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\begin{document}
\maketitle
\section{Robust Extraction of Quantitative Information from Histology Images}
\paragraph{Quentin Caudron Romain Garnier \emph{with Bryan Grenfell and Andrea
Graham}}
\subsubsection{Outline}
\begin{itemize}
\itemsep1pt\parskip0pt\parsep0pt
\item
Image processing
\item
Extracted measures
\item
Preliminary analysis
\item
Future directions
\end{itemize}
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\item
Age as random effect \textless{}---
\end{enumerate}
{[}``interface\_hepatitis'', ``confluent\_necrosis'',
``portal\_inflammation'', ``ln\_ap\_ri''{]}
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\PY{n}{plt}\PY{o}{.}\PY{n}{axes}\PY{p}{(}\PY{n}{aspect} \PY{o}{=} \PY{l+m+mi}{1}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{gca}\PY{p}{(}\PY{p}{)}\PY{o}{.}\PY{n}{add\PYZus{}artist}\PY{p}{(}\PY{n}{c}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{p1} \PY{o}{/} \PY{n}{norms}\PY{p}{,} \PY{n}{p2} \PY{o}{/} \PY{n}{norms}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{xlim}\PY{p}{(}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{ylim}\PY{p}{(}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}
\PY{k}{for} \PY{n}{i}\PY{p}{,} \PY{n}{text} \PY{o+ow}{in} \PY{n+nb}{enumerate}\PY{p}{(}\PY{n}{df}\PY{o}{.}\PY{n}{columns}\PY{p}{)} \PY{p}{:}
\PY{n}{plt}\PY{o}{.}\PY{n}{annotate}\PY{p}{(}\PY{n}{text}\PY{p}{,} \PY{n}{xy} \PY{o}{=} \PY{p}{[}\PY{n}{p1}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{p}{,} \PY{n}{p2}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{p}{]}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{tight\PYZus{}layout}\PY{p}{(}\PY{p}{)}
\PY{k}{def} \PY{n+nf}{test\PYZus{}all\PYZus{}linear}\PY{p}{(}\PY{n}{df}\PY{p}{,} \PY{n}{y}\PY{p}{,} \PY{n}{x}\PY{p}{,} \PY{n}{return\PYZus{}significant} \PY{o}{=} \PY{n+nb+bp}{False}\PY{p}{,} \PY{n}{group} \PY{o}{=} \PY{n+nb+bp}{None}\PY{p}{)} \PY{p}{:}
\PY{c}{\PYZsh{} All possible combinations of independent variables}
\PY{n}{independent} \PY{o}{=} \PY{n}{combinatorial}\PY{p}{(}\PY{n}{x}\PY{p}{)}
\PY{n}{fits} \PY{o}{=} \PY{p}{\PYZob{}}\PY{p}{\PYZcb{}}
\PY{n}{pval} \PY{o}{=} \PY{p}{\PYZob{}}\PY{p}{\PYZcb{}}
\PY{n}{linmodels} \PY{o}{=} \PY{p}{\PYZob{}}\PY{p}{\PYZcb{}}
\PY{n}{qsum} \PY{o}{=} \PY{p}{\PYZob{}}\PY{p}{\PYZcb{}}
\PY{n}{aic} \PY{o}{=} \PY{p}{\PYZob{}}\PY{p}{\PYZcb{}}
\PY{c}{\PYZsh{} For all dependent variables, one at a time}
\PY{k}{for} \PY{n}{dependent} \PY{o+ow}{in} \PY{n}{y} \PY{p}{:}
\PY{k}{print} \PY{l+s}{\PYZdq{}}\PY{l+s}{Fitting for }\PY{l+s+si}{\PYZpc{}s}\PY{l+s}{.}\PY{l+s}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n}{dependent}
\PY{c}{\PYZsh{} For all combinations of independent variables}
\PY{k}{for} \PY{n}{covariate} \PY{o+ow}{in} \PY{n}{independent} \PY{p}{:}
\PY{c}{\PYZsh{} Standard mixed model}
\PY{k}{if} \PY{n}{group} \PY{o+ow}{is} \PY{n+nb+bp}{None} \PY{p}{:}
\PY{c}{\PYZsh{} Fit a linear model}
\PY{n}{subset} \PY{o}{=} \PY{n}{delayer}\PY{p}{(}\PY{p}{[}\PY{n}{covariate}\PY{p}{,} \PY{n}{dependent}\PY{p}{]}\PY{p}{)}
\PY{n}{df2} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{n}{delayer}\PY{p}{(}\PY{n}{subset}\PY{p}{)}\PY{p}{]}\PY{o}{.}\PY{n}{dropna}\PY{p}{(}\PY{p}{)}
\PY{n}{df2}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{ones}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{df2}\PY{p}{)}\PY{p}{)}
\PY{n}{ols} \PY{o}{=} \PY{n}{sm}\PY{o}{.}\PY{n}{GLS}\PY{p}{(}\PY{n}{endog} \PY{o}{=} \PY{n}{df2}\PY{p}{[}\PY{n}{dependent}\PY{p}{]}\PY{p}{,} \PY{n}{exog} \PY{o}{=} \PY{n}{df2}\PY{p}{[}\PY{n}{delayer}\PY{p}{(}\PY{p}{[}\PY{n}{covariate}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{)}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{fit}\PY{p}{(}\PY{p}{)}
\PY{c}{\PYZsh{} Save the results}
\PY{k}{if} \PY{p}{(}\PY{n}{return\PYZus{}significant} \PY{o+ow}{and} \PY{n}{ols}\PY{o}{.}\PY{n}{f\PYZus{}pvalue} \PY{o}{\PYZlt{}} \PY{l+m+mf}{0.05}\PY{p}{)} \PY{o+ow}{or} \PY{p}{(}\PY{o+ow}{not} \PY{n}{return\PYZus{}significant}\PY{p}{)} \PY{p}{:}
\PY{n}{linmodels}\PY{o}{.}\PY{n}{setdefault}\PY{p}{(}\PY{n}{dependent}\PY{p}{,} \PY{p}{[}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{ols}\PY{p}{)}
\PY{n}{fits}\PY{o}{.}\PY{n}{setdefault}\PY{p}{(}\PY{n}{dependent}\PY{p}{,} \PY{p}{[}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{ols}\PY{o}{.}\PY{n}{rsquared}\PY{p}{)}
\PY{n}{pval}\PY{o}{.}\PY{n}{setdefault}\PY{p}{(}\PY{n}{dependent}\PY{p}{,} \PY{p}{[}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{ols}\PY{o}{.}\PY{n}{f\PYZus{}pvalue}\PY{p}{)}
\PY{n}{aic}\PY{o}{.}\PY{n}{setdefault}\PY{p}{(}\PY{n}{dependent}\PY{p}{,} \PY{p}{[}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{ols}\PY{o}{.}\PY{n}{aic}\PY{p}{)}
\PY{c}{\PYZsh{} Mixed effects model}
\PY{k}{else} \PY{p}{:}
\PY{n}{subset} \PY{o}{=} \PY{n}{delayer}\PY{p}{(}\PY{p}{[}\PY{n}{covariate}\PY{p}{,} \PY{n}{dependent}\PY{p}{,} \PY{n}{group}\PY{p}{]}\PY{p}{)}
\PY{n}{df2} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{n}{delayer}\PY{p}{(}\PY{n}{subset}\PY{p}{)}\PY{p}{]}\PY{o}{.}\PY{n}{dropna}\PY{p}{(}\PY{p}{)}
\PY{c}{\PYZsh{} Fit a mixed effects model}
