Gene‐Based Association Analysis for Censored Traits Via Fixed Effect Functional Regressions

Genetic studies of survival outcomes have been proposed and conducted recently, but statistical methods for identifying genetic variants that affect disease progression are rarely developed. Motivated by our ongoing real studies, here we develop Cox proportional hazard models using functional regression (FR) to perform gene‐based association analysis of survival traits while adjusting for covariates. The proposed Cox models are fixed effect models where the genetic effects of multiple genetic variants are assumed to be fixed. We introduce likelihood ratio test (LRT) statistics to test for associations between the survival traits and multiple genetic variants in a genetic region. Extensive simulation studies demonstrate that the proposed Cox RF LRT statistics have well‐controlled type I error rates. To evaluate power, we compare the Cox FR LRT with the previously developed burden test (BT) in a Cox model and sequence kernel association test (SKAT), which is based on mixed effect Cox models. The Cox FR LRT statistics have higher power than or similar power as Cox SKAT LRT except when 50%/50% causal variants had negative/positive effects and all causal variants are rare. In addition, the Cox FR LRT statistics have higher power than Cox BT LRT. The models and related test statistics can be useful in the whole genome and whole exome association studies. An age‐related macular degeneration dataset was analyzed as an example.

[1]  M. Boehnke,et al.  Meta-analysis of Complex Diseases at Gene Level with Generalized Functional Linear Models , 2015, Genetics.

[2]  Momiao Xiong,et al.  Genome-wide gene–gene interaction analysis for next-generation sequencing , 2015, European Journal of Human Genetics.

[3]  Wei Chen,et al.  Gene Level Meta-Analysis of Quantitative Traits by Functional Linear Models , 2015, Genetics.

[4]  Momiao Xiong,et al.  Pleiotropy Analysis of Quantitative Traits at Gene Level by Multivariate Functional Linear Models , 2015, Genetic epidemiology.

[5]  Alexander F. Wilson,et al.  Generalized Functional Linear Models for Gene‐Based Case‐Control Association Studies , 2014, Genetic epidemiology.

[6]  Qing Lu,et al.  Functional Analysis of Variance for Association Studies , 2014, PloS one.

[7]  Momiao Xiong,et al.  Epistasis analysis for quantitative traits by functional regression model , 2014, Genome research.

[8]  Thomas Lumley,et al.  Sequence Kernel Association Test for Survival Traits , 2014, Genetic epidemiology.

[9]  Momiao Xiong,et al.  Functional Linear Models for Association Analysis of Quantitative Traits , 2013, Genetic epidemiology.

[10]  Gabriëlle H S Buitendijk,et al.  Seven New Loci Associated with Age-Related Macular Degeneration , 2013, Nature Genetics.

[11]  M. Rieder,et al.  Optimal unified approach for rare-variant association testing with application to small-sample case-control whole-exome sequencing studies. , 2012, American journal of human genetics.

[12]  Momiao Xiong,et al.  Quantitative trait locus analysis for next-generation sequencing with the functional linear models , 2012, Journal of Medical Genetics.

[13]  Momiao Xiong,et al.  Smoothed functional principal component analysis for testing association of the entire allelic spectrum of genetic variation , 2012, European Journal of Human Genetics.

[14]  R. Kay The Analysis of Survival Data , 2012 .

[15]  Piotr Kokoszka,et al.  Inference for Functional Data with Applications , 2012 .

[16]  Xihong Lin,et al.  Kernel machine SNP‐set analysis for censored survival outcomes in genome‐wide association studies , 2011, Genetic epidemiology.

[17]  Tianxi Cai,et al.  Kernel Machine Approach to Testing the Significance of Multiple Genetic Markers for Risk Prediction , 2011, Biometrics.

[18]  Momiao Xiong,et al.  Association studies for next-generation sequencing. , 2011, Genome research.

[19]  F. Ferraty,et al.  The Oxford Handbook of Functional Data Analysis , 2011, Oxford Handbooks Online.

[20]  H. Hakonarson,et al.  ANNOVAR: functional annotation of genetic variants from high-throughput sequencing data , 2010, Nucleic acids research.

[21]  E. Zeggini,et al.  An Evaluation of Statistical Approaches to Rare Variant Analysis in Genetic Association Studies , 2009, Genetic epidemiology.

[22]  S. Browning,et al.  A Groupwise Association Test for Rare Mutations Using a Weighted Sum Statistic , 2009, PLoS genetics.

[23]  S. Leal,et al.  Methods for detecting associations with rare variants for common diseases: application to analysis of sequence data. , 2008, American journal of human genetics.

[24]  Zhaohui S. Qin,et al.  A second generation human haplotype map of over 3.1 million SNPs , 2007, Nature.

[25]  B. Rosner,et al.  Association of CFH Y402H and LOC387715 A69S with progression of age-related macular degeneration. , 2007, JAMA.

[26]  S. Gabriel,et al.  Calibrating a coalescent simulation of human genome sequence variation. , 2005, Genome research.

[27]  Ralf Bender,et al.  Generating survival times to simulate Cox proportional hazards models , 2005, Statistics in medicine.

[28]  George A. Williams,et al.  The Age-Related Eye Disease Study (AREDS): design implications. AREDS report no. 1. , 1999, Controlled clinical trials.

[29]  Jim Freeman,et al.  Stochastic Processes (Second Edition) , 1996 .

[30]  Marie Frei,et al.  Functional Data Analysis With R And Matlab , 2016 .

[31]  Ivana K. Kim,et al.  A large genome-wide association study of age-related macular degeneration highlights contributions of rare and common variants , 2015, Nature Genetics.

[32]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[33]  R. Fisher XV.—The Correlation between Relatives on the Supposition of Mendelian Inheritance. , 1919, Transactions of the Royal Society of Edinburgh.

[34]  L. Penrose,et al.  THE CORRELATION BETWEEN RELATIVES ON THE SUPPOSITION OF MENDELIAN INHERITANCE , 2022 .