% This example file for NIH submissions was originally written
% by Bruce Donald (http://www.cs.duke.edu/brd/).
% 
% You may freely use, modify and/or distribute this file.
% 
\documentclass[11pt]{NIHAug2008}
%\documentclass{article}
%\documentclass[12pt]{article}%
% last revision:
\def\mydate{2005-06-09 13:58:03 brd}


%%%%%%% Two column control
\newif\ifdotwocol
\dotwocoltrue   % two col
%\dotwocolfalse   % one col
\long\def\twocol#1#2{\ifdotwocol{#1}\else{#2}\fi}
%%%%%%%

\def\mybeforeequation{\footnotesize}
%\def\mybeforeequation{\small}
%\def\mybeforeequation{}

\def\myafterequation{\renewcommand\baselinestretch{1.1}}
%\def\myafterequation{}

%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%

\def\citeusmark{$^{\textstyle \star}$}
\def\citeus#1#2{\cite{#1}}

\def\crow#1#2{#2}

\usepackage{denselists}
%\usepackage{scaledfullpage}
\usepackage[dvips]{graphicx,floatflt}
\usepackage{color}
\usepackage{boxedminipage}
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{url}
%\usepackage{mathptmx}
%\usepackage{nih}		% PHS 398 Forms
%\usepackage{nihblank}		% For printing on Blank PHS 398 Forms
%\usepackage{confidential}
\usepackage[square, comma]{natbib}
\usepackage{wrapfig}
\usepackage{wrapft}
\pagestyle{empty}

\def\Paper{grant application}
\def\paper{application}
\def\refappendix{Sec.}

%Note from brd
\long\def\todo#1{{\bf{To do:}} #1}
%\long\def\todo#1{}
\long\def\squeezable#1{#1}

%\def\a5{$\alpha_{_5}$
\def\a5{5}

%\def\mycaptionsize{\normalsize}
%\def\mycaptionsize{\small}
%\def\mycaptionsize{\small}
\def\mycaptionsize{\footnotesize}
\def\mycodesize{\footnotesize}
\def\myeqnsize{\small}

\def\sheading#1{{\bf #1:}\ }
\def\sheading#1{\subsubsection{#1}}
%\def\sheading#1{\bigskip {\bf #1.}}

\def\ssheading#1{\noindent {\bf #1.}\ } 

\newtheorem{hypothesis}{Hypothesis}
\long\def\hyp#1{\begin{hypothesis} #1 \end{hypothesis}}

\newenvironment{closeenumerate}{\begin{list}{\arabic{enumi}.}{\topsep=0in\itemsep=0in\parsep=0in\usecounter{enumi}}}{\end{list}}
\def\CR{\hspace{0pt}}           % ``invisible'' space for line break

\newif\ifdbspacing
%\dbspacingtrue  % For double spacing
\dbspacingfalse  % For normal spacing

\ifdbspacing
 \doublespacing
 \newcommand{\capspacing}{\doublespace\mycaptionsize}
\else
 \newcommand{\capspacing}{\mycaptionsize}
\fi

\def\rulefigure{\smallskip\hrule}

% \def\codesize{\normalsize}
\def\codesize{\small}

\newtheorem{proposition}{Proposition}
\newtheorem{lemma}{Lemma}


\newcommand{\nc}{\newcommand}
\nc{\pv}{{\slshape P} value}
\nc{\pvs}{{\slshape P} value }

\nc{\mysection}[1]{\vspace{-2mm} 
	\section{#1}
	\vspace{-2mm}}
\nc{\mysubsection}[1]{\vspace{-2mm} 
	\subsection{#1}
	\vspace{-2mm}}
\nc{\mysubsubsection}[1]{\vspace{-2mm} 
	\subsubsection{#1}
	\vspace{-2mm}}

