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Analyzed the data: FK OL LAH. Contributed reagents/materials/analysis tools: FK OL LAH. Wrote the paper: FK OL LAH.

The authors have declared that no competing interests exist.

Statistical association between a single nucleotide polymorphism (SNP) genotype and a quantitative trait in genome-wide association studies is usually assessed using a linear regression model, or, in the case of non-normally distributed trait values, using the Kruskal-Wallis test. While linear regression models assume an additive mode of inheritance via equi-distant genotype scores, Kruskal-Wallis test merely tests global differences in trait values associated with the three genotype groups. Both approaches thus exhibit suboptimal power when the underlying inheritance mode is dominant or recessive. Furthermore, these tests do not perform well in the common situations when only a few trait values are available in a rare genotype category (disbalance), or when the values associated with the three genotype categories exhibit unequal variance (variance heterogeneity). We propose a maximum test based on Marcus-type multiple contrast test for relative effect sizes. This test allows model-specific testing of either dominant, additive or recessive mode of inheritance, and it is robust against variance heterogeneity. We show how to obtain mode-specific simultaneous confidence intervals for the relative effect sizes to aid in interpreting the biological relevance of the results. Further, we discuss the use of a related all-pairwise comparisons contrast test with range preserving confidence intervals as an alternative to Kruskal-Wallis heterogeneity test. We applied the proposed maximum test to the Bogalusa Heart Study dataset, and gained a remarkable increase in the power to detect association, particularly for rare genotypes. Our simulation study also demonstrated that the proposed non-parametric tests control family-wise error rate in the presence of non-normality and variance heterogeneity contrary to the standard parametric approaches. We provide a publicly available R library nparcomp that can be used to estimate simultaneous confidence intervals or compatible multiplicity-adjusted p-values associated with the proposed maximum test.

Genome-wide association studies involving large population-based samples have become a common strategy employed for the identification of common variants that affect a particular trait or play a role in disease. A majority of these studies involve comparing allele frequencies of di-allelic markers (e.g., SNPs) in cases and controls (see e.g.,

Alternatively, continuous endpoints (i.e., quantitative traits), such as uromodulin

Nonparametric approaches do not require normality. However, the often used nonparametric Kruskal-Wallis test

Recommendations given in the ‘Strengthening the Reporting of Genetic Association studies’ report

We describe a Behrens-Fisher version of multiple contrast test for relative effects

A real data example with the right skewed distributed phenotype

Model | Effect-Estimator | 95%-Simultaneous Intervals | Adjusted p-Value |

Dominant | −0.240 | [−0.378; −0.082] | 0.0058 |

Additive | −0.250 | [−0.387; −0.092] | 0.0043 |

Recessive | −0.053 | [−0.119; 0.015] | 0.13 |

Let

This general model (2) does not contain any parameters that could be used to describe a difference between the distributions. Therefore, the distribution functions

For the formulation of nonparametric genetic effects, let

Thus, the case of

To test the individual hypothesis

Particularly in psychiatric epidemiology, different mental scores are often used as phenotypes, see e.g.

Sometimes phenotypes with values below a detection limit occur, see e.g.

The new nonparametric multiple contrast test

The upper confidence limit of the additive model is most distant to

In summary, using the multiple contrast tests yields specific information regarding the genetic mode of inheritance as well as simultaneous confidence intervals.

We evaluated the empirical type-I error rates and the powers of nonparametric multiple contrast tests via extensive simulation studies. All simulations were performed using the publicly available software R (version 2.12.1;

The trait genotypes for

Since the expectation of a multimodal distribution is the weighted sum of the single expectations, the parameter settings on

We simulated the nonparametric multiple contrast tests

It follows from

To investigate the power of the different procedures mentioned above, different parameter settings on the variance explained by the quantitative trait (

For a convenient application of the developed procedures, the R-software package

A nonparametric approach to evaluate the association between a di-allelic marker and a non-normal distributed quantitative trait is proposed for simple population-based studies. Using a Marcus-type multiple contrast test for relative effects allows model-specific testing of either dominant, additive or recessive mode of inheritance. Furthermore, an all-pairwise comparisons contrast test is proposed as an alternative to the Kruskal-Wallis heterogeneity test. Procedures for obtaining related simultaneous confidence intervals or multiplicity-adjusted p-values are provided. The advantage of obtaining confidence intervals is their interpretability in terms of stochastic order for studies with individuals according to

Adjustment against multiple covariates is an important issue in unbiased testing association. The adjustment against population stratification, e.g. by principle components

To estimate the unknown relative effect

It was shown that

Alternatively, a pairwise rankings version is available which can be easily derived from two-sample tests. They behave similarly to the global rankings approach, but they can lead to paradoxical results.

As mentioned in the previous section, the three genetic effects