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\end{itemize}  \item C-alpha \cite{Neale_2011}: %Test the variance of the effect size for variants in a specific genomic window (No effect, increase or decrease risk).  \begin{itemize}  \item C-alpha test of \cite{Neale_2011} is a variance components approach that assumes the effects of variants are random. random with mean zero.  \item C-alpha procedure tests the variance of genetic effects under the assumption that variants observed in cases and controls are a mixture of risk, protective or neutral variants.  \item \citeNP{Neale_2011} found that C-alpha showed greater power than burden test when protective and risk variant exist.  \end{itemize}  \item We applied VTWOD function in R package RVtests \cite{Xu_2012} for VT-test and SKAT function in R package SKAT for C-alpha test across the simulated region by using sliding windows of 20 SNVs overlapping by 5 SNVs.  \end{itemize}    \item Joint-modeling method methods  \begin{itemize}  \item CAVIARBF \cite{Chen_2015} is a fine-mapping method that uses marginal test statistics for the SNVs and their pairwise association to approximate the Bayesian multivariate multivariate(or multiple ??)  regression of phenotypes onto variants that is implemented in BIMBAM \cite{Servin_2007}. However, CAVIARBF is much faster than BIMBAM because it computes Bayes factors using only the SNVs in each causal model. These Bayes factors can be used to calculate the posterior probability of SNVs being causal in the region (the posterior inclusion probability). \begin{itemize}  \item To compute the probability of SNVs being causal, a  set of models and their Bayes factors have to be considered. Let $p$ be the total number of SNVs in a candidate region, then theall possible  number of possible  causal models is $2^p$. To reduce the number of causal models to evaluate and save computational time and effort, CAVIARBF imposes a limit, $L$, on the number of causal variants. So, this limitation reduces the number of models to evaluate in the model space from $2^p$ to $ \sum_{i=0}^{L} \dbinom{p}{i} $, where $L$ is the number of causal SNVs in the model. Since there were 2747 SNVs in our example dataset, to keep the computational load down, we considered $L=2$ throughout this investigation..   \end{itemize}  \item Elastic-net \cite{Zou_2005} is a hybrid regularization and variable selection method that linearly combines the L1 and L2 regularization penalties of the Lasso \cite{Tibshirani_2011} and Ridge \cite{Cessie_1992} methods in multivariate multiple  regression. \begin{itemize}  \item This combination of Lasso and Ridge penalties provides a more precise prediction than using multiple regression, when SNVs are in high linkage disequilibrium \cite{Cho_2009}.  \item In addition, the elastic-net can accommodate situations in which the number of predictors exceeds the number of observations. We used the elastic-net to select risk SNVs by considering only the main effects.% WE CONSIDER ONLY MAIN EFFECTS FOR SNVs IN OUR ELASTIC NET MODELS.