\newcommand*{\bm}[1]{ {\boldmath \mbox{$ #1 $}}}

% \newcommand*{\mmtlv}{mTLV}
% \newcommand*{\mmtlvgam}{mTLV$_{\gamma}$}
% \newcommand*{\mmtlvsig}{mTLV$_{\sigma}$}
% \newcommand*{\mmtlvgamsig}{mTLV$_{\gamma,\sigma}$}
% \newcommand*{\mmlv}{mLV}
% \newcommand*{\mmt}{mT}
% 
% \newcommand*{\mmtlvs}{mTLV }
% \newcommand*{\mmtlvgams}{mTLV$_{\gamma}$ }
% \newcommand*{\mmtlvsigs}{mTLV$_{\sigma}$ }
% \newcommand*{\mmtlvgamsigs}{mTLV$_{\gamma,\sigma}$ }
% \newcommand*{\mmlvs}{mLV }
% \newcommand*{\mmts}{mT }
% 
% \newcommand*{\onetoN}{\{1,\ 2,\ \dots,\ N \} }
% \newcommand*{\onetoni}{\{1,\ 2,\ \dots,\ n_i \} }
% \newcommand*{\sumYij}{\sum_j Y_{ij}}
% \newcommand*{\sumyij}{\sum_j y_{ij}}
% \newcommand*{\sumXij}{\sum_j X_{ij}}
% \newcommand*{\sumxij}{\sum_j x_{ij}}
% \newcommand*{\sumYit}{\sum_j Y_{i}(t)}
% \newcommand*{\sumyit}{\sum_j y_{i}(t)}
% \newcommand*{\sumXit}{\sum_j X_{i}(t)}
% \newcommand*{\sumxit}{\sum_j x_{i}(t)}
% 
% \newcommand*{\muijcy}{\mu_{ij}^{c,y}}
% \newcommand*{\muijmy}{\mu_{ij}^{m,y}}
% \newcommand*{\muijcz}{\mu_{ij}^{c,z}}
% \newcommand*{\muijmz}{\mu_{ij}^{m,z}}
% 
% 
% \newcommand*{\muijc}{\mu_{ij}^c}
% \newcommand*{\muijm}{\mu_{ij}^m}
% 
% \newcommand*{\muitc}{\mu_{i}^c(t)}
% \newcommand*{\muitm}{\mu_{i}^m(t)}
% 
% \newcommand*{\bmmuic}{\bm{\mu}_{i}^c}
% \newcommand*{\bmmuim}{\bm{\mu}_{i}^m}
% 
% \newcommand*{\bmRi}{\bm{R}_i}
% \newcommand*{\bmri}{\bm{r}_i}
% 
% \newcommand*{\bmZi}{\bm{Z}_i}
% \newcommand*{\bmzi}{\bm{z}_i}
% 
% \newcommand*{\bmDi}{\bm{D}_i}
% \newcommand*{\bmdi}{\bm{d}_i}
% 
% \newcommand*{\bmWi}{\bm{W}_i}
% \newcommand*{\bwdi}{\bm{w}_i}
% 
% \newcommand*{\bmYi}{\bm{Y}_i}
% \newcommand*{\bmyi}{\bm{y}_i}
% \newcommand*{\bmYinot}{\bm{Y}_{i,-1}}
% \newcommand*{\bmyinot}{\bm{y}_{i,-1}}
% 
% \newcommand*{\bmSi}{\bm{S}_i}
% \newcommand*{\bmsi}{\bm{s}_i}
% \newcommand*{\Sij}{S_{ij}}
% \newcommand*{\sij}{s_{ij}}
% 
% 
% \newcommand*{\bmXi}{\bm{X}_i}
% \newcommand*{\bmxi}{\bm{x}_i}
% \newcommand*{\bmXinot}{\bm{X}_{i,-1}}
% \newcommand*{\bmxinot}{\bm{x}_{i,-1}}
% 
% 
% 
% \newcommand*{\bmXij}{\bm{X}_{ij}}
% \newcommand*{\bmxij}{\bm{x}_{ij}}
% 
% \newcommand*{\bmUi}{\bm{U}_i}
% \newcommand*{\bmui}{\bm{u}_i}
% 
% \newcommand*{\bmAi}{\bm{A}_i}
% \newcommand*{\bmai}{\bm{a}_i}
% 
% \newcommand*{\syi}{s(\bmyi)}
% \newcommand*{\sYi}{s(\bmYi)}
