Other Options

Eqtl essentially finds the peaks in the likelihood ratio graph of the results from Zmapqtl. It goes along the chromosome, and determines whether the likelihood ratio test statistic is increasing or decreasing. Upon a change, it picks out the position and estimates of other parameters. The user can specify that the peaks of interest need be higher than some ``Significance threshold'' to be considered QTLs. The default is 3.84, that is, any peak that is less than 3.84 is ignored. This can be changed with the -S option. If you have run Zmapqtl and done a permutation test, Eqtl automatically reads the output and sets the significance threshold subject to the value of the size, set with the -a option. For a size of $\alpha$, the the $100(1-\alpha)$-percentile is calculated from the experimentwise test values.

The final option is a flag to output LOD scores rather than likelihood ratios. The default behavior of the QTL Cartographer system is to use a likelihood ratio test statistic (LR) rather than a LOD score. For a hypotheses $H_i$, let $L_i$ be the likelihood of the data given the hypothesis. For a pair of hypotheses $H_0$ and $H_1$, this would yield $L_0$ and $L_1$. The LOD score is defined as

$$LOD = -\log \frac{L_0}{L_1}$$

The likelihood ratio test statistic (LR) is

$$LR = -2\ln \frac{L_0}{L_1} = -2 \ln 10^{-LOD} = 2(\ln 10) LOD = 4.605 LOD$$

and thus

$$LOD = -\log \exp(-\frac{LR}{2}) = \frac{1}{2}(\log e) LR = 0.217 LR$$