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.

在许多病例对照遗传关联研究中，可以鉴定出可能具有常见遗传因素和疾病状态的继发表型。但是，仅在病例受试者中观察到了第二表型，但可以用作疾病状态的替代标记。如果由于成本和数据来源不同，仅在病例组中有关于次要表型的信息时，拟合忽略补充表型数据的线性回归模型可能会提供关于遗传关联的有限知识。在此，纳入了现有的科学知识，即对照对象的缺失第二表型值在一定范围内，并且建立了截短的联合似然函数以估计基因型和其他协变量在模型中的作用。