Advances in Incomplete Data Methods for Statistical Genetics

Handling incomplete or missing data is a common aspect of modern statistical methods. In this thesis, I focus on novel solutions for current problems pertaining to statistical genetics that can be framed in the context of incomplete data. In particular, three methods are proposed that are underpinned by the EM algorithm, arguably the most common yet powerful approach to make statistical inference in the presence of incomplete data. First, motivated by developments in metagenomic sequencing data and the apparent systematic exclusion of the X-chromosome in genetic studies, I propose a finite mixture regression model (FMM) that infers association between a genetic variant in the X-chromosome and an operational taxonomic unit. The proposed FMM accounts for complex biological mechanisms governing the X-chromosome, namely X-chromosome inactivation (XCI), escape of XCI, and skewed or non-random XCI by introducing an latent indicator variable. Second, I investigate two-phase sampling designs in post-genome-wide association studies (GWASs), which can be a cost-effective strategy to infer association between missing-by-design sequencing data and a trait of interest. In phase 1, given a GWAS-identified genetic region, a subsample is selected for which expensive targeted-sequence data are collected using outcome measures and auxiliary covariates to inform the sampling. Phase 2 consists of performing inference using combined phase 1 2 data. In particular, I develop semi-parametric maximum likelihood for analysis and examine heuristic allocations to select the phase 2 subsample. Lastly, derived from the second project, I propose two strategies that aim to optimally select subjects for sequencing when the subsample size is fixed due to budget constraints. These strategies aim to minimize features of the variance-covariance matrix based on predefined optimality criteria found in previous literature and common to experimental design. The proposed strategies implement such minimization via (1) Lagrange multipliers and (2) a genetic algorithm. In all cases, the proposed methods are evaluated through comprehensive simulation studies. In addition, I illustrate their usage in real genetic studies or realistic synthetic data in absence thereof. Overall, the methods perform satisfactorily, moreover, these findings can serve as the basis of further research.Ph.D