General introduction

Background

The foundations of modern genetics laid down in Johann Gregor Mendel’s pioneering work have resulted in the understanding that certain hereditary traits can exist in different versions (alleles), introducing the notion of homozygosity and heterozygosity. It paved the way for the comprehension of heredity mechanisms with the establishment of the first genetic maps by Thomas Hunt Morgan and the definition of genetic heritability by Ronald Fisher which suggests that the expression of a trait (phenotype) is subject to both genetic and environmental factors. These groundbreaking works led to the linkage analysis studies whose purpose is to map genes involved in the expression of diseases. These approaches, effective in locating genes involved in the expression of a simple qualitative trait, have proven less reliable in mapping complex diseases. Indeed, there may be multiple interaction between genes underlying these phenotypes and the effects of these genes may vary with exposure to environmental and other non-genetic risk factors.

These limitations have driven the development of another discipline: Genome-Wide Associations Studies (GWAS). These studies aim to identify single nucleotide polymorphisms (SNP), i.e. genetic markers that occur at different frequencies between unrelated samples of affected individuals and unaffected controls, implied in the expression of a given phenotype. These studies exploit the fact that it is easier to establish large cohorts of affected individuals sharing a genetic risk factor for a complex disease in the general population than within individual families, as it is the case with traditional linkage analysis.

In addition, recent advances in genotyping technology have made it possible to genotype the entire DNA sequence of an individual at a moderate cost and within a reasonable time. Therefore, it became necessary to develop new statistical methods able to process this type of massive data.

Problematic

From a statistical point of view, looking for these genetic markers can be supported by hypothesis testing. The standard approach in GWAS is based on univariate linear regression, with affected individuals being tested against healthy individuals at one or more loci. Classical testing schemes are subject to false positives, that is SNP that are falsely identified as significant. One way around this problem is to apply a correction for the False Discovery Rate (FDR, Benjamini and Hochberg 1995). Unfortunately, this increases the risk of missing true associations that have only a small effect on the phenotype, which is usually the case in GWAS.

Although GWAS have been successful in the identification of genetic variants associated with complex multifactorial diseases (Crohn’s disease, diabetes I and II, coronary artery disease…(WTCCC 2007)), only a small proportion of the phenotypic variations expected from classical family studies have been explained (Manolio and Visscher 2009). This missing heritability may have multiple causes amongst the following: strong correlations between genetic variants, population structure, epistasis (gene by gene interactions), disease associated with rare variants…

Objectives

The main objectives of this thesis are to develop new methodologies, in the context of GWAS, that can face part of the limitations mentioned above. More specifically we developed two new approaches: the first one, entitled LEOS, is a blockwise approach for GWAS analysis which leverages the correlation structure among the genomic variants to reduce the number of statistical hypotheses to be tested, while the second, named SICOMORE, focuses on the detection of interactions between groups of metagenomic and genetic markers to better understand the complex relationship between environment and genome in the expression of a given phenotype.

Contributions

This thesis work gave rise to the writing of two scientific articles, one for each methodology. The method LEOS described in Chapter 4 is under minor review in the journal BMC bioinformatics while the method SICOMORE described in Chapter 5 has been published as an article of a national conference (\(50^{th}\) Journées de la statistique) but the extended version was still in a preprint status at the time this manuscript was written.

The proposed methods have been implemented in computer programs: LEOS is proposed as a webserver tool while SICOMORE is available through an R package (a vignette, added at the end of the manuscript, is available for this package).

This work has also led to several oral communications and poster presentations in the following conferences:

  • Statistical Methods for Post Genomic Data in 2017 (poster presentation LEOS)

  • International Society for Computational Biology conference in 2017 (poster presentation LEOS)

  • Statistical Methods in Biopharmacy in 2017 (oral presentation LEOS).

  • Journées de statistique in 2018 (oral presentation SICOMORE)

Contents of the manuscript

This manuscript is composed of five different chapters. The first three chapters will focus on the genetic, statistical and GWAS context while our two proposed methodologies will be presented in Chapters 4 and 5. Chapter 1 will remind the genetic precepts fundamental to the understanding of our work while Chapter 2 will introduce the concept of statistical learning and Chapter 3 will provide an extensive introduction to GWAS by presenting some state-of-the-art statistical methods. We will also discuss the results obtained on our proposed approaches at the end of Chapters 4 and 5 before providing a general conclusion in a last section.

References

Benjamini, Yoav, and Yosef Hochberg. 1995. “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing.” Journal of the Royal Statistical Society: Series B 57 (1): 289–300.

Manolio, T. A., and P. M. Visscher. 2009. “Finding the Missing Heritability of Complex Diseases.” Nature 461 (7265): 747–53.

WTCCC. 2007. “Genome-Wide Association Study of 14,000 Cases of Seven Common Diseases and 3,000 Shared Controls.” Nature 447 (7145): 661–78.