scholarly journals Functional response regression model on correlated longitudinal microbiome sequencing data

2021 ◽  
pp. 096228022110616
Author(s):  
Bo Chen ◽  
Wei Xu
Keyword(s):  
Regression Model ◽  
Functional Response ◽  
Type I Error ◽  
Generalized Least Squares ◽  
Functional Regression ◽  
Type I ◽  
Power Performance ◽  
Sequencing Data ◽  
Functional Responses ◽  
Response Data

Functional regression has been widely used on longitudinal data, but it is not clear how to apply functional regression to microbiome sequencing data. We propose a novel functional response regression model analyzing correlated longitudinal microbiome sequencing data, which extends the classic functional response regression model only working for independent functional responses. We derive the theory of generalized least squares estimators for predictors’ effects when functional responses are correlated, and develop a data transformation technique to solve the computational challenge for analyzing correlated functional response data using existing functional regression method. We show by extensive simulations that our proposed method provides unbiased estimations for predictors’ effect, and our model has accurate type I error and power performance for correlated functional response data, compared with classic functional response regression model. Finally we implement our method to a real infant gut microbiome study to evaluate the relationship of clinical factors to predominant taxa along time.

The Robustness of the Likelihood Ratio Chi-Square Test for Structural Equation Models: A Meta-Analysis

2001 ◽  
Vol 26 (1) ◽  
pp. 105-132 ◽  
Author(s):  
Douglas A. Powell ◽  
William D. Schafer
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Type I Error ◽  
Meta Analysis ◽  
Generalized Least Squares ◽  
Error Rates ◽  
Type I ◽  
Chi Square ◽  
Distribution Free ◽  
Projection Techniques

The robustness literature for the structural equation model was synthesized following the method of Harwell which employs meta-analysis as developed by Hedges and Vevea. The study focused on the explanation of empirical Type I error rates for six principal classes of estimators: two that assume multivariate normality (maximum likelihood and generalized least squares), elliptical estimators, two distribution-free estimators (asymptotic and others), and latent projection. Generally, the chi-square tests for overall model fit were found to be sensitive to non-normality and the size of the model for all estimators (with the possible exception of the elliptical estimators with respect to model size and the latent projection techniques with respect to non-normality). The asymptotic distribution-free (ADF) and latent projection techniques were also found to be sensitive to sample sizes. Distribution-free methods other than ADF showed, in general, much less sensitivity to all factors considered.

Effects of Test Level Discrimination and Difficulty on Answer-Copying Indices

2018 ◽  
Vol 7 (1) ◽  
pp. 32
Author(s):  
Onder Sunbul ◽  
Seha Yormaz
Keyword(s):  
Type I Error ◽  
Error Rates ◽  
Type I ◽  
Test Length ◽  
Power Performance ◽  
Detection Rates ◽  
Power Rate ◽  
Test Level ◽  
Answer Copying ◽  
Better Than

In this study Type I Error and the power rates of ω and GBT (generalized binomial test) indices were investigated for several nominal alpha levels and for 40 and 80-item test lengths with 10,000-examinee sample size under several test level restrictions. As a result, Type I error rates of both indices were found to be below the acceptable nominal alpha levels.  The power study showed that average test difficulty was very effective for power (true detection) rates of indices. Clear patterns were observed for the increase of test difficulty in favor of both ω and GBT power rate. Contrary to expectations; average test discrimination was not as effective as average test difficulty. The results of the interaction effects of item discrimination and difficulty showed that for the cases whose b parameters were lower than 0 with weak discrimination, indices had weak power for both ω and GBT. In addition, for the cases whose b parameter levels were below zero with high discrimination indices, the power performance of both answer-copying indices were very weak. Results for test length showed that with the increase of test length the power rate of both ω and GBT tended to increase. Also, ω performed slightly better than GBT or very close to GBT for 80-item test length however, ω performed better than GBT in terms of power rate for the cases with 40-item test length

An optimal kernel-based multivariate U-statistic to test for associations with multiple phenotypes

Biostatistics ◽  
2020 ◽  
Author(s):  
Y Wen ◽  
Qing Lu
Keyword(s):  
Type I Error ◽  
Asymptotic Properties ◽  
Pleiotropic Effect ◽  
Whole Genome Sequencing Data ◽  
Type I ◽  
Test Statistics ◽  
Sequencing Data ◽  
Multiple Phenotypes ◽  
Complex Relationships ◽  
Optimal Kernel

Summary Set-based analysis that jointly considers multiple predictors in a group has been broadly conducted for association tests. However, their power can be sensitive to the distribution of phenotypes, and the underlying relationships between predictors and outcomes. Moreover, most of the set-based methods are designed for single-trait analysis, making it hard to explore the pleiotropic effect and borrow information when multiple phenotypes are available. Here, we propose a kernel-based multivariate U-statistics (KMU) that is robust and powerful in testing the association between a set of predictors and multiple outcomes. We employed a rank-based kernel function for the outcomes, which makes our method robust to various outcome distributions. Rather than selecting a single kernel, our test statistics is built based on multiple kernels selected in a data-driven manner, and thus is capable of capturing various complex relationships between predictors and outcomes. The asymptotic properties of our test statistics have been developed. Through simulations, we have demonstrated that KMU has controlled type I error and higher power than its counterparts. We further showed its practical utility by analyzing a whole genome sequencing data from Alzheimer’s Disease Neuroimaging Initiative study, where novel genes have been detected to be associated with imaging phenotypes.

