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tables-diff-exp-questions.tex
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tables-diff-exp-questions.tex
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\begin{frame}
\frametitle{Comparing two groups}
\textblockcolour{white}
\TPMargin{7pt}
\begin{textblock*}{153mm}(2mm,13mm)
\renewcommand{\arraystretch}{1.5}
\begin{tabular}{>{\centering}m{2.92cm} c c p{1.0cm} m{1.92cm}}
\hline
\hline
Example question & Model & $H_0$ & Test & Other \\
\hline
\hline
Is the expression of MYC different between Cancer (C) and Non-cancer (N)
patients? & $MYC \sim Group$ & $\mu_{\textsc{nc}} = \mu_{\textsc{c}}$ & t-test& \\
\hline
Is the expression of any genes in this array different between Cancer (C)
and Non-cancer (N) patients? & $\begin{aligned} MYC & \sim Group\\
P53 & \sim Group\\
\ldots &\\
\ldots & \sim Group
\end{aligned}$
&
$\begin{aligned} \mu_{\textsc{nc}}^{\textsc{myc}} & = \mu_{\textsc{c}}^{\textsc{myc}}\\
\mu_{\textsc{nc}}^{\textsc{p53}} & = \mu_{\textsc{c}}^{\textsc{p53}}\\
\ldots & \\
\mu_{\textsc{nc}}^{\ldots} & = \mu_{\textsc{c}}^{\ldots}
\end{aligned}$
&Many t-tests & Empirical Bayes (EB). FDR\\
\hline
Is the expression of MYC different between Cancer (C) and Non-cancer (N)
patients when we control for other factors (age, sex, \ldots)? & $MYC \sim
Group + Age + Sex$ & $\mu_{\textsc{nc}} = \mu_{\textsc{c}}$ & t-test &
{\tiny Type or relationship of others (non-linear, etc). Interactions}\\
\hline
Is the expression of any genes in this array different between Cancer (C) and Non-cancer
(N) patients when we control for other factors?&
$\begin{aligned}
MYC & \sim Group + Age + Sex\\
P53 & \sim Group + Age + Sex\\
\ldots& \\
\ldots & \sim Group + Age + Sex
\end{aligned}$
&
$\begin{aligned} \mu_{\textsc{nc}}^{\textsc{myc}} & = \mu_{\textsc{c}}^{\textsc{myc}}\\
\mu_{\textsc{nc}}^{\textsc{p53}} & = \mu_{\textsc{c}}^{\textsc{p53}}\\
\ldots & \\
\mu_{\textsc{nc}}^{\ldots} & = \mu_{\textsc{c}}^{\ldots}
\end{aligned}$
&Many t-tests & Empirical Bayes. FDR. {\tiny Type or relationship of others (non-linear, etc). Interactions}\\
\hline
\end{tabular}
\end{textblock*}
\end{frame}
\begin{frame}
\frametitle{Comparing three or more groups}
\renewcommand{\arraystretch}{1.5}
%\begin{tabular}{p{5.0cm}ccp{2.2cm}p{2.0cm}}
%\begin{tabular}{>{\centering}m{4.9cm} c c m{1.8cm} m{1.8cm}}
\textblockcolour{white}
\TPMargin{5pt}
\begin{textblock*}{153mm}(-1mm,8mm)
\renewcommand{\arraystretch}{1.5}
\begin{tabular}{>{\centering}m{2.12cm} c c p{1.0cm} m{1.52cm}}
% \begin{tabular}{>{\centering}m{4.3cm} c c p{1.8cm} m{1.8cm}}
\hline
\hline
Example question & Model & $H_0$ & Test & Other \\
\hline
\hline
Is the expression of MYC different between patients with Colon (C),
Prostate (P),
Lung (L), and Neck (N) cancer? & $MYC \sim Group$ &
$\mu_{\textsc{c}} = \mu_{\textsc{p}} = \mu_{\textsc{l}} =
\mu_{\textsc{n}}$ & ANOVA \qquad {\tiny (F test)}& Might want to do some
pairwise comparisons.\\
\hline
Is the expression of any genes in this array different between patients with Colon (C),
Prostate (P), Lung (L), and Neck (N) cancer? &
$\begin{aligned} MYC & \sim Group\\
P53 & \sim Group\\
\ldots &\\
\ldots & \sim Group
\end{aligned}$
&
$\begin{aligned}
\mu_{\textsc{c}}^{\textsc{myc}} & = \mu_{\textsc{p}}^{\textsc{myc}} =
\mu_{\textsc{l}}^{\textsc{myc}} = \mu_{\textsc{n}}^{\textsc{myc}}\\
\mu_{\textsc{c}}^{\textsc{p53}} & = \mu_{\textsc{p}}^{\textsc{p53}} =
\mu_{\textsc{l}}^{\textsc{p53}} = \mu_{\textsc{n}}^{\textsc{p53}}\\
\ldots & \\
\mu_{\textsc{c}}^{\textsc{\ldots}} & = \mu_{\textsc{p}}^{\textsc{\ldots}} =
\mu_{\textsc{l}}^{\textsc{\ldots}} = \mu_{\textsc{n}}^{\textsc{\ldots}}\\
\end{aligned}$
& Many ANOVAs & EB. FDR. Might want to do some
pairwise comparisons.\\
\hline
Is the expression of MYC different between patients with Colon (C),
Prostate (P),
Lung (L), and Neck (N) cancer when we control for other factors?