% 
% \newcommand*{\sxi}{s(\bmxi)}
% \newcommand*{\sXi}{s(\bmXi)}
% 
% \newcommand*{\bmnu}{\bm{\nu}}
% \newcommand*{\bmNu}{\bm{\Nu}}
% 
% \newcommand*{\Yit}{Y_i(t)}
% \newcommand*{\yit}{y_i(t)}
% \newcommand*{\Yij}{Y_{ij}}
% \newcommand*{\yij}{y_{ij}}
% 
% \newcommand*{\Xit}{X_i(t)}
% \newcommand*{\xit}{x_i(t)}
% \newcommand*{\Xij}{X_{ij}}
% \newcommand*{\xij}{x_{ij}}
% 
% \newcommand*{\Zit}{Z_i(t)}
% \newcommand*{\zit}{z_i(t)}
% \newcommand*{\Zij}{Z_{ij}}
% \newcommand*{\zij}{z_{ij}}
% 
% \newcommand*{\Tij}{T_{ij}}
% \newcommand*{\tij}{t_{ij}}
% 
% \newcommand*{\bmAij}{\bm{A}_{ij}}
% \newcommand*{\bmaij}{\bm{a}_{ij}}
% \newcommand*{\bmAit}{\bm{A}_{i}(t)}
% \newcommand*{\bmait}{\bm{a}_{i}(t)}
% 
% \newcommand*{\etaij}{\eta_{ij}}
% 
% \newcommand*{\bmbeta}{\bm{\beta}}
% \newcommand*{\bmalpha}{\bm{\alpha}}
% \newcommand*{\bmmui}{\bm{\mu}_i}
% \newcommand*{\bmDeltai}{\bm{\Delta}_i}
% 
% \newcommand*{\Yibar}{\overline{Y}_i}
% \newcommand*{\yibar}{\overline{y}_i}
% \newcommand*{\Xibar}{\overline{X}_i}
% \newcommand*{\xibar}{\overline{x}_i}
% 
% \newcommand*{\sumjYij}{\sum_j Y_{ij}}
% \newcommand*{\sumjyij}{\sum_j y_{ij}}
% \newcommand*{\sumtYit}{\sum_t Y_{i}(t)}
% \newcommand*{\sumtyit}{\sum_t y_{i}(t)}
% 
% \newcommand*{\sumjXij}{\sum_j X_{ij}}
% \newcommand*{\sumjxij}{\sum_j x_{ij}}
% 
% \newcommand*{\YitoYini}{\{Y_{i1}, \dots, Y_{in_i}\}}
% \newcommand*{\yitoyini}{\{y_{i1}, \dots, y_{in_i}\}}
% 
% \newcommand*{\XitoXini}{\{X_{i1}, \dots, X_{in_i}\}}
% \newcommand*{\xitoxini}{\{x_{i1}, \dots, x_{in_i}\}}
% 
% \newcommand*{\bmXitobmXini}{\{\bm{X}_{i1}, \dots, \bm{X}_{in_i}\}}
% \newcommand*{\bmxitobmxini}{\{\bm{x}_{i1}, \dots, \bm{x}_{in_i}\}}
% 
% \newcommand*{\piSi}{\pi_{S_i}}
% \newcommand*{\pisi}{\pi_{s_i}}
% 
% \newcommand*{\pisumjyij}{\pi(\sumjyij)}
% \newcommand*{\pibmyistar}{\pi({\bmyi}^*)}
% \newcommand*{\pibmyi}{\pi(\bmyi)}
% \newcommand*{\piyij}{\pi(\yij)}
% \newcommand*{\piyibar}{\pi(\yibar)}
% \newcommand*{\piyione}{\pi(y_{i1})}
% 
% \newcommand*{\pisumjzij}{\pi(\sumjzij)}
% \newcommand*{\pibmzi}{\pi(\bmzi)}
% \newcommand*{\pizij}{\pi(\zij)}
% \newcommand*{\pizibar}{\pi(\zibar)}
% 
% \newcommand*{\pinot}{\pi( \overline{\{0,n_i\}})}
% \newcommand*{\pizero}{\pi(0)}
% \newcommand*{\pione}{\pi(1)}
% \newcommand*{\pini}{\pi(n_i)}
% 