\PY{n}{ols} \PY{o}{=} \PY{n}{MixedLM}\PY{p}{(}\PY{n}{endog} \PY{o}{=} \PY{n}{df2}\PY{p}{[}\PY{n}{dependent}\PY{p}{]}\PY{p}{,} \PY{n}{exog} \PY{o}{=} \PY{n}{df2}\PY{p}{[}\PY{n}{covariate}\PY{p}{]}\PY{p}{,} \PY{n}{groups} \PY{o}{=} \PY{n}{df2}\PY{p}{[}\PY{n}{group}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{fit}\PY{p}{(}\PY{p}{)}
\PY{c}{\PYZsh{} Calculate AIC}
\PY{n}{linmodels}\PY{o}{.}\PY{n}{setdefault}\PY{p}{(}\PY{n}{dependent}\PY{p}{,} \PY{p}{[}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{ols}\PY{p}{)}
\PY{n}{fits}\PY{o}{.}\PY{n}{setdefault}\PY{p}{(}\PY{n}{dependent}\PY{p}{,} \PY{p}{[}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{l+m+mi}{2} \PY{o}{*} \PY{p}{(}\PY{n}{ols}\PY{o}{.}\PY{n}{k\PYZus{}fe} \PY{o}{+} \PY{l+m+mi}{1}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{l+m+mi}{2} \PY{o}{*} \PY{n}{ols}\PY{o}{.}\PY{n}{llf}\PY{p}{)}
\PY{n}{pval}\PY{o}{.}\PY{n}{setdefault}\PY{p}{(}\PY{n}{dependent}\PY{p}{,} \PY{p}{[}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{ols}\PY{o}{.}\PY{n}{pvalues}\PY{p}{)}
\PY{k}{if} \PY{n}{group} \PY{o+ow}{is} \PY{o+ow}{not} \PY{n+nb+bp}{None} \PY{p}{:}
\PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n}{y} \PY{p}{:}
\PY{n}{f} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{n}{fits}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{p}{)}
\PY{n}{models} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{n}{linmodels}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{p}{)}
\PY{n}{idx} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{where}\PY{p}{(}\PY{n}{f} \PY{o}{\PYZhy{}} \PY{n}{f}\PY{o}{.}\PY{n}{min}\PY{p}{(}\PY{p}{)} \PY{o}{\PYZlt{}}\PY{o}{=} \PY{l+m+mi}{2}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}
\PY{n}{bestmodelDoF} \PY{o}{=} \PY{p}{[}\PY{n}{j}\PY{o}{.}\PY{n}{k\PYZus{}fe} \PY{k}{for} \PY{n}{j} \PY{o+ow}{in} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{n}{linmodels}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{p}{)}\PY{p}{[}\PY{n}{idx}\PY{p}{]}\PY{p}{]}
\PY{n}{bestmodels} \PY{o}{=} \PY{p}{[}\PY{n}{idx}\PY{p}{[}\PY{n}{j}\PY{p}{]} \PY{k}{for} \PY{n}{j} \PY{o+ow}{in} \PY{n}{np}\PY{o}{.}\PY{n}{where}\PY{p}{(}\PY{n}{bestmodelDoF} \PY{o}{==} \PY{n}{np}\PY{o}{.}\PY{n}{min}\PY{p}{(}\PY{n}{bestmodelDoF}\PY{p}{)}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{]}
\PY{n}{qsum}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{models}\PY{p}{[}\PY{n}{idx}\PY{p}{[}\PY{n}{np}\PY{o}{.}\PY{n}{where}\PY{p}{(}\PY{n}{f}\PY{p}{[}\PY{n}{bestmodels}\PY{p}{]} \PY{o}{==} \PY{n}{np}\PY{o}{.}\PY{n}{min}\PY{p}{(}\PY{n}{f}\PY{p}{[}\PY{n}{bestmodels}\PY{p}{]}\PY{p}{)}\PY{p}{)}\PY{p}{]}\PY{p}{]}
\PY{k}{return} \PY{n}{linmodels}\PY{p}{,} \PY{n}{fits}\PY{p}{,} \PY{n}{pval}\PY{p}{,} \PY{n}{qsum}
\PY{k}{return} \PY{n}{linmodels}\PY{p}{,} \PY{n}{fits}\PY{p}{,} \PY{n}{pval}\PY{p}{,} \PY{n}{aic}
\PY{k}{def} \PY{n+nf}{summary}\PY{p}{(}\PY{n}{models}\PY{p}{)} \PY{p}{:}
\PY{c}{\PYZsh{} Generate list of everything}
\PY{n}{r2} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{n}{m}\PY{o}{.}\PY{n}{r2} \PY{k}{for} \PY{n}{dependent} \PY{o+ow}{in} \PY{n}{models}\PY{o}{.}\PY{n}{keys}\PY{p}{(}\PY{p}{)} \PY{k}{for} \PY{n}{m} \PY{o+ow}{in} \PY{n}{models}\PY{p}{[}\PY{n}{dependent}\PY{p}{]}\PY{p}{]}\PY{p}{)}
\PY{n}{p} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{n}{m}\PY{o}{.}\PY{n}{f\PYZus{}stat}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{p\PYZhy{}value}\PY{l+s}{\PYZdq{}}\PY{p}{]} \PY{k}{for} \PY{n}{dependent} \PY{o+ow}{in} \PY{n}{models}\PY{o}{.}\PY{n}{keys}\PY{p}{(}\PY{p}{)} \PY{k}{for} \PY{n}{m} \PY{o+ow}{in} \PY{n}{models}\PY{p}{[}\PY{n}{dependent}\PY{p}{]}\PY{p}{]}\PY{p}{)}
\PY{n}{mod} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{n}{m} \PY{k}{for} \PY{n}{dependent} \PY{o+ow}{in} \PY{n}{models}\PY{o}{.}\PY{n}{keys}\PY{p}{(}\PY{p}{)} \PY{k}{for} \PY{n}{m} \PY{o+ow}{in} \PY{n}{models}\PY{p}{[}\PY{n}{dependent}\PY{p}{]}\PY{p}{]}\PY{p}{)}
\PY{n}{dependent} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{n}{dependent} \PY{k}{for} \PY{n}{dependent} \PY{o+ow}{in} \PY{n}{models}\PY{o}{.}\PY{n}{keys}\PY{p}{(}\PY{p}{)} \PY{k}{for} \PY{n}{m} \PY{o+ow}{in} \PY{n}{models}\PY{p}{[}\PY{n}{dependent}\PY{p}{]}\PY{p}{]}\PY{p}{)}
\PY{c}{\PYZsh{} Sort by R2}
\PY{n}{idx} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{argsort}\PY{p}{(}\PY{n}{r2}\PY{p}{)}\PY{p}{[}\PY{p}{:}\PY{p}{:}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]}
\PY{c}{\PYZsh{} Output string}
\PY{n}{s} \PY{o}{=} \PY{l+s}{\PYZdq{}}\PY{l+s+si}{\PYZpc{}d}\PY{l+s}{ significant regressions.}\PY{l+s+se}{\PYZbs{}n}\PY{l+s+se}{\PYZbs{}n}\PY{l+s}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n+nb}{len}\PY{p}{(}\PY{n}{r2}\PY{p}{)}
\PY{n}{s} \PY{o}{+}\PY{o}{=} \PY{l+s}{\PYZdq{}}\PY{l+s}{Ten most correlated :}\PY{l+s+se}{\PYZbs{}n}\PY{l+s+se}{\PYZbs{}n}\PY{l+s}{\PYZdq{}}
\PY{c}{\PYZsh{} Print a summary of the top ten correlations}
\PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n}{idx}\PY{p}{[}\PY{p}{:}\PY{l+m+mi}{10}\PY{p}{]} \PY{p}{:}
