deletions | additions       diff --git a/subsection_Several_popular_methods_begin__.tex b/subsection_Several_popular_methods_begin__.tex  index 67ec9bb..7b52ecd 100644  --- a/subsection_Several_popular_methods_begin__.tex  +++ b/subsection_Several_popular_methods_begin__.tex 
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\end{itemize}  \item True trees (MT-rank of the coalescent events, \cite{Burkett_2014}): Detect co-clustering of the disease trait and variants on genealogical trees.   \begin{itemize}  \itemIn practice, the true trees are unknown. However, the cluster statistics based on true trees represent a best case insofar as tree uncertainty is eliminated.  A previous simulation study \cite{Burkett_2014} of Burkett et al.  established the optimality of these tests tree based approach  for detecting association. We therefore include two versions of Mantel test as a benchmark for comparison. Note that we define a 'phenotype' for each haplotype within an individual. An Therefore, an  individualthus  has two phenotypes rather than one. \begin{itemize}  \item Version 1: Naive-Mantel test, phenotype is scored according to whether or not haplotype comes from a case.  \item Version 2: Informed-Mantel test, phenotype is scored according to whether or not haplotype comes from a case and carries a risk variant.