Abstract
The confidence interval for the map location of quantitative trait loci (QTL) is a very important quantity for geneticists. The one LOD support interval has been proved to be a biased confidence interval. Moreover the distribution of the LOD score has been shown to depend on the value of the QTL effect, which is why the LOD score cannot be used to build an unbiased confidence interval when the value of the QTL effect is unknown. A new confidence interval based on a maximun likelihood ratio test and using statistics whose asymptotic distribution does not depend on the QTL effect, has been proposed and proved to lead to an asymptotically similar confidence interval. The major difficulty of this method is the computation of the correct threshold for the maximum likelihood ratio test. An approximation for the threshold is proposed in this paper. When the value of the QTL effect is known, an unbiased confidence region could be built using the LOD score. A simulation study is carried out to compare the average length of this region, which is unobtainable for an unknown value of the QTL effect, to the average length of the asymptotically similar confidence interval. It shows that the required property of similarity does not increase the confidence interval length significantly for QTL having a small effect, and leads to an increase of about 5cM length for a 1 Morgan chromosome when the value of the QTL is great. An empirical symmetrical confidence interval could be constructed with the empirical distribution function of the maximun likelihood estimation for the QTL position. The simulation study shows that, when a QTL is detected, the average length of the asymptotically similar confidence interval could be half the length of the empirical symmetrical one. This great difference can be explained by the fact that the asymptotically similar confidence interval is dependent of the interval mapping test of detection whereas the empirical symmetrical one is independent of the actual data.
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