% \newcommand*{\pigtclow}{\pi(\geq c_1)}
% \newcommand*{\piclow}{\pi(<c_1)}
% \newcommand*{\picmid}{\pi(c_1,c_2)}
% \newcommand*{\pichigh}{\pi(>c_2)}
% 
% \newcommand*{\pihbmyi}{\pi[h(\bmyi)]}
% \newcommand*{\pihstarbmyi}{\pi[h^*(\bmyi)]}
% 
% \newcommand*{\iccx}{$\rho_x$}
% \newcommand*{\iccxs}{$\rho_x$ }
% 
% \newcommand*{\icc}[1]{$\rho_{#1}$}
% \newcommand*{\iccs}[1]{$\rho_{#1}$}
% 
% \newcommand*{\p}{\partial}
% \newcommand*{\dLidthetavec}{\frac{\p L_i}{\p \mathbf{\theta}}}
% \newcommand*{\dLicdthetavec}{\frac{\p L_i^c}{\p \mathbf{\theta}}}
% \newcommand*{\dLisdthetavec}{\frac{\p L_i^s}{\p \mathbf{\theta}}}
% \newcommand*{\dLidtheta}[1]{\frac{\p L_i}{\p \theta_{#1}}}
% \newcommand*{\dLidbeta}[1]{\frac{\p L_i}{\p \beta_{#1}}}
% \newcommand*{\dLidgamma}{\frac{\p L_i}{\p \gamma}}
% \newcommand*{\dLidsigma}{\frac{\p L_i}{\p \sigma}}
% \newcommand*{\dsqLidthetasq}{\frac{\p^2 L_i}{\p \theta_{1} \p \theta_{2}}}
% \newcommand*{\dLizdtheta}[1]{\frac{\p L_{i,z}}{\p \theta_{#1}}}
% \newcommand*{\dLizdbeta}[1]{\frac{\p L_{i,z}}{\p \beta_{#1}}}
% \newcommand*{\dLizdgamma}{\frac{\p L_{i,z}}{\p \gamma}}
% \newcommand*{\dLizdsigma}{\frac{\p L_{i,z}}{\p \sigma}}
% \newcommand*{\dsqLizdthetasq}{\frac{\p^2 L_{i,z}}{\p \theta_{1} \p \theta_{2}}}
% 
% \newcommand*{\dsqldthetavecsq}{\frac{\p^2 l}{\p \mathbf{\theta} \p \mathbf{\theta}^t}}
% \newcommand*{\dsqlcdthetavecsq}{\frac{\p^2 l^c}{\p \mathbf{\theta} \p \mathbf{\theta}^t}} 
% \newcommand*{\dsqlsdthetavecsq}{\frac{\p^2 l^s}{\p \mathbf{\theta} \p \mathbf{\theta}^t}} 
% 
% \newcommand*{\dsqldbetasq}{\frac{\p^2 l}{\p {\mathbf{\beta}^m}^2}}
% \newcommand*{\dsqldgammasq}{\frac{\p^2 l}{\p \gamma^2}}
% \newcommand*{\dsqldsigmasq}{\frac{\p^2 l}{\p \sigma^2}}
% \newcommand*{\dsqldbetasigma}{\frac{\p^2 l}{\p \mathbf{\beta}^m \p \sigma}}
% \newcommand*{\dsqldgammasigma}{\frac{\p^2 l}{\p \gamma \p \sigma}}
% \newcommand*{\dsqldbetagamma}{\frac{\p^2 l}{\p \mathbf{\beta}^m \p \gamma}}
% 
% \newcommand*{\dsqldalphasq}{\frac{\p^2 l}{\p \mathbf{\alpha}^2}}
% \newcommand*{\dsqldbetaalpha}{\frac{\p^2 l}{\p \mathbf{\beta}^m \p \mathbf{\alpha}}}
% \newcommand*{\dsqlcdalphasq}{\frac{\p^2 l^c}{\p \mathbf{\alpha}^2}}
% \newcommand*{\dsqlcdbetaalpha}{\frac{\p^2 l^c}{\p \mathbf{\beta}^m \p \mathbf{\alpha}}}
% \newcommand*{\dsqlsdalphasq}{\frac{\p^2 l^s}{\p \mathbf{\alpha}^2}}
