Biomaterial Database

On testing an unspecified function through a linear mixed effects model with multiple variance components. 2012

Yuanjia Wang, and Huaihou Chen

Department of Biostatistics, Mailman School of Public Health, Columbia University, New York, NY 10032, USA. yuanjia.wang@columbia.edu

We examine a generalized F-test of a nonparametric function through penalized splines and a linear mixed effects model representation. With a mixed effects model representation of penalized splines, we imbed the test of an unspecified function into a test of some fixed effects and a variance component in a linear mixed effects model with nuisance variance components under the null. The procedure can be used to test a nonparametric function or varying-coefficient with clustered data, compare two spline functions, test the significance of an unspecified function in an additive model with multiple components, and test a row or a column effect in a two-way analysis of variance model. Through a spectral decomposition of the residual sum of squares, we provide a fast algorithm for computing the null distribution of the test, which significantly improves the computational efficiency over bootstrap. The spectral representation reveals a connection between the likelihood ratio test (LRT) in a multiple variance components model and a single component model. We examine our methods through simulations, where we show that the power of the generalized F-test may be higher than the LRT, depending on the hypothesis of interest and the true model under the alternative. We apply these methods to compute the genome-wide critical value and p-value of a genetic association test in a genome-wide association study (GWAS), where the usual bootstrap is computationally intensive (up to 10(8) simulations) and asymptotic approximation may be unreliable and conservative.

UI	MeSH Term	Description	Entries
D002318	Cardiovascular Diseases	Pathological conditions involving the CARDIOVASCULAR SYSTEM including the HEART; the BLOOD VESSELS; or the PERICARDIUM.	Adverse Cardiac Event,Cardiac Events,Major Adverse Cardiac Events,Adverse Cardiac Events,Cardiac Event,Cardiac Event, Adverse,Cardiac Events, Adverse,Cardiovascular Disease,Disease, Cardiovascular,Event, Cardiac
D002874	Chromosome Mapping	Any method used for determining the location of and relative distances between genes on a chromosome.	Gene Mapping,Linkage Mapping,Genome Mapping,Chromosome Mappings,Gene Mappings,Genome Mappings,Linkage Mappings,Mapping, Chromosome,Mapping, Gene,Mapping, Genome,Mapping, Linkage,Mappings, Chromosome,Mappings, Gene,Mappings, Genome,Mappings, Linkage
D003198	Computer Simulation	Computer-based representation of physical systems and phenomena such as chemical processes.	Computational Modeling,Computational Modelling,Computer Models,In silico Modeling,In silico Models,In silico Simulation,Models, Computer,Computerized Models,Computer Model,Computer Simulations,Computerized Model,In silico Model,Model, Computer,Model, Computerized,Model, In silico,Modeling, Computational,Modeling, In silico,Modelling, Computational,Simulation, Computer,Simulation, In silico,Simulations, Computer
D003627	Data Interpretation, Statistical	Application of statistical procedures to analyze specific observed or assumed facts from a particular study.	Data Analysis, Statistical,Data Interpretations, Statistical,Interpretation, Statistical Data,Statistical Data Analysis,Statistical Data Interpretation,Analyses, Statistical Data,Analysis, Statistical Data,Data Analyses, Statistical,Interpretations, Statistical Data,Statistical Data Analyses,Statistical Data Interpretations
D004812	Epidemiologic Methods	Research techniques that focus on study designs and data gathering methods in human and animal populations.	Epidemiologic Method,Epidemiological Methods,Methods, Epidemiologic,Epidemiological Method,Method, Epidemiologic,Method, Epidemiological,Methods, Epidemiological
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000465	Algorithms	A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.	Algorithm
D000704	Analysis of Variance	A statistical technique that isolates and assesses the contributions of categorical independent variables to variation in the mean of a continuous dependent variable.	ANOVA,Analysis, Variance,Variance Analysis,Analyses, Variance,Variance Analyses
D015994	Incidence	The number of new cases of a given disease during a given period in a specified population. It also is used for the rate at which new events occur in a defined population. It is differentiated from PREVALENCE, which refers to all cases in the population at a given time.	Attack Rate,Cumulative Incidence,Incidence Proportion,Incidence Rate,Person-time Rate,Secondary Attack Rate,Attack Rate, Secondary,Attack Rates,Cumulative Incidences,Incidence Proportions,Incidence Rates,Incidence, Cumulative,Incidences,Person time Rate,Person-time Rates,Proportion, Incidence,Rate, Attack,Rate, Incidence,Rate, Person-time,Rate, Secondary Attack,Secondary Attack Rates
D016014	Linear Models	Statistical models in which the value of a parameter for a given value of a factor is assumed to be equal to a + bx, where a and b are constants. The models predict a linear regression.	Linear Regression,Log-Linear Models,Models, Linear,Linear Model,Linear Regressions,Log Linear Models,Log-Linear Model,Model, Linear,Model, Log-Linear,Models, Log-Linear,Regression, Linear,Regressions, Linear