Abstract
In the case-parents trio design for testing candidate-gene association, the distribution of the data under the null hypothesis of no association is completely known. Therefore, the exact null distribution of any test statistic can be simulated by using Monte-Carlo method. In the literature, several robust tests have been proposed for testing the association in the case-parents trio design when the genetic model is unknown, but all these tests are based on the asymptotic null distributions of the test statistics. In this article, we promote the exact robust tests using Monte-Carlo simulations. It is because: (i) the asymptotic tests are not accurate in terms of the probability of type I error when sample size is small or moderate; (ii) asymptotic theory is not available for certain good candidates of test statistics. We examined the validity of the asymptotic distributions of some of the test statistics studied in the literature and found that in certain cases the probability of type I error is greatly inflated in the asymptotic tests. In this article, we also propose new robust test statistics which are statistically more reasonable but without asymptotic theory available. The powers of these robust statistics are compared with those of the existent statistics in the literature through a simulation study. It is found that these robust statistics are preferable to the others in terms of their efficiency and robustness.
Highlights
In testing the association between a candidate gene and a disease, the caseparents trio design proposed by Schaid and Sommer (1993) has been extensively studied in recent years
Schaid (1999) considered an un-constrained likelihood ratio test (LRT) procedure, Zheng, Freidlin and Gastwirth (2002) studied a test procedure which they coined as MAX3, and Zheng, Chen and Li (2003) proposed a restricted version of likelihood ratio test (RLRT)
We propose exact robust tests of which the asymptotic distributions are not available for the test statistics
Summary
In testing the association between a candidate gene and a disease, the caseparents trio design proposed by Schaid and Sommer (1993) has been extensively studied in recent years. Under the null hypothesis of no association, the distribution of the data in the case-parents design is completely known By this fact, the exact null distribution of any test statistic can be simulated by Monte-Carlo methods. We consider the exact robust tests using Monte-Carlo methods with case-parents design data. (iii) Though, in principle, the exact null distribution can be determined without resorting to Monte-Carlo simulation, as in the case of Fisher’s exact test, it is only feasible when the sample size is small. With a total sample size 1,000, the determination of the exact null distribution without resorting to Monte-Carlo simulation is practically impossible.
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