HARDY-WEINBERG EQUILIBRIUM ASSUMPTIONS IN CASE-CONTROL TESTS OF GENETIC ASSOCIATION

The case-control study design is commonly used in genetic association study with a binary trait using unrelated individuals from a population. To test association with a binary trait in a case-control or cohort study, the standard analysis is a chi-square test or logistic regression model that test to detect a difference in frequencies of alleles or genotypes. In this thesis, we derive the maximum likelihood estimator, using Chen and Chatterjee's methods, for standard 1 df genetic tests (dominant, recessive, and multiplicative). We then compare these methods that assume HWE with standard Wald tests and chi-squared tests that do not make the HWE assumption. We consider four different HWE scenarios: 1) when HWE holds in both cases and controls, 2) when HWE does not hold in cases and controls follow HWE, 3) when HWE does not hold in controls, and cases follow HWE and 4) when HWE does not hold in either cases or controls. Our results show that the performances of the three statistics (chi-squared, Wald, and Chen and Chatterjee Wald) are equivalent for multiplicative test under all four HWE scenarios. When HWE holds in both cases and controls, the performances of the three statistics are also equivalent, except for variations attributable to type I error issues. When HWE fails to hold in either cases or controls or both, the 2 df version of the Chan and Chatterjee Wald test (and to a lesser extent the dominant and recessive versions) detects this HWE departure and can therefore "find" a case-control difference even if there is not an allele frequency difference or even a genotype frequency difference. Our results will improve the design and analysis of genetic association studies. Such association studies are a crucial step in understanding the genetic components of many diseases that have a large impact on public health. Better understanding of the etiology of these diseases will lead in the long term to better prevention and treatment strategies