\relax \@writefile{toc}{\contentsline {chapter}{\numberline {4}EB Method for Multiple Genome Scans}{45}} \@writefile{toc}{\contentsline {author}{Kui Zhang,Howard Wiener,T. Mark Beasley,Christopher I. Amos,David B. Allison}{45}} \@writefile{lof}{\addvspace {10pt}} \@writefile{lot}{\addvspace {10pt}} \newlabel{ch:eblinkage}{{4}{45}} \@writefile{toc}{\contentsline {section}{\numberline {4.1}Abstract}{45}} \@writefile{toc}{\contentsline {section}{\numberline {4.2}Introduction}{46}} \@writefile{toc}{\contentsline {section}{\numberline {4.3}Methods}{48}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.1}Haseman-Elston Regression Analysis for a Single Genome Scan Study with $m$ Markers using Sib Pairs}{48}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.2}The Interval Mapping (IM) Method to Detect Linkage between Markers and QTLs and Estimate the QTL Location and Effect Based on $m$ Markers from a Single Genome Scan Study Using Sib Pair}{49}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.3}Empirical Bayes Model (Bayesian Hierarchical Normal Model)}{49}} \newlabel{formula:001}{{4.1}{49}} \newlabel{formula:002}{{4.2}{50}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.4}Application of the Empirical Bayes Method to Each Marker Based on $k$ Studies with $m$ markers and Identical Marker Map}{50}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.5}The IM-EB Method to Detect Linkage between Markers and QTLs and Estimate the QTL Location and Effect Based on $m$ Markers and $k$ Genome Scan Studies Using Sib Pairs}{50}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3.6}Simulation Designs}{51}} \@writefile{toc}{\contentsline {section}{\numberline {4.4}Results}{52}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.4.1}The Type I Error Rate and Power of the IM-EB method to Detect Linkage between Markers and QTLs}{52}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.4.2}The Accuracy of the IM-EB estimates for QTL Location and QTL Effect}{54}} \@writefile{toc}{\contentsline {section}{\numberline {4.5}Discussion}{55}} \@writefile{toc}{\contentsline {section}{\numberline {4.6}Acknowledgement}{55}} \@writefile{toc}{\contentsline {section}{\numberline {4.7}Figures and Tables}{56}} \@writefile{lof}{\contentsline {figure}{\numberline {4.1}{\ignorespaces The actual map for 15 micro-satellite markers from the National Institute of Mental Health Alzheimer's Diseases Genetics Initiative and the locations of two hypothetical QTLs used in simulations. The minimum distances between the marker and two QTLs, 65cM and 35cM from the p-terminus of the chromosome, are 9cM and 4cM, respectively.}}{57}} \newlabel{figure:001}{{4.1}{57}} \@writefile{lof}{\contentsline {figure}{\numberline {4.2}{\ignorespaces The type I error rates of the IM-EB estimator at the 65cM from the p-terminus of the chromosome with 5, 10, and 15 studies. The QTL in all studies were positioned 65cM from the p-terminus of the chromosome. In the primary study, the heritability of QTL was set to 15\% and the number of background study having non-zero QTL effect varied.}}{58}} \newlabel{figure:002}{{4.2}{58}} \@writefile{lof}{\contentsline {figure}{\numberline {4.3}{\ignorespaces The power of the IM estimator and IM-EB estimator with 5, 10, and 15 studies at 65cM from the p-terminus of the chromosome. The QTL in all studies was positioned 65cM from the p-terminus of the chromosome. In the primary study, the heritability of QTL was set to 15\% and the number of background study having non-zero QTL effect varied.}}{59}} \newlabel{figure:003}{{4.3}{59}} \@writefile{lof}{\contentsline {figure}{\numberline {4.4}{\ignorespaces The power of the IM estimator and IM-EB estimator with 5, 10, and 15 studies at the marker loci. In all studies, including the primary study and background studies, the heritability was set to 15\%. In the primary study and half of the background studies, the QTL was positioned 65cM from the p-terminus of the chromosome. In another half of the background studies, the QTL was positioned 35cM from the p-terminus of the chromosome.}}{60}} \newlabel{figure:004}{{4.4}{60}} \@writefile{lot}{\contentsline {table}{\numberline {4.1}{\ignorespaces The mean and MSE (in parentheses) for the point estimates of QTL location.}}{61}} \newlabel{table:001}{{4.1}{61}} \@writefile{lot}{\contentsline {table}{\numberline {4.2}{\ignorespaces The mean and MSE (in parentheses) for the point estimates of QTL effect.}}{62}} \newlabel{table:002}{{4.2}{62}} \@setckpt{Zhang/Zhang1}{ \setcounter{page}{63} \setcounter{equation}{2} \setcounter{enumi}{0} \setcounter{enumii}{0} \setcounter{enumiii}{0} \setcounter{enumiv}{0} \setcounter{footnote}{0} \setcounter{mpfootnote}{0} \setcounter{part}{0} \setcounter{chapter}{4} \setcounter{section}{7} \setcounter{subsection}{0} \setcounter{subsubsection}{0} \setcounter{paragraph}{0} \setcounter{subparagraph}{0} \setcounter{example}{0} \setcounter{theorem}{0} \setcounter{proposition}{0} \setcounter{lemma}{0} \setcounter{corollary}{0} \setcounter{definition}{0} \setcounter{exercise}{0} \setcounter{dummy}{0} \setcounter{figure}{4} \setcounter{table}{2} \setcounter{NAT@ctr}{0} \setcounter{r@tfl@t}{0} \setcounter{parentequation}{0} \setcounter{subfigure}{0} \setcounter{lofdepth}{1} \setcounter{subtable}{0} \setcounter{lotdepth}{1} }