\PY{n}{s} \PY{o}{+}\PY{o}{=} \PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s+si}{\PYZpc{}s}\PY{l+s}{ \PYZti{} }\PY{l+s+si}{\PYZpc{}s}\PY{l+s+se}{\PYZbs{}n}\PY{l+s}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{p}{(}\PY{n}{dependent}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{ + }\PY{l+s}{\PYZdq{}}\PY{o}{.}\PY{n}{join}\PY{p}{(}\PY{n}{mod}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{o}{.}\PY{n}{x}\PY{o}{.}\PY{n}{columns}\PY{p}{[}\PY{p}{:}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{p}{)}\PY{p}{)}
\PY{n}{s} \PY{o}{+}\PY{o}{=} \PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{R\PYZca{}2 = }\PY{l+s+si}{\PYZpc{}f}\PY{l+s+se}{\PYZbs{}t}\PY{l+s}{p = }\PY{l+s+si}{\PYZpc{}f}\PY{l+s+se}{\PYZbs{}n}\PY{l+s+se}{\PYZbs{}n}\PY{l+s}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{p}{(}\PY{n}{r2}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{p}{,} \PY{n}{p}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{k}{print} \PY{n}{s}
\PY{k}{def} \PY{n+nf}{rstr}\PY{p}{(}\PY{n}{y}\PY{p}{,} \PY{n}{x}\PY{p}{)} \PY{p}{:}
\PY{n}{formatstr} \PY{o}{=} \PY{l+s}{\PYZdq{}}\PY{l+s+si}{\PYZpc{}s}\PY{l+s}{ \PYZti{} }\PY{l+s}{\PYZdq{}} \PY{o}{\PYZpc{}} \PY{n}{y}
\PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n}{x}\PY{p}{[}\PY{p}{:}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]} \PY{p}{:}
\PY{n}{formatstr} \PY{o}{+}\PY{o}{=} \PY{n+nb}{str}\PY{p}{(}\PY{n}{i}\PY{p}{)}
\PY{n}{formatstr} \PY{o}{+}\PY{o}{=} \PY{l+s}{\PYZdq{}}\PY{l+s}{ + }\PY{l+s}{\PYZdq{}}
\PY{n}{formatstr} \PY{o}{+}\PY{o}{=} \PY{n+nb}{str}\PY{p}{(}\PY{n}{x}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}
\PY{k}{return} \PY{n}{formatstr}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}14}]:} \PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k+kn}{as} \PY{n+nn}{np}
\PY{k+kn}{from} \PY{n+nn}{sklearn.neighbors} \PY{k+kn}{import} \PY{n}{KernelDensity}
\PY{k+kn}{from} \PY{n+nn}{matplotlib} \PY{k+kn}{import} \PY{n}{rcParams}
\PY{k+kn}{import} \PY{n+nn}{matplotlib.pyplot} \PY{k+kn}{as} \PY{n+nn}{plt}
\PY{k+kn}{import} \PY{n+nn}{seaborn}
\PY{k+kn}{import} \PY{n+nn}{pandas} \PY{k+kn}{as} \PY{n+nn}{pd}
\PY{k+kn}{import} \PY{n+nn}{itertools}
\PY{k+kn}{from} \PY{n+nn}{sklearn} \PY{k+kn}{import} \PY{n}{linear\PYZus{}model}\PY{p}{,} \PY{n}{ensemble}\PY{p}{,} \PY{n}{decomposition}\PY{p}{,} \PY{n}{cross\PYZus{}validation}\PY{p}{,} \PY{n}{preprocessing}
\PY{k+kn}{from} \PY{n+nn}{statsmodels.regression.mixed\PYZus{}linear\PYZus{}model} \PY{k+kn}{import} \PY{n}{MixedLM}
\PY{k+kn}{import} \PY{n+nn}{statsmodels.api} \PY{k+kn}{as} \PY{n+nn}{sm}
\PY{k+kn}{from} \PY{n+nn}{statsmodels.regression.linear\PYZus{}model} \PY{k+kn}{import} \PY{n}{OLSResults}
\PY{k+kn}{from} \PY{n+nn}{statsmodels.tools.tools} \PY{k+kn}{import} \PY{n}{add\PYZus{}constant}
\PY{o}{\PYZpc{}}\PY{k}{matplotlib} \PY{n}{inline}
\PY{n}{rcParams}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{figure.figsize}\PY{l+s}{\PYZdq{}}\PY{p}{]} \PY{o}{=} \PY{p}{(}\PY{l+m+mi}{14}\PY{p}{,} \PY{l+m+mi}{8}\PY{p}{)}
\PY{c}{\PYZsh{} RAW DATA}
\PY{n}{raw\PYZus{}physical} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{read\PYZus{}csv}\PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{../data/physical.csv}\PY{l+s}{\PYZdq{}}\PY{p}{)}
\PY{n}{raw\PYZus{}histo} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{read\PYZus{}csv}\PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{../data/tawfik.csv}\PY{l+s}{\PYZdq{}}\PY{p}{)}
\PY{n}{ent} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{read\PYZus{}csv}\PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{../4x/results/entropy.csv}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{o}{.}\PY{n}{drop}\PY{p}{(}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Unnamed: 0}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{)}
\PY{n}{foci} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{read\PYZus{}csv}\PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{../4x/results/foci.csv}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{o}{.}\PY{n}{drop}\PY{p}{(}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Unnamed: 0}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{)}
\PY{n}{lac} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{read\PYZus{}csv}\PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{../4x/results/normalised\PYZus{}lacunarity.csv}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{o}{.}\PY{n}{drop}\PY{p}{(}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Unnamed: 0}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{)}
\PY{n}{gabor} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{read\PYZus{}csv}\PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{../4x/results/gabor\PYZus{}filters.csv}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{o}{.}\PY{n}{drop}\PY{p}{(}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Unnamed: 0}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{)}
\PY{n}{ts} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{read\PYZus{}csv}\PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{../4x/results/tissue\PYZus{}sinusoid\PYZus{}ratio.csv}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{o}{.}\PY{n}{drop}\PY{p}{(}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Unnamed: 0}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{)}