% \newcommand*{\dsqlsdbetaalpha}{\frac{\p^2 l^s}{\p \mathbf{\beta}^m \p \mathbf{\alpha}}}
% 
% \newcommand*{\dsqlcdbetasq}{\frac{\p^2 l^c}{\p {\mathbf{\beta}^m}^2}}
% \newcommand*{\dsqlcdgammasq}{\frac{\p^2 l^c}{\p \gamma^2}}
% \newcommand*{\dsqlcdsigmasq}{\frac{\p^2 l^c}{\p \sigma^2}}
% \newcommand*{\dsqlcdbetasigma}{\frac{\p^2 l^c}{\p \mathbf{\beta}^m \p \sigma}}
% \newcommand*{\dsqlcdgammasigma}{\frac{\p^2 l^c}{\p \gamma \p \sigma}}
% \newcommand*{\dsqlcdbetagamma}{\frac{\p^2 l^c}{\p \mathbf{\beta}^m \p \gamma}}
% 
% \newcommand*{\dsqlsdbetasq}{\frac{\p^2 l^s}{\p {\mathbf{\beta}^m}^2}}
% \newcommand*{\dsqlsdgammasq}{\frac{\p^2 l^s}{\p \gamma^2}}
% \newcommand*{\dsqlsdsigmasq}{\frac{\p^2 l^s}{\p \sigma^2}}
% \newcommand*{\dsqlsdbetasigma}{\frac{\p^2 l^s}{\p \mathbf{\beta}^m \p \sigma}}
% \newcommand*{\dsqlsdgammasigma}{\frac{\p^2 l^s}{\p \gamma \p \sigma}}
% \newcommand*{\dsqlsdbetagamma}{\frac{\p^2 l^s}{\p \mathbf{\beta}^m \p \gamma}}
% 
% \newcommand*{\dlidtheta}[1]{\frac{\p l_i}{\p \theta_{#1}}}
% \newcommand*{\dsqlidthetasq}{\frac{\p^2 l_i}{\p \theta_{1} \p \theta_{2}}}
% 
% \newcommand*{\Lizero}{L_{i(0)}}
% \newcommand*{\dLizerodtheta}[1]{\frac{\p L_{i(0)}}{\p \theta_{#1}}}
% \newcommand*{\dsqLizerodthetasq}{\frac{\p^2 L_{i(0)}}{\p \theta_{1} \p \theta_{2}}}
% \newcommand*{\lizero}{l_{i(0)}}
% \newcommand*{\dlizerodtheta}[1]{\frac{\p l_{i(0)}}{\p \theta_{#1}}}
% \newcommand*{\dsqlizerodthetasq}{\frac{\p^2 l_{i(0)}}{\p \theta_{1} \p \theta_{2}}}
% 
% \newcommand*{\Lione}{L_{i(1)}}
% \newcommand*{\dLionedtheta}[1]{\frac{\p L_{i(1)}}{\p \theta_{#1}}}
% \newcommand*{\dsqLionedthetasq}{\frac{\p^2 L_{i(1)}}{\p \theta_{1} \p \theta_{2}}}
% \newcommand*{\lione}{l_{i(1)}}
% \newcommand*{\dlionedtheta}[1]{\frac{\p l_{i(1)}}{\p \theta_{#1}}}
% \newcommand*{\dsqlionedthetasq}{\frac{\p^2 l_{i(1)}}{\p \theta_{1} \p \theta_{2}}}
% 
% \newcommand*{\Litwo}{L_{i(2)}}
% \newcommand*{\litwo}{l_{i(2)}}
% 
% \newcommand*{\Licor}{L_{i,cor}}
% \newcommand*{\dLicordtheta}[1]{\frac{\p L_{i,cor}}{\p \theta_{#1}}}
% \newcommand*{\dsqLicordthetasq}{\frac{\p^2 L_{i,cor}}{\p \theta_{1} \p \theta_{2}}}
% \newcommand*{\licor}{l_{i,cor}}
% \newcommand*{\dlicordtheta}[1]{\frac{\p l_{i,cor}}{\p \theta_{#1}}}
% \newcommand*{\dsqlicordthetasq}{\frac{\p^2 l_{i,cor}}{\p \theta_{1} \p \theta_{2}}}
