Genome-wide association study using truncated likelihood with incomplete information for stratum specific missingness

In many case–control genetic association studies, a secondary phenotype that may have common genetic factors with disease status can be identified. However, the secondary phenotype is observed only for case subjects but may be used as a surrogate marker for disease status. When information on the secondary phenotype is available only for a case group, due to cost and different data sources, fitting a linear regression model that ignores supplementary phenotype data may provide limited knowledge regarding the genetic associations. Herein, existing scientific information that the missing secondary phenotype values of control subjects lie in a certain range is incorporated, and a truncated joint likelihood function is established to estimate the effects of genotype and other covariates in the model. The performance of the proposed method is investigated through numerical studies and, for illustration, the procedure is applied to rheumatoid arthritis data provided by the Genetic Analysis Workshop 16.