\PY{n}{raw\PYZus{}image} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{merge}\PY{p}{(}\PY{n}{lac}\PY{p}{,} \PY{n}{ent}\PY{p}{,}
\PY{n}{on}\PY{o}{=}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Sheep}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Image}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{merge}\PY{p}{(}\PY{n}{foci}\PY{p}{,}
\PY{n}{on}\PY{o}{=}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Sheep}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Image}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{merge}\PY{p}{(}\PY{n}{gabor}\PY{p}{,}
\PY{n}{on}\PY{o}{=}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Sheep}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Image}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{merge}\PY{p}{(}\PY{n}{ts}\PY{p}{,}
\PY{n}{on}\PY{o}{=}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Sheep}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Image}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{)}
\PY{n}{raw\PYZus{}image}\PY{o}{.}\PY{n}{rename}\PY{p}{(}\PY{n}{columns} \PY{o}{=} \PY{p}{\PYZob{}} \PY{l+s}{\PYZdq{}}\PY{l+s}{meanSize}\PY{l+s}{\PYZdq{}} \PY{p}{:} \PY{l+s}{\PYZdq{}}\PY{l+s}{FociSize}\PY{l+s}{\PYZdq{}}\PY{p}{,}
\PY{l+s}{\PYZdq{}}\PY{l+s}{TSRatio}\PY{l+s}{\PYZdq{}} \PY{p}{:} \PY{l+s}{\PYZdq{}}\PY{l+s}{TissueToSinusoid}\PY{l+s}{\PYZdq{}}\PY{p}{,}
\PY{l+s}{\PYZdq{}}\PY{l+s}{Count}\PY{l+s}{\PYZdq{}} \PY{p}{:} \PY{l+s}{\PYZdq{}}\PY{l+s}{FociCount}\PY{l+s}{\PYZdq{}} \PY{p}{\PYZcb{}}\PY{p}{,} \PY{n}{inplace}\PY{o}{=}\PY{n+nb+bp}{True}\PY{p}{)}
\PY{c}{\PYZsh{} CLEAN DATA}
\PY{n}{physcols} \PY{o}{=} \PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Weight}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Sex}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{AgeAtDeath}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Foreleg}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Hindleg}\PY{l+s}{\PYZdq{}}\PY{p}{]}
\PY{n}{imagecols} \PY{o}{=} \PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Entropy}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Lacunarity}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Inflammation}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Scale}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Directionality}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{FociCount}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{FociSize}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{TissueToSinusoid}\PY{l+s}{\PYZdq{}}\PY{p}{]}
\PY{n}{histcols} \PY{o}{=} \PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Lobular\PYZus{}collapse}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Interface\PYZus{}hepatitis}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Confluent\PYZus{}necrosis}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Ln\PYZus{}ap\PYZus{}ri}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Portal\PYZus{}inflammation}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{BD\PYZus{}hyperplasia}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Fibrosis}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{TawfikTotal}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Mean\PYZus{}hep\PYZus{}size}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Min\PYZus{}hep\PYZus{}size}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Max\PYZus{}hep\PYZus{}size}\PY{l+s}{\PYZdq{}}\PY{p}{]}
\PY{c}{\PYZsh{} IMAGE}
\PY{c}{\PYZsh{} Set FociSize to zero if FociCount is zero}
\PY{c}{\PYZsh{} Drop stdSize}
\PY{n}{image} \PY{o}{=} \PY{n}{raw\PYZus{}image}
\PY{n}{image} \PY{o}{=} \PY{n}{image}\PY{o}{.}\PY{n}{drop}\PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{stdSize}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{)}
\PY{n}{image}\PY{o}{.}\PY{n}{FociSize}\PY{p}{[}\PY{n}{raw\PYZus{}image}\PY{o}{.}\PY{n}{FociCount} \PY{o}{==} \PY{l+m+mi}{0}\PY{p}{]} \PY{o}{=} \PY{l+m+mi}{0}
\PY{c}{\PYZsh{} HISTO}
\PY{n}{histo} \PY{o}{=} \PY{n}{raw\PYZus{}histo}
\PY{n}{histo} \PY{o}{=} \PY{n}{histo}\PY{o}{.}\PY{n}{drop}\PY{p}{(}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Vessels}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Vacuol}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Pigment}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Std\PYZus{}hep\PYZus{}size}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{)}
\PY{c}{\PYZsh{} PHYSICAL}
\PY{n}{physical} \PY{o}{=} \PY{n}{raw\PYZus{}physical}
\PY{n}{physical} \PY{o}{=} \PY{n}{physical}\PY{o}{.}\PY{n}{drop}\PY{p}{(}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{CurrTag}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{DeathDate}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Category}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{)}
\PY{n}{physical}
\PY{c}{\PYZsh{} COMPLETE DATASET}