% 
% \newcommand*{\Lic}{L_i^c}
% \newcommand*{\dLicdtheta}[1]{\frac{\p L_i^c}{\p \theta_{#1}}}
% \newcommand*{\dsqLicdthetasq}{\frac{\p^2 L_i^c}{\p \theta_{1} \p \theta_{2}}}
% \newcommand*{\lic}{l_i^c}
% \newcommand*{\dlicdtheta}[1]{\frac{\p l_i^c}{\p \theta_{#1}}}
% \newcommand*{\dsqlicdthetasq}{\frac{\p^2 l_i^c}{\p \theta_{1} \p \theta_{2}}}
% 
% \newcommand*{\dlcdtheta}[1]{\frac{\p l^c}{\p \theta_{#1}}}
% \newcommand*{\dsqlcdthetasq}{\frac{\p^2 l^c}{\p \theta_{1} \p \theta_{2}}}
% 
% \newcommand*{\dsqldthetasqa}{\frac{\p^2 l}{\p \theta_{1}^2}}
% \newcommand*{\dsqlcdthetasqa}{\frac{\p^2 l^c}{\p \theta_{1}^2}}
% \newcommand*{\dsqlsdthetasqa}{\frac{\p^2 l^s}{\p \theta_{1}^2}}
% 
% \newcommand*{\dDeltadtheta}[1]{\frac{\p \Delta_{ij}}{\p \theta_{#1}}}
% \newcommand*{\dsqDeltadthetasq}{\frac{\p^2 \Delta_{ij}}{\p \theta_{1} \p \theta_{2}}}
% 
% \newcommand*{\dgammadtheta}[1]{\frac{\p \gamma}{\p \theta_{#1}}}
% \newcommand*{\dsqgammadthetasq}{\frac{\p^2 \gamma}{\p \theta_{1} \p \theta_{2}}}
% 
% \newcommand*{\dsigmadtheta}[1]{\frac{\p \sigma}{\p \theta_{#1}}}
% \newcommand*{\dsqsigmadthetasq}{\frac{\p^2 \sigma}{\p \theta_{1} \p \theta_{2}}}
% 
% \newcommand*{\phizdz}{\phi(z_i)dz_i}
% \newcommand*{\mupc}{\mu_{ij}^{pc,z}}
% \newcommand*{\dmupcdtheta}[1]{\frac{\p \mupc}{\p \theta_{#1}}}
% \newcommand*{\dsqmupcdthetasq}{\frac{\p^2 \mupc}{\p \theta_{1} \p \theta_{2}}}
% \newcommand*{\mupclag}{\mu_{ij-1}^{pc,z}}
% \newcommand*{\dmupclagdtheta}[1]{\frac{\p \mupclag}{\p \theta_{#1}}}
% \newcommand*{\dsqmupclagdthetasq}{\frac{\p^2 \mupclag}{\p \theta_{1} \p \theta_{2}}}
% \newcommand*{\hzero}{h_{0,ij}}
% \newcommand*{\hone}{h_{1,ij}}
% \newcommand*{\dhzerodtheta}[1]{\frac{\p \hzero}{\p \theta_{#1}}}
% \newcommand*{\dsqhzerodthetasq}{\frac{\p^2 \hzero}{\p \theta_{1} \p \theta_{2}}}
% \newcommand*{\dhonedtheta}[1]{\frac{\p \hone}{\p \theta_{#1}}}
% \newcommand*{\dsqhonedthetasq}{\frac{\p^2 \hone}{\p \theta_{1} \p \theta_{2}}}
% 
% 
% \newcommand*{\yminmuc}{y_{ij} - \muc}
% \newcommand*{\mum}{\mu_{ij}^m}
% \newcommand*{\dmumdtheta}[1]{\frac{\p \mum}{\p \theta_{#1}}}
% \newcommand*{\dsqmumdthetasq}{\frac{\p^2 \mum}{\p \theta_{1} \p \theta_{2}}}
% \newcommand*{\Rix}{R_i(\bm{X}_i)}
% 
% \newcommand*{\ods}{ODS}
% \newcommand*{\odss}{ODS }

