Robust allele-based association analyses of complex genetic data

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Association analysis is at the heart of current genetic studies of heritable and complex human traits. These studies are typically large-scale, analyzing tens of thousands or more individuals, often through worldwide consortium efforts, by scanning through millions or more genetic markers across the genome for the ones associated with trait(s) of interest. The work is interdisciplinary in nature, but a significant part of the research is developing statistically powerful and computationally efficient methods that select candidates for follow-up biological study and interpretation. In this context, the allele-based association test, comparing difference in allele frequency between cases and controls, is an intuitive, easy-to-implement and locally most powerful method. But the seminal work of Sasieni (1997, Biometrics) highlighted the importance of the Hardy-Weinberg equilibrium (HWE) assumption, thus cementing the current use of genotype-based association test. Subjected to frequent use and intense scrutiny, a myriad of theoretical deficiencies are being noted and analytical difficulties are being encountered in analyzing increasingly more complex data. In this research, we propose a potentially paradigm-shifting new allele-based regression framework. The foundational formulation is deceptively simple, but we show that the new framework encompasses many existing methods as special cases, and it is generalizable for more complex data and flexible for other inferential purposes beyond association. Specifically, the proposed research reformulates the classical Pearson chi-square test of HWE as score tests derived from two distinct regression models. Building upon this, we will derive a generalized robust allele-based association test, and we will investigate its connections with exiting genotype-based counterparts including a class of quasi-likelihood score tests. We will also expand the statistical model and tailor it to a number of other genetic studies including imprinting and data-integration, among others. Finally, the proposed research serves as a proof of principle, demonstrating that classical statistical techniques, such as regression, remain relevant and powerful for complex genome data science.