\PY{n}{raw\PYZus{}data} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{merge}\PY{p}{(}\PY{n}{pd}\PY{o}{.}\PY{n}{merge}\PY{p}{(}\PY{n}{image}\PY{p}{,} \PY{n}{histo}\PY{p}{,} \PY{n}{on}\PY{o}{=}\PY{l+s}{\PYZdq{}}\PY{l+s}{Sheep}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{n}{how}\PY{o}{=}\PY{l+s}{\PYZdq{}}\PY{l+s}{outer}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{p}{,} \PY{n}{physical}\PY{p}{,} \PY{n}{on}\PY{o}{=}\PY{l+s}{\PYZdq{}}\PY{l+s}{Sheep}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{n}{how}\PY{o}{=}\PY{l+s}{\PYZdq{}}\PY{l+s}{outer}\PY{l+s}{\PYZdq{}}\PY{p}{)}
\PY{n}{raw\PYZus{}data}\PY{o}{.}\PY{n}{to\PYZus{}csv}\PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{../data/tentative\PYZus{}complete.csv}\PY{l+s}{\PYZdq{}}\PY{p}{)}
\PY{c}{\PYZsh{} AVERAGED BY SHEEP}
\PY{n}{data} \PY{o}{=} \PY{n}{raw\PYZus{}data}
\PY{n}{data}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Inflammation}\PY{l+s}{\PYZdq{}}\PY{p}{]} \PY{o}{=} \PY{n}{data}\PY{o}{.}\PY{n}{FociCount} \PY{o}{*} \PY{n}{data}\PY{o}{.}\PY{n}{FociSize}
\PY{n}{sheep} \PY{o}{=} \PY{n}{rescale}\PY{p}{(}\PY{n}{data}\PY{o}{.}\PY{n}{groupby}\PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{Sheep}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)}\PY{p}{)}
\PY{n}{age} \PY{o}{=} \PY{n}{rescale}\PY{p}{(}\PY{n}{data}\PY{o}{.}\PY{n}{groupby}\PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{AgeAtDeath}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{p}{)}\PY{p}{)}
\PY{c}{\PYZsh{} REGRESSIONS : fixed effects, grouped by sheep}
\PY{n}{df} \PY{o}{=} \PY{n}{sheep}\PY{p}{[}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Portal\PYZus{}inflammation}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{FociSize}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{]}\PY{o}{.}\PY{n}{dropna}\PY{p}{(}\PY{p}{)}
\PY{n}{df}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{ones}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{df}\PY{p}{)}\PY{p}{)}
\PY{n}{portal\PYZus{}inflammation} \PY{o}{=} \PY{n}{sm}\PY{o}{.}\PY{n}{GLS}\PY{p}{(}\PY{n}{endog} \PY{o}{=} \PY{n}{df}\PY{o}{.}\PY{n}{Portal\PYZus{}inflammation}\PY{p}{,} \PY{n}{exog} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{FociSize}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{fit}\PY{p}{(}\PY{p}{)}\PY{o}{.}\PY{n}{summary}\PY{p}{(}\PY{p}{)}
\PY{c}{\PYZsh{}portal\PYZus{}inflammation = portal\PYZus{}inflammation.summary()}
\PY{k}{del} \PY{n}{portal\PYZus{}inflammation}\PY{o}{.}\PY{n}{tables}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}
\PY{n}{df} \PY{o}{=} \PY{n}{sheep}\PY{p}{[}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{BD\PYZus{}hyperplasia}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Scale}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Directionality}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{FociSize}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{]}\PY{o}{.}\PY{n}{dropna}\PY{p}{(}\PY{p}{)}
\PY{n}{df}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{ones}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{df}\PY{p}{)}\PY{p}{)}
\PY{n}{hyperplasia} \PY{o}{=} \PY{n}{sm}\PY{o}{.}\PY{n}{GLS}\PY{p}{(}\PY{n}{endog} \PY{o}{=} \PY{n}{df}\PY{o}{.}\PY{n}{BD\PYZus{}hyperplasia}\PY{p}{,} \PY{n}{exog} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{FociSize}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Scale}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Directionality}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{fit}\PY{p}{(}\PY{p}{)}\PY{o}{.}\PY{n}{summary}\PY{p}{(}\PY{p}{)}
\PY{c}{\PYZsh{}hyperplasia.summary()}
\PY{k}{del} \PY{n}{hyperplasia}\PY{o}{.}\PY{n}{tables}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}
\PY{c}{\PYZsh{} REGRESSIONS : fixed effects, grouped by age}
\PY{n}{df} \PY{o}{=} \PY{n}{age}\PY{p}{[}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Max\PYZus{}hep\PYZus{}size}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Entropy}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Directionality}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{]}\PY{o}{.}\PY{n}{dropna}\PY{p}{(}\PY{p}{)}
\PY{n}{df}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{ones}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{df}\PY{p}{)}\PY{p}{)}
\PY{n}{maxhepsize} \PY{o}{=} \PY{n}{sm}\PY{o}{.}\PY{n}{GLS}\PY{p}{(}\PY{n}{endog} \PY{o}{=} \PY{n}{df}\PY{o}{.}\PY{n}{Max\PYZus{}hep\PYZus{}size}\PY{p}{,} \PY{n}{exog} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Entropy}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Directionality}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{fit}\PY{p}{(}\PY{p}{)}\PY{o}{.}\PY{n}{summary}\PY{p}{(}\PY{p}{)}
\PY{k}{del} \PY{n}{maxhepsize}\PY{o}{.}\PY{n}{tables}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}
\PY{n}{df} \PY{o}{=} \PY{n}{age}\PY{p}{[}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Lobular\PYZus{}collapse}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{FociSize}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{]}\PY{o}{.}\PY{n}{dropna}\PY{p}{(}\PY{p}{)}
\PY{n}{df}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{ones}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{df}\PY{p}{)}\PY{p}{)}
