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Parametric and semiparametric mixture models have been widely used in applications from many areas, and it is often of interest to test the homogeneity in these models. However, hypothesis testing is non standard due to the fact that several regularity conditions do not hold under the null hypothesis. We consider a semiparametric mixture case–control model, in the sense that the density ratio of two distributions is assumed to be of an exponential form, while the baseline density is unspecified. This model was first considered by Qin and Liang (2011, biometrics), and they proposed a modified score statistic for testing homogeneity. In this article, we consider alternative testing procedures based on supremum statistics, which could improve power against certain types of alternatives. We demonstrate the connection and comparison among the proposed and existing approaches. In addition, we provide a unified theoretical justification of the supremum test and other existing test statistics from an empirical likelihood perspective. The finite-sample performance of the supremum test statistics was evaluated in simulation studies. [ABSTRACT FROM AUTHOR]

Functional data arise frequently in biomedical studies, where it is often of interest to investigate the association between functional predictors and a scalar response variable. While functional linear models (FLM) are widely used to address these questions, hypothesis testing for the functional association in the FLM framework remains challenging. A popular approach to testing the functional effects is through dimension reduction by functional principal component (PC) analysis. However, its power performance depends on the choice of the number of PCs, and is not systematically studied. In this article, we first investigate the power performance of the Wald-type test with varying thresholds in selecting the number of PCs for the functional covariates, and show that the power is sensitive to the choice of thresholds. To circumvent the issue, we propose a new method of ordering and selecting principal components to construct test statistics. The proposed method takes into account both the association with the response and the variation along each eigenfunction. We establish its theoretical properties and assess the finite sample properties through simulations. Our simulation results show that the proposed test is more robust against the choice of threshold while being as powerful as, and often more powerful than, the existing method. We then apply the proposed method to the cerebral white matter tracts data obtained from a diffusion tensor imaging tractography study. [ABSTRACT FROM AUTHOR]

Summary We consider likelihood ratio tests (LRT) and their modifications for homogeneity in admixture models. The admixture model is a two-component mixture model, where one component is indexed by an unknown parameter while the parameter value for the other component is known. This model is widely used in genetic linkage analysis under heterogeneity in which the kernel distribution is binomial. For such models, it is long recognized that testing for homogeneity is nonstandard, and the LRT statistic does not converge to a conventional χ2 distribution. In this article, we investigate the asymptotic behavior of the LRT for general admixture models and show that its limiting distribution is equivalent to the supremum of a squared Gaussian process. We also discuss the connection and comparison between LRT and alternative approaches such as modifications of LRT and score tests, including the modified LRT (, Statistica Sinica 16, 805-823). The LRT is an omnibus test that is powerful to detect general alternative hypotheses. In contrast, alternative approaches may be slightly more powerful to detect certain type of alternatives, but much less powerful for others. Our results are illustrated by simulation studies and an application to a genetic linkage study of schizophrenia. [ABSTRACT FROM AUTHOR]

Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well if the data exhibits heavy‐tailedness or outliers. To address this challenge, a new robust FPCA approach based on a functional pairwise spatial sign (PASS) operator, termed PASS FPCA, is introduced. We propose robust estimation procedures for eigenfunctions and eigenvalues. Theoretical properties of the PASS operator are established, showing that it adopts the same eigenfunctions as the standard covariance operator and also allows recovering ratios between eigenvalues. We also extend the proposed procedure to handle functional data measured with noise. Compared to existing robust FPCA approaches, the proposed PASS FPCA requires weaker distributional assumptions to conserve the eigenspace of the covariance function. Specifically, existing work are often built upon a class of functional elliptical distributions, which requires inherently symmetry. In contrast, we introduce a class of distributions called the weakly functional coordinate symmetry (weakly FCS), which allows for severe asymmetry and is much more flexible than the functional elliptical distribution family. The robustness of the PASS FPCA is demonstrated via extensive simulation studies, especially its advantages in scenarios with nonelliptical distributions. The proposed method was motivated by and applied to analysis of accelerometry data from the Objective Physical Activity and Cardiovascular Health Study, a large‐scale epidemiological study to investigate the relationship between objectively measured physical activity and cardiovascular health among older women. [ABSTRACT FROM AUTHOR]

To study disease association with risk factors in epidemiologic studies, cross-sectional sampling is often more focused and less costly for recruiting study subjects who have already experienced initiating events. For time-to-event outcome, however, such a sampling strategy may be length biased. Coupled with censoring, analysis of length-biased data can be quite challenging, due to induced informative censoring in which the survival time and censoring time are correlated through a common backward recurrence time. We propose to use the proportional mean residual life model of Oakes & Dasu (Biometrika 77, 409–10, 1990) for analysis of censored length-biased survival data. Several nonstandard data structures, including censoring of onset time and cross-sectional data without follow-up, can also be handled by the proposed methodology. [ABSTRACT FROM PUBLISHER]

The development of next-generation sequencing technologies has allowed researchers to study comprehensively the contribution of genetic variation particularly rare variants to complex diseases. To date many sequencing analyses of rare variants have focused on marginal genetic effects and have not explored the potential role environmental factors play in modifying genetic risk. Analysis of gene-environment interaction (GxE) for rare variants poses considerable challenges because of variant rarity and paucity of subjects who carry the variants while being exposed. To tackle this challenge, we propose a hierarchical model to jointly assess the GxE effects of a set of rare variants for example, in a gene or regulatory region, leveraging the information across the variants. Under this model, GxE is modeled by two components. The first component incorporates variant functional information as weights to calculate the weighted burden of variant alleles across variants, and then assess their GxE interaction with the environmental factor. Since this information is a priori known, this component is fixed effects in the model. The second component involves residual GxE effects that have not been accounted for by the fixed effects. In this component, the residual GxE effects are postulated to follow an unspecified distribution with mean 0 and variance [Formula: see text] We develop a novel testing procedure by deriving two independent score statistics for the fixed effects and the variance component separately. We propose two data-adaptive combination approaches for combining these two score statistics and establish the asymptotic distributions. An extensive simulation study shows that the proposed approaches maintain the correct type I error and the power is comparable to or better than existing methods under a wide range of scenarios. Finally we illustrate the proposed methods by a exome-wide GxE analysis with NSAIDs use in colorectal cancer. [ABSTRACT FROM AUTHOR]