Dataset Information

Statistical distributions of test statistics used for quantitative trait association mapping in structured populations.

ABSTRACT:

Background

Spurious associations between single nucleotide polymorphisms and phenotypes are a major issue in genome-wide association studies and have led to underestimation of type 1 error rate and overestimation of the number of quantitative trait loci found. Many authors have investigated the influence of population structure on the robustness of methods by simulation. This paper is aimed at developing further the algebraic formalization of power and type 1 error rate for some of the classical statistical methods used: simple regression, two approximate methods of mixed models involving the effect of a single nucleotide polymorphism (SNP) and a random polygenic effect (GRAMMAR and FASTA) and the transmission/disequilibrium test for quantitative traits and nuclear families. Analytical formulae were derived using matrix algebra for the first and second moments of the statistical tests, assuming a true mixed model with a polygenic effect and SNP effects.

Results

The expectation and variance of the test statistics and their marginal expectations and variances according to the distribution of genotypes and estimators of variance components are given as a function of the relationship matrix and of the heritability of the polygenic effect. These formulae were used to compute type 1 error rate and power for any kind of relationship matrix between phenotyped and genotyped individuals for any level of heritability. For the regression method, type 1 error rate increased with the variability of relationships and with heritability, but decreased with the GRAMMAR method and was not affected with the FASTA and quantitative transmission/disequilibrium test methods.

Conclusions

The formulae can be easily used to provide the correct threshold of type 1 error rate and to calculate the power when designing experiments or data collection protocols. The results concerning the efficacy of each method agree with simulation results in the literature but were generalized in this work. The power of the GRAMMAR method was equal to the power of the FASTA method at the same type 1 error rate. The power of the quantitative transmission/disequilibrium test was low. In conclusion, the FASTA method, which is very close to the full mixed model, is recommended in association mapping studies.

SUBMITTER: Teyssedre S

PROVIDER: S-EPMC3817592 | biostudies-literature | 2012 Nov

REPOSITORIES: biostudies-literature

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Publications

Statistical distributions of test statistics used for quantitative trait association mapping in structured populations.

Teyssèdre Simon S Elsen Jean-Michel JM Ricard Anne A

Genetics, selection, evolution : GSE 20121112

<h4>Background</h4>Spurious associations between single nucleotide polymorphisms and phenotypes are a major issue in genome-wide association studies and have led to underestimation of type 1 error rate and overestimation of the number of quantitative trait loci found. Many authors have investigated the influence of population structure on the robustness of methods by simulation. This paper is aimed at developing further the algebraic formalization of power and type 1 error rate for some of the c ...[more]

PMID: 23146127

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Project description:BackgroundWe introduce a QTL-mapping algorithm based on Statistical Machine Learning (SML) that is conceptually quite different to existing methods as there is a strong focus on generalisation ability. Our approach combines ridge regression, recursive feature elimination, and estimation of generalisation performance and marker effects using bootstrap resampling. Model performance and marker effects are determined using independent testing samples (individuals), thus providing better estimates. We compare the performance of SML against Composite Interval Mapping (CIM), Bayesian Interval Mapping (BIM) and single Marker Regression (MR) on synthetic datasets and a multi-trait and multi-environment dataset of the progeny for a cross between two barley cultivars.ResultsIn an analysis of the synthetic datasets, SML accurately predicted the number of QTL underlying a trait while BIM tended to underestimate the number of QTL. The QTL identified by SML for the barley dataset broadly coincided with known QTL locations. SML reported approximately half of the QTL reported by either CIM or MR, not unexpected given that neither CIM nor MR incorporates independent testing. The latter makes these two methods susceptible to producing overly optimistic estimates of QTL effects, as we demonstrate for MR. The QTL resolution (peak definition) afforded by SML was consistently superior to MR, CIM and BIM, with QTL detection power similar to BIM. The precision of SML was underscored by repeatedly identifying, at < or = 1-cM precision, three QTL for four partially related traits (heading date, plant height, lodging and yield). The set of QTL obtained using a 'raw' and a 'curated' version of the same genotypic dataset were more similar to each other for SML than for CIM or MR.ConclusionThe SML algorithm produces better estimates of QTL effects because it eliminates the optimistic bias in the predictive performance of other QTL methods. It produces narrower peaks than other methods (except BIM) and hence identifies QTL with greater precision. It is more robust to genotyping and linkage mapping errors, and identifies markers linked to QTL in the absence of a genetic map.

Project description:BackgroundSingle nucleotide polymorphisms (SNPs) which capture a significant impact on a trait can be identified with genome-wide association studies. High linkage disequilibrium (LD) among SNPs makes it difficult to identify causative variants correctly. Thus, often target regions instead of single SNPs are reported. Sample size has not only a crucial impact on the precision of parameter estimates, it also ensures that a desired level of statistical power can be reached. We study the design of experiments for fine-mapping of signals of a quantitative trait locus in such a target region.MethodsA multi-locus model allows to identify causative variants simultaneously, to state their positions more precisely and to account for existing dependencies. Based on the commonly applied SNP-BLUP approach, we determine the z-score statistic for locally testing non-zero SNP effects and investigate its distribution under the alternative hypothesis. This quantity employs the theoretical instead of observed dependence between SNPs; it can be set up as a function of paternal and maternal LD for any given population structure.ResultsWe simulated multiple paternal half-sib families and considered a target region of 1 Mbp. A bimodal distribution of estimated sample size was observed, particularly if more than two causative variants were assumed. The median of estimates constituted the final proposal of optimal sample size; it was consistently less than sample size estimated from single-SNP investigation which was used as a baseline approach. The second mode pointed to inflated sample sizes and could be explained by blocks of varying linkage phases leading to negative correlations between SNPs. Optimal sample size increased almost linearly with number of signals to be identified but depended much stronger on the assumption on heritability. For instance, three times as many samples were required if heritability was 0.1 compared to 0.3. An R package is provided that comprises all required tools.ConclusionsOur approach incorporates information about the population structure into the design of experiments. Compared to a conventional method, this leads to a reduced estimate of sample size enabling the resource-saving design of future experiments for fine-mapping of candidate variants.

Dataset Information

Statistical distributions of test statistics used for quantitative trait association mapping in structured populations.

Background

Results

Conclusions

Publications

Statistical distributions of test statistics used for quantitative trait association mapping in structured populations.

Similar Datasets

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