocular and inter-ocular flanks at shorter SOAs is consistent with lateral connections in primary visual cortex. The temporal aspects of longer SOA, dichoptic CDT suppression observed in this study are consistent with prior studies of illusory contour perception. Conclusion: I propose the novel hypothesis that the CDT suppression produced by dichoptic collinear flanks at longer SOAs is due to one-way, contrast adaptation from lateral propagation that produced the effect of a collinear, illusory contour. This hypothesis was supported by the results of a supplemental, orthogonal flank experiment