Use of the expected log likelihood to evaluate designs for mapping quantitative trait loci
Many traits of economic importance are determined by quantitative trait loci (QTL). QTL can be detected by their linkage to marker loci. Many different experimental designs have been proposed for detecting QTL. The relative merits of these designs can be evaluated by their power to detect a QTL segregating in a population. The test statistic most commonly used for detection of QTL is the log likelihood ratio. It has been suggested that the expected log likelihood ratio may be a good indicator of the power of a particular experimental design. In this study, two methods were used to calculate this expected value and their usefulness evaluated by simulation. The first approach approximated the expected value of the log likelihood assuming y is distributed as a mixture of multivariate normal distributions. The second approach calculated the exact log likelihood by approximating the distribution of y with a single multivariate normal distribution that has the same mean and variance-covariance structure as the mixture distribution. The utility of these approximations were studied by computing the power and the mean of the log likelihood ratio for several designs by computer simulation and relating these results to the expected value of the log likelihood for both approaches. The expected value of the log likelihood calculated using the first approach had a poor relationship with power, but the expected value of the log likelihood ratio calculated using the second approach had a strong correlation with the mean of the log likelihood ratio. Because the mean of the log likelihood ratio did not have a strong correlation with the power, this mean may not be a good indicator of the power of a design. Therefore, any approximation of the mean of the log likelihood ratio also may not be a good indicator of the power.