Generating the posterior distribution

To estimate the position of the disease mutation and the confidence interval, TreeLD creates the posterior distribution of the locus of the disease mutation based on the output of the treepeeling step. To calculate the likelihood of a tree under the disease mutation model, the program averages over the likelihood for each set of penetrance variables. By then averaging over all trees at one focal point, the posterior likelihood of that focal point to be the locus of disease mutation is calculated. This averaging process can be overly influenced by outliers. Section 8.2 describes the impact of outliers in more detail and offers advice on how to reduce their impact.

Figure 7: Example of an Analysis window after a treepeeling run for a case-control dataset. The red dots indicate the $\chi^2$-values of the individual markers as indicated by the left vertical axis, the continuous line indicates the posterior loglikelihood to carry the disease locus as indicated by the right vertical axis and the dashed yellow box marks the credible region.

Under most circumstances, the location with the highest posterior likelihood is the best estimate for the location of the disease mutation. (This might not be true if this maximum is an isolated peak, see 8.2 for further discussion.) If a credible region has been in generated as described in 6.3, it is displayed in the Analysis Window as a dashed box.

It should be pointed out that the displayed continuous distribution is an estimate from values that have been generated at different focal points. Therefore the resolution of this distribution is dependent on the number of focal points it is based on. A posterior distribution that is based on more focal points will usually result in a more precise estimate of the location of disease mutation and a tighter credible region. See 8.3 for some suggestions about the optimal densities.