\PY{n}{lobular\PYZus{}collapse} \PY{o}{=} \PY{n}{sm}\PY{o}{.}\PY{n}{GLS}\PY{p}{(}\PY{n}{endog} \PY{o}{=} \PY{n}{df}\PY{o}{.}\PY{n}{Lobular\PYZus{}collapse}\PY{p}{,} \PY{n}{exog} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{FociSize}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{fit}\PY{p}{(}\PY{p}{)}\PY{o}{.}\PY{n}{summary}\PY{p}{(}\PY{p}{)}
\PY{k}{del} \PY{n}{lobular\PYZus{}collapse}\PY{o}{.}\PY{n}{tables}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}
\PY{n}{df} \PY{o}{=} \PY{n}{age}\PY{p}{[}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Interface\PYZus{}hepatitis}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Lacunarity}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{]}\PY{o}{.}\PY{n}{dropna}\PY{p}{(}\PY{p}{)}
\PY{n}{df}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{ones}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{df}\PY{p}{)}\PY{p}{)}
\PY{n}{interface\PYZus{}hepatitis} \PY{o}{=} \PY{n}{sm}\PY{o}{.}\PY{n}{GLS}\PY{p}{(}\PY{n}{endog} \PY{o}{=} \PY{n}{df}\PY{o}{.}\PY{n}{Interface\PYZus{}hepatitis}\PY{p}{,} \PY{n}{exog} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Lacunarity}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{fit}\PY{p}{(}\PY{p}{)}\PY{o}{.}\PY{n}{summary}\PY{p}{(}\PY{p}{)}
\PY{k}{del} \PY{n}{interface\PYZus{}hepatitis}\PY{o}{.}\PY{n}{tables}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}
\PY{n}{df} \PY{o}{=} \PY{n}{age}\PY{p}{[}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Fibrosis}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Inflammation}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{]}\PY{o}{.}\PY{n}{dropna}\PY{p}{(}\PY{p}{)}
\PY{n}{df}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{ones}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{df}\PY{p}{)}\PY{p}{)}
\PY{n}{fibrosis} \PY{o}{=} \PY{n}{sm}\PY{o}{.}\PY{n}{GLS}\PY{p}{(}\PY{n}{endog} \PY{o}{=} \PY{n}{df}\PY{o}{.}\PY{n}{Fibrosis}\PY{p}{,} \PY{n}{exog} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Inflammation}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{fit}\PY{p}{(}\PY{p}{)}\PY{o}{.}\PY{n}{summary}\PY{p}{(}\PY{p}{)}
\PY{k}{del} \PY{n}{fibrosis}\PY{o}{.}\PY{n}{tables}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}
\PY{c}{\PYZsh{} PCA}
\PY{n}{s} \PY{o}{=} \PY{n}{sheep}\PY{o}{.}\PY{n}{dropna}\PY{p}{(}\PY{n}{subset}\PY{o}{=}\PY{n}{delayer}\PY{p}{(}\PY{p}{[}\PY{n}{imagecols}\PY{p}{,} \PY{n}{histcols}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{n}{pca} \PY{o}{=} \PY{n}{decomposition}\PY{o}{.}\PY{n}{PCA}\PY{p}{(}\PY{n}{n\PYZus{}components}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{)}
\PY{n}{pcax} \PY{o}{=} \PY{n}{pca}\PY{o}{.}\PY{n}{fit\PYZus{}transform}\PY{p}{(}\PY{n}{s}\PY{p}{[}\PY{n}{imagecols}\PY{p}{]}\PY{p}{)}
\PY{n}{pcay} \PY{o}{=} \PY{n}{pca}\PY{o}{.}\PY{n}{fit\PYZus{}transform}\PY{p}{(}\PY{n}{s}\PY{p}{[}\PY{n}{histcols}\PY{p}{]}\PY{p}{)}
\PY{n}{pca} \PY{o}{=} \PY{n}{sm}\PY{o}{.}\PY{n}{GLS}\PY{p}{(}\PY{n}{endog} \PY{o}{=} \PY{n}{pcay}\PY{p}{[}\PY{p}{:}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{]}\PY{p}{[}\PY{p}{:}\PY{p}{,} \PY{n}{np}\PY{o}{.}\PY{n}{newaxis}\PY{p}{]}\PY{p}{,} \PY{n}{exog} \PY{o}{=} \PY{n}{add\PYZus{}constant}\PY{p}{(}\PY{n}{pcax}\PY{p}{)}\PY{p}{)}\PY{o}{.}\PY{n}{fit}\PY{p}{(}\PY{p}{)}\PY{o}{.}\PY{n}{summary}\PY{p}{(}\PY{p}{)}
\PY{k}{del} \PY{n}{pca}\PY{o}{.}\PY{n}{tables}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}
\PY{c}{\PYZsh{} REGRESSIONS : mixed effects, intercept on age at death}
\PY{n}{df} \PY{o}{=} \PY{n}{age}\PY{p}{[}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Fibrosis}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Inflammation}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{]}\PY{o}{.}\PY{n}{dropna}\PY{p}{(}\PY{p}{)}
\PY{n}{df}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{ones}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{df}\PY{p}{)}\PY{p}{)}
\PY{n}{fibrosis} \PY{o}{=} \PY{n}{sm}\PY{o}{.}\PY{n}{GLS}\PY{p}{(}\PY{n}{endog} \PY{o}{=} \PY{n}{df}\PY{o}{.}\PY{n}{Fibrosis}\PY{p}{,} \PY{n}{exog} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{Inflammation}\PY{l+s}{\PYZdq{}}\PY{p}{,} \PY{l+s}{\PYZdq{}}\PY{l+s}{Intercept}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{fit}\PY{p}{(}\PY{p}{)}\PY{o}{.}\PY{n}{summary}\PY{p}{(}\PY{p}{)}
\PY{k}{del} \PY{n}{fibrosis}\PY{o}{.}\PY{n}{tables}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}19}]:} \PY{n}{a} \PY{o}{=} \PY{n}{portal\PYZus{}inflammation}\PY{o}{.}\PY{n}{summary}\PY{p}{(}\PY{p}{)}
\PY{k}{del} \PY{n}{a}\PY{o}{.}\PY{n}{tables}\PY{p}{[}\PY{l+m+mi}{2}\PY{p}{]}
\PY{n}{a}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}19}]:} <class 'statsmodels.iolib.summary.Summary'>
"""
GLS Regression Results
===============================================================================
Dep. Variable: Portal\_inflammation R-squared: 0.280
Model: GLS Adj. R-squared: 0.273
Method: Least Squares F-statistic: 37.34
Date: Tue, 28 Oct 2014 Prob (F-statistic): 2.12e-08
Time: 23:35:30 Log-Likelihood: 14.996
No. Observations: 98 AIC: -25.99
Df Residuals: 96 BIC: -20.82
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [95.0\% Conf. Int.]
