Estimating Variance Components in Functional Linear Models With Applications to Genetic Heritability

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Quantifying heritability is the first step in understanding the contribution of genetic variation to the risk architecture of complex human diseases and traits. Heritability can be estimated for univariate phenotypes from nonfamily data using linear mixed effects models. There is, however, no fully developed methodology for defining or estimating heritability from longitudinal studies. By examining longitudinal studies, researchers have the opportunity to better understand the genetic influence on the temporal development of diseases, which can be vital for populations with rapidly changing phenotypes such as children or the elderly. To define and estimate heritability for longitudinally measured phenotypes, we present a framework based on functional data analysis, FDA. While our procedures have important genetic consequences, they also represent a substantial development for FDA. In particular, we present a very general methodology for constructing optimal, unbiased estimates of variance components in functional linear models. Such a problem is challenging as likelihoods and densities do not readily generalize to infinite-dimensional settings. Our procedure can be viewed as a functional generalization of the minimum norm quadratic unbiased estimation procedure, MINQUE, presented by C. R. Rao, and is equivalent to residual maximum likelihood, REML, in univariate settings. We apply our methodology to the Childhood Asthma Management Program, CAMP, a 4-year longitudinal study examining the long term effects of daily asthma medications on children.

Original languageEnglish (US)
Pages (from-to)407-422
Number of pages16
JournalJournal of the American Statistical Association
Volume111
Issue number513
DOIs
StatePublished - Jan 2 2016

Fingerprint

Functional Linear Model
Heritability
Variance Components
Longitudinal Study
Phenotype
Asthma
Univariate
Methodology
MINQUE
Residual Maximum Likelihood
Linear Mixed Effects Model
Functional Data Analysis
Restricted Maximum Likelihood
Unbiased Estimation
Components of Variance
Genetic Variation
Estimate
Likelihood
Norm
Generalise

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

@article{b79e29cc0d504e39a5fe9c10b8546fdc,
title = "Estimating Variance Components in Functional Linear Models With Applications to Genetic Heritability",
abstract = "Quantifying heritability is the first step in understanding the contribution of genetic variation to the risk architecture of complex human diseases and traits. Heritability can be estimated for univariate phenotypes from nonfamily data using linear mixed effects models. There is, however, no fully developed methodology for defining or estimating heritability from longitudinal studies. By examining longitudinal studies, researchers have the opportunity to better understand the genetic influence on the temporal development of diseases, which can be vital for populations with rapidly changing phenotypes such as children or the elderly. To define and estimate heritability for longitudinally measured phenotypes, we present a framework based on functional data analysis, FDA. While our procedures have important genetic consequences, they also represent a substantial development for FDA. In particular, we present a very general methodology for constructing optimal, unbiased estimates of variance components in functional linear models. Such a problem is challenging as likelihoods and densities do not readily generalize to infinite-dimensional settings. Our procedure can be viewed as a functional generalization of the minimum norm quadratic unbiased estimation procedure, MINQUE, presented by C. R. Rao, and is equivalent to residual maximum likelihood, REML, in univariate settings. We apply our methodology to the Childhood Asthma Management Program, CAMP, a 4-year longitudinal study examining the long term effects of daily asthma medications on children.",
author = "Reimherr, {Matthew Logan} and Dan Nicolae",
year = "2016",
month = "1",
day = "2",
doi = "10.1080/01621459.2015.1016224",
language = "English (US)",
volume = "111",
pages = "407--422",
journal = "Journal of the American Statistical Association",
issn = "0162-1459",
publisher = "Taylor and Francis Ltd.",
number = "513",

}

Estimating Variance Components in Functional Linear Models With Applications to Genetic Heritability. / Reimherr, Matthew Logan; Nicolae, Dan.

In: Journal of the American Statistical Association, Vol. 111, No. 513, 02.01.2016, p. 407-422.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Estimating Variance Components in Functional Linear Models With Applications to Genetic Heritability

AU - Reimherr, Matthew Logan

AU - Nicolae, Dan

PY - 2016/1/2

Y1 - 2016/1/2

N2 - Quantifying heritability is the first step in understanding the contribution of genetic variation to the risk architecture of complex human diseases and traits. Heritability can be estimated for univariate phenotypes from nonfamily data using linear mixed effects models. There is, however, no fully developed methodology for defining or estimating heritability from longitudinal studies. By examining longitudinal studies, researchers have the opportunity to better understand the genetic influence on the temporal development of diseases, which can be vital for populations with rapidly changing phenotypes such as children or the elderly. To define and estimate heritability for longitudinally measured phenotypes, we present a framework based on functional data analysis, FDA. While our procedures have important genetic consequences, they also represent a substantial development for FDA. In particular, we present a very general methodology for constructing optimal, unbiased estimates of variance components in functional linear models. Such a problem is challenging as likelihoods and densities do not readily generalize to infinite-dimensional settings. Our procedure can be viewed as a functional generalization of the minimum norm quadratic unbiased estimation procedure, MINQUE, presented by C. R. Rao, and is equivalent to residual maximum likelihood, REML, in univariate settings. We apply our methodology to the Childhood Asthma Management Program, CAMP, a 4-year longitudinal study examining the long term effects of daily asthma medications on children.

AB - Quantifying heritability is the first step in understanding the contribution of genetic variation to the risk architecture of complex human diseases and traits. Heritability can be estimated for univariate phenotypes from nonfamily data using linear mixed effects models. There is, however, no fully developed methodology for defining or estimating heritability from longitudinal studies. By examining longitudinal studies, researchers have the opportunity to better understand the genetic influence on the temporal development of diseases, which can be vital for populations with rapidly changing phenotypes such as children or the elderly. To define and estimate heritability for longitudinally measured phenotypes, we present a framework based on functional data analysis, FDA. While our procedures have important genetic consequences, they also represent a substantial development for FDA. In particular, we present a very general methodology for constructing optimal, unbiased estimates of variance components in functional linear models. Such a problem is challenging as likelihoods and densities do not readily generalize to infinite-dimensional settings. Our procedure can be viewed as a functional generalization of the minimum norm quadratic unbiased estimation procedure, MINQUE, presented by C. R. Rao, and is equivalent to residual maximum likelihood, REML, in univariate settings. We apply our methodology to the Childhood Asthma Management Program, CAMP, a 4-year longitudinal study examining the long term effects of daily asthma medications on children.

UR - http://www.scopus.com/inward/record.url?scp=84969844589&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84969844589&partnerID=8YFLogxK

U2 - 10.1080/01621459.2015.1016224

DO - 10.1080/01621459.2015.1016224

M3 - Article

AN - SCOPUS:84969844589

VL - 111

SP - 407

EP - 422

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 513

ER -