Functional response of kokanee salmon (Oncorhynchus nerka) to Daphnia at different light levels

2002 ◽  
Vol 59 (4) ◽  
pp. 707-716 ◽  
Author(s):  
Marci L Koski ◽  
Brett M Johnson
Keyword(s):  
Functional Response ◽  
Oncorhynchus Nerka ◽  
Search Time ◽  
Type I ◽  
Type Ii ◽  
Functional Responses ◽  
Foraging Mode ◽  
Kokanee Salmon ◽  
Light Levels ◽  
Type Ii Functional Response

In laboratory experiments, fingerling kokanee salmon (Oncorhynchus nerka, 3–8 g) were presented with varying densities of zooplankton prey (Daphnia spp.) ranging from 3 to 55 Daphnia·L–1, under three light intensities (30, 15, and 0.1 lx). Kokanee exhibited a type I functional response at 0.1 lx (Daphnia consumption·min–1 = 1.74 prey·L–1), a light level typical of moonlit epilimnetic conditions, but shifted to a type II functional response at higher light levels. Both 15 and 30 lx light levels occur during crepuscular periods when kokanee feeding is maximal in the wild, and consumption rates at these light levels were not significantly different (Daphnia consumption·min–1 = (163.6 prey·L–1)(42.2 prey·L–1)–1). The shift from the type I to type II functional response may be attributed to a foraging mode switch and the incorporation of search time instead of random encounters with prey. Using these models to simulate feeding rates in a Colorado reservoir, attenuation of light intensity and prey density between the epilimnion and hypolimnion resulted in a 100-fold increase in predicted feeding duration. Functional responses that incorporate environmental characteristics like light are important components of foraging models that seek to understand fish consumption, growth, and behavior.

scholarly journals An Investigation of Chi-Square and Entropy Based Methods of Item-Fit Using Item Level Contamination in Item Response Theory

2020 ◽  
Vol 18 (2) ◽  
pp. 2-43
Author(s):  
William R. Dardick ◽  
Brandi A. Weiss
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Type I Error ◽  
Type I ◽  
Power Performance ◽  
Empirical Power ◽  
Response Theory ◽  
Chi Square ◽  
Item Fit ◽  
Item Level

New variants of entropy as measures of item-fit in item response theory are investigated. Monte Carlo simulation(s) examine aberrant conditions of item-level misfit to evaluate relative (compare EMRj, X2, G2, S-X2, and PV-Q1) and absolute (Type I error and empirical power) performance. EMRj has utility in discovering misfit.

scholarly journals Effects of Multicollinearity on Type I Error of Some Methods of Detecting Heteroscedasticity in Linear Regression Model

2020 ◽  
Vol 10 (04) ◽  
pp. 664-677
Author(s):  
Olusegun Olatayo Alabi ◽  
Kayode Ayinde ◽  
Omowumi Esther Babalola ◽  
Hamidu Abimbola Bello ◽  
Edward Charles Okon
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Type I Error ◽  
Type I

scholarly journals Integrative analysis of sequencing and array genotype data for discovering disease associations with rare mutations

2015 ◽  
Vol 112 (4) ◽  
pp. 1019-1024 ◽  
Author(s):  
Yi-Juan Hu ◽  
Yun Li ◽  
Paul L. Auer ◽  
Dan-Yu Lin
Keyword(s):  
Type I Error ◽  
Rare Variants ◽  
Extreme Values ◽  
Association Studies ◽  
Cost Effective ◽  
Type I ◽  
Genome Wide Association Studies ◽  
Score Statistic ◽  
Sequencing Data ◽  
Association Tests

In the large cohorts that have been used for genome-wide association studies (GWAS), it is prohibitively expensive to sequence all cohort members. A cost-effective strategy is to sequence subjects with extreme values of quantitative traits or those with specific diseases. By imputing the sequencing data from the GWAS data for the cohort members who are not selected for sequencing, one can dramatically increase the number of subjects with information on rare variants. However, ignoring the uncertainties of imputed rare variants in downstream association analysis will inflate the type I error when sequenced subjects are not a random subset of the GWAS subjects. In this article, we provide a valid and efficient approach to combining observed and imputed data on rare variants. We consider commonly used gene-level association tests, all of which are constructed from the score statistic for assessing the effects of individual variants on the trait of interest. We show that the score statistic based on the observed genotypes for sequenced subjects and the imputed genotypes for nonsequenced subjects is unbiased. We derive a robust variance estimator that reflects the true variability of the score statistic regardless of the sampling scheme and imputation quality, such that the corresponding association tests always have correct type I error. We demonstrate through extensive simulation studies that the proposed tests are substantially more powerful than the use of accurately imputed variants only and the use of sequencing data alone. We provide an application to the Women’s Health Initiative. The relevant software is freely available.

