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A Simulation Study of Bootstrap Approaches to Estimate Confidence Intervals in DeFries-Fulker Regression Models (with Application to the Heritability of BMI Changes in the NLSY).

ABSTRACT: The univariate bootstrap is a relatively recently developed version of the bootstrap (Lee and Rodgers in Psychol Methods 3(1): 91, 1998). DeFries-Fulker (DF) analysis is a regression model used to estimate parameters in behavioral genetic models (DeFries and Fulker in Behav Genet 15(5): 467-473, 1985). It is appealing for its simplicity; however, it violates certain regression assumptions such as homogeneity of variance and independence of errors that make calculation of standard errors and confidence intervals problematic. Methods have been developed to account for these issues (Kohler and Rodgers in Behav Genet 31(2): 179-191, 2001), however the univariate bootstrap represents a unique means of doing so that is presaged by suggestions from previous DF research (e.g., Cherny et al. in Behav Genet 22(2): 153-162, 1992). In the present study we use simulations to examine the performance of the univariate bootstrap in the context of DF analysis. We compare a number of possible bootstrap schemes as well as more traditional confidence interval methods. We follow up with an empirical demonstration, applying results of the simulation to models estimated to investigate changes in body mass index in adults from the National Longitudinal Survey of Youth 1979 data.

SUBMITTER: O'Keefe P

PROVIDER: S-EPMC7065829 | biostudies-literature | 2020 Mar

REPOSITORIES: biostudies-literature

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A Simulation Study of Bootstrap Approaches to Estimate Confidence Intervals in DeFries-Fulker Regression Models (with Application to the Heritability of BMI Changes in the NLSY).

O'Keefe Patrick P Rodgers Joseph Lee JL

Behavior genetics 20200210 2

The univariate bootstrap is a relatively recently developed version of the bootstrap (Lee and Rodgers in Psychol Methods 3(1): 91, 1998). DeFries-Fulker (DF) analysis is a regression model used to estimate parameters in behavioral genetic models (DeFries and Fulker in Behav Genet 15(5): 467-473, 1985). It is appealing for its simplicity; however, it violates certain regression assumptions such as homogeneity of variance and independence of errors that make calculation of standard errors and conf ...[more]

PMID: 32040643

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Project description:In many scientific studies, the underlying data-generating process is unknown and multiple statistical models are considered to describe it. For example, in a factorial experiment we might consider models involving just main effects, as well as those that include interactions. Model-averaging is a commonly-used statistical technique to allow for model uncertainty in parameter estimation. In the frequentist setting, the model-averaged estimate of a parameter is a weighted mean of the estimates from the individual models, with the weights typically being based on an information criterion, cross-validation, or bootstrapping. One approach to building a model-averaged confidence interval is to use a Wald interval, based on the model-averaged estimate and its standard error. This has been the default method in many application areas, particularly those in the life sciences. The MA-Wald interval, however, assumes that the studentized model-averaged estimate has a normal distribution, which can be far from true in practice due to the random, data-driven model weights. Recently, the model-averaged tail area Wald interval (MATA-Wald) has been proposed as an alternative to the MA-Wald interval, which only assumes that the studentized estimate from each model has a N(0, 1) or t-distribution, when that model is true. This alternative to the MA-Wald interval has been shown to have better coverage in simulation studies. However, when we have a response variable that is skewed, even these relaxed assumptions may not be valid, and use of these intervals might therefore result in poor coverage. We propose a new interval (MATA-SBoot) which uses a parametric bootstrap approach to estimate the distribution of the studentized estimate for each model, when that model is true. This method only requires that the studentized estimate from each model is approximately pivotal, an assumption that will often be true in practice, even for skewed data. We illustrate use of this new interval in the analysis of a three-factor marine global change experiment in which the response variable is assumed to have a lognormal distribution. We also perform a simulation study, based on the example, to compare the lower and upper error rates of this interval with those for existing methods. The results suggest that the MATA-SBoot interval can provide better error rates than existing intervals when we have skewed data, particularly for the upper error rate when the sample size is small.

Project description:The goal of expression quantitative trait loci (eQTL) studies is to identify the genetic variants that influence the expression levels of the genes in an organism. High throughput technology has made such studies possible: in a given tissue sample, it enables us to quantify the expression levels of approximately 20 000 genes and to record the alleles present at millions of genetic polymorphisms. While obtaining this data is relatively cheap once a specimen is at hand, obtaining human tissue remains a costly endeavor: eQTL studies continue to be based on relatively small sample sizes, with this limitation particularly serious for tissues as brain, liver, etc.-often the organs of most immediate medical relevance. Given the high-dimensional nature of these datasets and the large number of hypotheses tested, the scientific community has adopted early on multiplicity adjustment procedures. These testing procedures primarily control the false discoveries rate for the identification of genetic variants with influence on the expression levels. In contrast, a problem that has not received much attention to date is that of providing estimates of the effect sizes associated with these variants, in a way that accounts for the considerable amount of selection. Yet, given the difficulty of procuring additional samples, this challenge is of practical importance. We illustrate in this work how the recently developed conditional inference approach can be deployed to obtain confidence intervals for the eQTL effect sizes with reliable coverage. The procedure we propose is based on a randomized hierarchical strategy with a 2-fold contribution: (1) it reflects the selection steps typically adopted in state of the art investigations and (2) it introduces the use of randomness instead of data-splitting to maximize the use of available data. Analysis of the GTEx Liver dataset (v6) suggests that naively obtained confidence intervals would likely not cover the true values of effect sizes and that the number of local genetic polymorphisms influencing the expression level of genes might be underestimated.

Dataset Information

A Simulation Study of Bootstrap Approaches to Estimate Confidence Intervals in DeFries-Fulker Regression Models (with Application to the Heritability of BMI Changes in the NLSY).

Publications

A Simulation Study of Bootstrap Approaches to Estimate Confidence Intervals in DeFries-Fulker Regression Models (with Application to the Heritability of BMI Changes in the NLSY).

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