Genome-wide association studies have been successful in identifying loci that underlie continuous traits measured at a single time point. To additionally consider continuous traits longitudinally, it is desirable to look at SNP effects at baseline and over time using linear-mixed effects models. Estimation and interpretation of two coefficients in the same model raises concern regarding the optimal control of type I error. To investigate this issue, we calculate type I error and power under an alternative for joint tests, including the two degree of freedom likelihood ratio test, and compare this to single degree of freedom tests for each effect separately at varying alpha levels. We show which joint tests are the optimal way to control the type I error and also illustrate that information can be gained by joint testing in situations where either or both SNP effects are underpowered. We also show that closed form power calculations can approximate simulated power for the case of balanced data, provide reasonable approximations for imbalanced data, but overestimate power for complicated residual error structures. We conclude that a two degree of freedom test is an attractive strategy in a hypothesis-free genome-wide setting and recommend its use for genome-wide studies employing linear-mixed effects models.
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