A longitudinal complex likelihood ratio test for pleiotropy

Abstract

. To test pleiotropy based on longitudinal data, two main difficulties are the construction of test statistics and the formulation of decision-making criteria. In particular, the commonly used log-likelihood ratio test is not available since there does not exist a likelihood function and the estimation is based on estimating equations in general. To address this and construct a statistic similar to the -2 log-likelihood ratio test statistic, we propose a new concept, a complex log-likelihood function, such that its first derivative is equal to a given estimating function. In consequence, the -2 complex log-likelihood ratio test is constructed for testing genetic pleiotropy, and the validity of the test procedure is established. An extensive simulation study is performed, which suggests that the proposed method works well for practical situations. Furthermore, it is applied to a set of longitudinal data on tropical storms.