& $MYC \sim Group + Age + Sex$ &
$\mu_{\textsc{c}} = \mu_{\textsc{p}} = \mu_{\textsc{l}} =
\mu_{\textsc{n}}$ & ANOVA & Might want to do some
pairwise comparisons. {\tiny Type or relationship of others (non-linear, etc). Interactions}\\
\hline
Is the expression of any genes in this array different between patients with Colon (C),
Prostate (P),
Lung (L), and Neck (N) cancer when we control for other factors?&
$\begin{aligned} MYC & \sim Group + Age + Sex\\
P53 & \sim Group + Age + Sex\\
\ldots &\\
\ldots & \sim Group + Age + Sex\end{aligned}$
&
$\begin{aligned}
\mu_{\textsc{c}}^{\textsc{myc}} & = \mu_{\textsc{p}}^{\textsc{myc}} =
\mu_{\textsc{l}}^{\textsc{myc}} = \mu_{\textsc{n}}^{\textsc{myc}}\\
\mu_{\textsc{c}}^{\textsc{p53}}& = \mu_{\textsc{p}}^{\textsc{p53}} =
\mu_{\textsc{l}}^{\textsc{p53}} = \mu_{\textsc{n}}^{\textsc{p53}}\\
\ldots & \\
\mu_{\textsc{c}}^{\textsc{\ldots}} & = \mu_{\textsc{p}}^{\textsc{\ldots}} =
\mu_{\textsc{l}}^{\textsc{\ldots}} = \mu_{\textsc{n}}^{\textsc{\ldots}}\\
\end{aligned}$
& Many ANOVAs& EB. FDR. Might want to do some
pairwise comparisons. {\tiny Type or relationship of others (non-linear, etc). Interactions} \\
\hline
\end{tabular}
\end{textblock*}
\end{frame}
\begin{frame}
\frametitle{Relationship with a numerical variable: regression}
\renewcommand{\arraystretch}{1.5}
%\begin{tabular}{p{5.0cm}ccp{2.2cm}p{2.0cm}}
%\begin{tabular}{>{\centering}m{4.9cm} c c m{1.8cm} m{1.8cm}}
\textblockcolour{white}
\TPMargin{8pt}
\begin{textblock*}{153mm}(4mm,18mm)
\renewcommand{\arraystretch}{1.5}
\begin{tabular}{>{\centering}m{2.92cm} c c p{1.0cm} m{1.92cm}}
% \begin{tabular}{>{\centering}m{4.3cm} c c p{1.8cm} m{1.8cm}}
\hline
\hline
Example question & Model & $H_0$ & Test & Other \\
\hline
\hline
Does the expression of MYC change (increase or decrease) with (as we
increase) cholesterol (numerical
variable)? & $MYC \sim cholest$ & $\beta = 0$ &Regression\quad {\tiny t-test} &
{\tiny (Non-linear?)}\\
\hline
\\
Does the expression of any genes in this array change with cholesterol?&
$\begin{aligned}
MYC & \sim cholest\\
P53 & \sim cholest\\
\ldots& \\
\ldots & \sim cholest
\end{aligned}$
&
$\begin{aligned}
\beta^{\textsc{myc}} &= 0\\
\beta^{\textsc{p53}} &= 0\\
\ldots\\
\beta^{\textsc{\ldots}} &= 0
\end{aligned}$
&
Many regressions
&
Empirical Bayes.
FDR
\\
\hline
Does the expression of MYC change with cholesterol when we control
for other factors? & $MYC \sim cholest + Age + Sex$ & $\beta = 0$
&Regression & {\tiny Type or relationship of others (non-linear, etc). Interactions}
\\
\hline
\\
Does the expression of any genes in this array change with cholesterol
when we control for other factors?&
$\begin{aligned}
MYC & \sim cholest + Age + Sex\\
P53 & \sim cholest + Age + Sex\\
\ldots& \\
\ldots & \sim cholest + Age + Sex
\end{aligned}$
&
$\begin{aligned}
\beta^{\textsc{myc}} &= 0\\
\beta^{\textsc{p53}} &= 0\\
\ldots\\
\beta^{\textsc{\ldots}} &= 0
\end{aligned}$
&
Many regressions
&
Empirical Bayes.
FDR. {\tiny Type or relationship of others (non-linear, etc). Interactions}
\\
\hline
\end{tabular}
\end{textblock*}
\end{frame}