Case-base-control designs
Most genome-wide association studies (GWASs) use randomly selected samples from the population (hereafter bases) as the control set. This approach is successful when the trait of interest is rare; otherwise, a loss in the statistical power to detect disease-associated variants is expected. To address this, a proposal to combine the three sample types, cases, controls and bases is introduced, for instances when the disease under study is prevalent. This is done by modelling the bases as a mixture of multinomial logistic functions of cases and controls, according to the disease prevalence. The maximum likelihood method is used to estimate the underlying parameters using the EM algorithm. Three classical tests of association; score, Walds, and likelihood ratio tests are derived and their power of detecting genetic associations under different designs is compared. Simulations show that combining the three samples can increase the power to detect disease-associated variants, though a very large base sample set can compensate for the lack of controls.