\thispagestyle{empty}
\begin{document}

%% ABSTRACT Page %%
%\newpage
%\thispagestyle{empty}
%\noindent
%{\large \bf Title} \\\\
%\noindent
%\begin{description}
%\item [Tatsuki Koyama, Ph.D.] Principal Investigator, xx\% effort
%\end{description}

%\vspace{10mm}
%\noindent
%{\bf Abstract} \\
%
%\newpage

\bigskip
\appendix 
%\mydate
	
%\setcounter{page}{} % or whatever
%\noindent{\Large\bf Research Plan}
% -- % -- % -- % -- % -- %
% -- % -- % -- % -- % -- %
\mysection{Specific Aims}

\noindent yada yada

\mysubsection{\normalsize Retrospective outcome dependent sampling for longitudinal data}

\noindent blah blah

\mysubsection{\normalsize Prospective subject-specific response biased sampling for longitudinal data}

\noindent woo hoo!

\mysubsection{\normalsize Prospective, time-dependent response biased sampling for longitudinal data}

\noindent hmm

\newpage
\mysection{Background and significance}

\mysubsection{Retrospective outcome dependent sampling for longitudinal data} \label{Back:Aim1}

\noindent ....................

\mysubsubsection{Example: The Childhoood Asthma Management Program (CAMP)}

\noindent .....................

\mysubsection{Prospective, subject-specific response biased sampling for longitudinal data} \label{Back:Aim2}

\noindent .....................................

\mysubsubsection{Example: CAMP}

\noindent .......................

\mysubsection{Prospective, time-dependent response biased sampling for longitudinal data} \label{Back:Aim3}

\noindent..........................

\mysubsubsection{Example: BioCycle Study} \label{BioCycle:Background}

\noindent ......................

\newpage
\mysection{Preliminary Studies}


\newpage
\mysection{Research Design and Methods}

\mysubsection{Aim 1.1: Retrospective, outcome dependent sampling for longitudinal binary response data} \label{Methods:Aim1.1}

\mysubsubsection{Our recent research on ODS for longitudinal data}

\mysubsubsection{Illustration of ODS with conditional maximum likelihood}
% 
% \begin{wrapfigure}[22]{r}{.6\textwidth}
% \vspace*{-1.10cm}
% \hspace*{.24cm}
% %\includegraphics[]{contourplots.pdf} \label{contourplot}
% \includegraphics[width=1\textwidth, height=.55\textwidth]{contourplots.pdf} \label{contourplot}
% \vspace*{-1cm}
% \caption{Log-likelihood Surface Plots}
% \end{wrapfigure}

\mysubsubsection{Proposed generalized sampling strategy with conditional likelihood}


\mysubsection{Aim 1.2: Retrospective, outcome dependent sampling for longitudinal continuous response data} \label{Methods:Aim1.2}

\mysubsubsection{ODS with univariate a response and conditional likelihood}

\mysubsubsection{Simulations}


\mysubsubsection{Application: CAMP} 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mysubsection{Aim 2.1: Prospective, response biased sampling for longitudinal binary response data} \label{Methods:Aim2.1}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\mysubsubsection{Analysis of case-control longitudinal studies}

\mysubsubsection{Proposed general analysis approaches with conditional likelihood}

\mysubsubsection{Proposed semi-parametric estimation}

\mysubsubsection{Simulations}


\mysubsubsection{Application: ADHD Study}  

\mysubsection{Aim 2.2: Prospective subject specific response biased sampling for continuous longitudinal response data}

\mysubsubsection{Proposed conditional likelihood approach}

\mysubsubsection{Simulations}

\mysubsubsection{Applications: CAMP and ADHD Study}

\mysubsection{Aim 3.1: Prospective, time-dependent response biased sampling for longitudinal binary response data}


\mysubsubsection{Partly deterministic sampling}

\mysubsubsection{Proposed conditional likelihood approach with $Z_{ij}$ stochastically related to $Y_{ij}$}


\mysubsubsection{Proposed semi-parametric estimation}

\mysubsubsection{Simulations}

\mysubsubsection{Application: BioCycle Study}

\mysubsection{Aim 3.2: Prospective, time-dependent response biased sampling for continuous response data}

\mysubsubsection{Proposed conditional likelihood approach}


\mysubsubsection{Simulations}

\mysubsubsection{Application: BioCycle Study}


\mysubsection{Software}

\mysubsection{Timeline}

\newpage

\begin{table}[htp]
\begin{center}
\caption[]{Timelines and year at which tasks will be completed}
\begin{tabular}{lcccc} \hline \hline
    & Methods     & Evaluation and         &          &         \\
Aim & developemnt & manusccript submission & Revision & Software \\ \hline
1.1 & Year 1 & Year 2 & Year 3 & Year 4 \\
1.2 & Year 2 & Year 3 & Year 4 &  \\ &&&& \\
2.1 & Year 1 & Year 2 & Year 3 & Year 4 \\
2.2 & Year 2 & Year 3 & Year 4 &  \\ &&&& \\
3.1 & Year 2 & Year 3 & Year 4 & \\
3.2 & Year 3 & Year 3 & Year 4 & \\ \hline \hline
\end{tabular}  
\end{center}
\end{table}
% -- % -- % -- % -- % -- %
% -- % -- % -- % -- % -- %
\newpage

\bibliographystyle{plain}
\nocite*{}
%\nocite*{}%Ande:sepa:1972,Bres:Zhao:logi:1988,Bres:Cain:logi:1988}
\newpage
\bibliography{Bibliography}

\end{document}