------------------------------------------------------------------------------
FociSize 0.5627 0.092 6.111 0.000 0.380 0.746
Intercept 0.3368 0.043 7.855 0.000 0.252 0.422
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
\end{Verbatim}
\subsection{Image Processing}
\subsubsection{Extraction}
\begin{itemize}
\itemsep1pt\parskip0pt\parsep0pt
\item
Automagical
\item
Reasonably quick
\end{itemize}
\subsubsection{Robust}
\begin{itemize}
\itemsep1pt\parskip0pt\parsep0pt
\item
Invariant to staining, slicing, field-related variation
\item
Capture intersample variation
\end{itemize}
\begin{figure}[htbp]
\centering
\includegraphics{figures/robust3.jpg}
\caption{image}
\end{figure}
\begin{figure}[htbp]
\centering
\includegraphics{figures/robust4.jpg}
\caption{image}
\end{figure}
\begin{figure}[htbp]
\centering
\includegraphics{figures/robust1.jpg}
\caption{image}
\end{figure}
\begin{figure}[htbp]
\centering
\includegraphics{figures/robust2.jpg}
\caption{image}
\end{figure}
\subsection{Structural and Textural Measures}
\begin{itemize}
\itemsep1pt\parskip0pt\parsep0pt
\item
characteristic \textbf{scale} of sinusoid widths
\item
\textbf{directional} amplitude of preferred sinusoid alignment
\item
\textbf{tissue to sinusoid} ratio
\item
\textbf{count} of inflammatory foci per image
\item
\textbf{mean size} of inflammatory foci per image
\item
information \textbf{entropy} of sinusoid distribution
\item
\textbf{lacunarity} ( clustering ) of sinusoids
\end{itemize}
\begin{figure}[htbp]
\centering
\includegraphics{figures/intra.png}
\caption{image}
\end{figure}
\begin{figure}[htbp]
\centering
\includegraphics{figures/inter2.png}
\caption{image}
\end{figure}
\subsection{Exploratory Analysis}
\subsubsection{by individual}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}29}]:} \PY{n}{portal\PYZus{}inflammation}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}29}]:} <class 'statsmodels.iolib.summary.Summary'>
"""
GLS Regression Results
===============================================================================
Dep. Variable: Portal\_inflammation R-squared: 0.280
Model: GLS Adj. R-squared: 0.273
Method: Least Squares F-statistic: 37.34
Date: Tue, 28 Oct 2014 Prob (F-statistic): 2.12e-08
Time: 23:40:10 Log-Likelihood: 14.996
No. Observations: 98 AIC: -25.99
Df Residuals: 96 BIC: -20.82
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [95.0\% Conf. Int.]
------------------------------------------------------------------------------
FociSize 0.5627 0.092 6.111 0.000 0.380 0.746
Intercept 0.3368 0.043 7.855 0.000 0.252 0.422
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
\end{Verbatim}
\begin{figure}[htbp]
\centering
\includegraphics{figures/portal_inflammation.png}
\caption{image}
\end{figure}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}31}]:} \PY{n}{hyperplasia}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}31}]:} <class 'statsmodels.iolib.summary.Summary'>
"""
GLS Regression Results
==============================================================================
Dep. Variable: BD\_hyperplasia R-squared: 0.306
Model: GLS Adj. R-squared: 0.284
Method: Least Squares F-statistic: 13.83
Date: Tue, 28 Oct 2014 Prob (F-statistic): 1.52e-07
Time: 23:40:10 Log-Likelihood: -3.9632
No. Observations: 98 AIC: 15.93
Df Residuals: 94 BIC: 26.27
Df Model: 3
Covariance Type: nonrobust
==================================================================================
coef std err t P>|t| [95.0\% Conf. Int.]
----------------------------------------------------------------------------------
FociSize 0.6698 0.113 5.902 0.000 0.444 0.895
Scale 0.5811 0.243 2.394 0.019 0.099 1.063
Directionality -0.4419 0.190 -2.330 0.022 -0.819 -0.065
Intercept -0.0504 0.079 -0.642 0.523 -0.206 0.105
==================================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
\end{Verbatim}
\begin{figure}[htbp]
\centering
\includegraphics{figures/hyperplasia.png}
\caption{image}
\end{figure}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}15}]:} \PY{n}{pca}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}15}]:} <class 'statsmodels.iolib.summary.Summary'>
"""
GLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.075
Model: GLS Adj. R-squared: 0.065
Method: Least Squares F-statistic: 7.723
Date: Wed, 29 Oct 2014 Prob (F-statistic): 0.00657
Time: 14:38:47 Log-Likelihood: -70.082
No. Observations: 97 AIC: 144.2
Df Residuals: 95 BIC: 149.3
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [95.0\% Conf. Int.]