scholarly journals Local Stability Analysis On Lotka-Volterra Predator-Prey Models Functional Responses With Constant prey Refuge

2021 ◽  
Author(s):  
Chongming Li
Keyword(s):  
Stability Analysis ◽  
Functional Response ◽  
Local Stability ◽  
Equilibrium Points ◽  
Saddle Points ◽  
Stable Node ◽  
Type I ◽  
Type Ii ◽  
Functional Responses ◽  
Type Ii Functional Response

The dynamical behaviours of the predators and prey can be described by studying the local stability of the planar systems. Type I functional response shows that the rate of consumption per predator is proportional to prey’s density while type II functional response is related to the situation that predators would reach satiation as they consumed sufficient amount of prey. We seek out a method of using transformation to reduce the number of parameters of original models and then study the stability analysis of equilibrium points. Under suitable restrictions on the new parameters, we prove that the positive interior equilibrium is a stable node for the system of type I and type II functional responses. Moreover, in the case of type II functional response, the boundary equilibria can have more types of stability other than saddle points.

scholarly journals On Robust Association Testing for Quantitative Traits and Rare Variants

2016 ◽  
Vol 6 (12) ◽  
pp. 3941-3950 ◽  
Author(s):  
Peng Wei ◽  
Ying Cao ◽  
Yiwei Zhang ◽  
Zhiyuan Xu ◽  
Il-Youp Kwak ◽  
...  
Keyword(s):  
Type I Error ◽  
Rare Variants ◽  
Error Rates ◽  
Routine Practice ◽  
Type I ◽  
Sequencing Data ◽  
High Data ◽  
Association Testing ◽  
Sequencing Technologies ◽  
Inflated Type

Abstract With the advance of sequencing technologies, it has become a routine practice to test for association between a quantitative trait and a set of rare variants (RVs). While a number of RV association tests have been proposed, there is a dearth of studies on the robustness of RV association testing for nonnormal distributed traits, e.g., due to skewness, which is ubiquitous in cohort studies. By extensive simulations, we demonstrate that commonly used RV tests, including sequence kernel association test (SKAT) and optimal unified SKAT (SKAT-O), are not robust to heavy-tailed or right-skewed trait distributions with inflated type I error rates; in contrast, the adaptive sum of powered score (aSPU) test is much more robust. Here we further propose a robust version of the aSPU test, called aSPUr. We conduct extensive simulations to evaluate the power of the tests, finding that for a larger number of RVs, aSPU is often more powerful than SKAT and SKAT-O, owing to its high data-adaptivity. We also compare different tests by conducting association analysis of triglyceride levels using the NHLBI ESP whole-exome sequencing data. The QQ plots for SKAT and SKAT-O were severely inflated (λ = 1.89 and 1.78, respectively), while those for aSPU and aSPUr behaved normally. Due to its relatively high robustness to outliers and high power of the aSPU test, we recommend its use complementary to SKAT and SKAT-O. If there is evidence of inflated type I error rate from the aSPU test, we would recommend the use of the more robust, but less powerful, aSPUr test.

scholarly journals Exploiting Family History in Aggregation Unit-based Genetic Association Tests

2021 ◽  
Author(s):  
Yanbing Wang ◽  
Han Chen ◽  
Gina Marie Peloso ◽  
Anita DeStefano ◽  
Josee Dupuis
Keyword(s):  
Family History ◽  
Association Analysis ◽  
Type I Error ◽  
Threshold Model ◽  
Disease Status ◽  
Case Control ◽  
Type I ◽  
Sequencing Data ◽  
Genotype Information ◽  
Conventional Methods

The development of sequencing technology calls for new powerful methods to detect disease associations and lower the cost of sequencing studies. Family history (FH) contains information on disease status of relatives, adding valuable information about the health problems and risk of diseases in probands. Incorporating data from FH is a cost-effective way to improve statistical evidence in genetic studies, and moreover, overcomes limitations in study designs with insufficient cases or missing genotype information for association analysis. We proposed family history aggregation unit-based test (FHAT) and optimal FHAT (FHAT-O) to exploit available FH for rare variant association analysis. Moreover, we extended liability threshold model of case-control status and FH (LT-FH) method in aggregated unit-based methods and compared that with FHAT and FHAT-O. The computational efficiency and flexibility of the FHAT and FHAT-O were demonstrated through both simulations and applications. We showed that FHAT, FHAT-O and LT-FH method offer reasonable control of the type I error unless case/control ratio is extremely unbalanced, in which case they result in smaller inflation than that observed with conventional methods excluding FH. We also demonstrated that FHAT and FHAT-O are more powerful than LT-FH method and conventional methods in many scenarios. By applying FHAT and FHAT-O to the analysis of all cause dementia and hypertension using the exome sequencing data from the UK Biobank, we showed that our methods can improve significance for known regions. Furthermore, we replicated the previous associations in all cause dementia and hypertension and detected novel regions through the exome-wide analysis.

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