------------------------------------------------------------------------------
const -2.949e-17 0.051 -5.77e-16 1.000 -0.102 0.102
x1 0.3865 0.139 2.779 0.007 0.110 0.663
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
\end{Verbatim}
\begin{figure}[htbp]
\centering
\includegraphics{figures/pca.png}
\caption{image}
\end{figure}
\subsection{Exploratory Analysis}
\subsubsection{by age class}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}6}]:} \PY{n}{fibrosis}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}6}]:} <class 'statsmodels.iolib.summary.Summary'>
"""
GLS Regression Results
==============================================================================
Dep. Variable: Fibrosis R-squared: 0.800
Model: GLS Adj. R-squared: 0.778
Method: Least Squares F-statistic: 36.07
Date: Wed, 29 Oct 2014 Prob (F-statistic): 0.000201
Time: 11:13:48 Log-Likelihood: 7.8003
No. Observations: 11 AIC: -11.60
Df Residuals: 9 BIC: -10.80
Df Model: 1
Covariance Type: nonrobust
================================================================================
coef std err t P>|t| [95.0\% Conf. Int.]
--------------------------------------------------------------------------------
Inflammation 1.0159 0.169 6.006 0.000 0.633 1.399
Intercept -0.0105 0.083 -0.126 0.902 -0.198 0.177
================================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
\end{Verbatim}
\begin{figure}[htbp]
\centering
\includegraphics{figures/fibrosis.png}
\caption{image}
\end{figure}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}7}]:} \PY{n}{lobular\PYZus{}collapse}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}7}]:} <class 'statsmodels.iolib.summary.Summary'>
"""
GLS Regression Results
==============================================================================
Dep. Variable: Lobular\_collapse R-squared: 0.586
Model: GLS Adj. R-squared: 0.540
Method: Least Squares F-statistic: 12.73
Date: Wed, 29 Oct 2014 Prob (F-statistic): 0.00605
Time: 11:13:48 Log-Likelihood: 2.2626
No. Observations: 11 AIC: -0.5252
Df Residuals: 9 BIC: 0.2706
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [95.0\% Conf. Int.]
------------------------------------------------------------------------------
FociSize 1.1379 0.319 3.567 0.006 0.416 1.860
Intercept 0.0460 0.159 0.289 0.779 -0.314 0.406
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
\end{Verbatim}
\begin{figure}[htbp]
\centering
\includegraphics{figures/lobular_collapse.png}
\caption{image}
\end{figure}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}8}]:} \PY{n}{interface\PYZus{}hepatitis}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}8}]:} <class 'statsmodels.iolib.summary.Summary'>
"""
GLS Regression Results
===============================================================================
Dep. Variable: Interface\_hepatitis R-squared: 0.659
Model: GLS Adj. R-squared: 0.621
Method: Least Squares F-statistic: 17.38
Date: Wed, 29 Oct 2014 Prob (F-statistic): 0.00242
Time: 11:13:48 Log-Likelihood: 2.3063
No. Observations: 11 AIC: -0.6126
Df Residuals: 9 BIC: 0.1832
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [95.0\% Conf. Int.]
------------------------------------------------------------------------------
Lacunarity -1.0224 0.245 -4.168 0.002 -1.577 -0.468
Intercept 0.9504 0.143 6.669 0.000 0.628 1.273
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
\end{Verbatim}
\begin{figure}[htbp]
\centering
\includegraphics{figures/interface_hepatitis.png}
\caption{image}
\end{figure}
\subsection{Exploratory analysis}
\subsubsection{with a random effect on age at death}
\begin{longtable}[c]{@{}lcl@{}}
\toprule\addlinespace
Dependent variable & Models AIC \textless{} 2 + AICmin & Primary
explanatory variables ( ordered )
\\\addlinespace
\midrule\endhead
Ishak score & 7 & entropy, tissue-to-sinusoid, focus count, focus size
\\\addlinespace
Lobular collapse & 5 & entropy, lacunarity, tissue-to-sinusoid, focus
count
\\\addlinespace
Confluent necrosis & 1 & entropy
\\\addlinespace
Interface hepatitis & 2 & entropy, tissue-to-sinusoid
\\\addlinespace
Portal inflammation & 4 & entropy, focus size, lacunarity, focus count,
scale, directionality
\\\addlinespace
Fibrosis & 2 & entropy, lacunarity, tissue-to-sinusoid
\\\addlinespace
Biliary hyperplasia & 1 & focus size
\\\addlinespace
Necrosis, apoptosis, random inflammation & 2 & entropy, lacunarity
\\\addlinespace
\bottomrule
\end{longtable}
\paragraph{Measures we like}
\begin{itemize}
\itemsep1pt\parskip0pt\parsep0pt
\item
entropy consistently explains histological measures when controlled
for age
\item
also important : tissue to sinusoid ratio, focus count and size,
lacunarity
\end{itemize}
\subsection{Future directions}
\subsubsection{Further exploration of the dataset}
\begin{itemize}
\item
145 sheep ( 89 females )
\item
11 age classes
\item
\end{itemize}
\begin{itemize}
\itemsep1pt\parskip0pt\parsep0pt
\item
4460 entries across 27 variables
\item
3330 with full image and histological information
\item
1196 for which \textbf{complete} information is available
\end{itemize}
\subsubsection{Narrow-field images}
\begin{itemize}
\itemsep1pt\parskip0pt\parsep0pt
\item
12536 images
\item
spatial distribution of nuclei
\end{itemize}
\begin{figure}[htbp]
\centering
\includegraphics{figures/10.jpg}
\caption{image}
\end{figure}
\begin{figure}[htbp]
\centering
\includegraphics{figures/Processed2.jpg}
\caption{image}
\end{figure}
\begin{figure}[htbp]
\centering
\includegraphics{figures/Segmented.jpg}
\caption{image}
\end{figure}
% Add a bibliography block to the postdoc
\end{document}
Datasets
Models
