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\begin{document}
\vspace*{0.2in}

% Title must be 250 characters or less.
\begin{flushleft}
{\Large
\textbf\newline{Using machine learning models to predict the initiation of renal replacement therapy among chronic kidney disease patients}
}
\newline
% Insert author names, affiliations and corresponding author email (do not include titles, positions, or degrees).
\\
Erik Dovgan\textsuperscript{1*},
Anton Gradišek\textsuperscript{1},
Mitja Luštrek\textsuperscript{1},
Mohy Uddin\textsuperscript{2},
Aldilas Achmad Nursetyo\textsuperscript{3},
Sashi Kiran Annavarajula\textsuperscript{4},
Yu-Chuan Li\textsuperscript{3},
Shabbir Syed-Abdul\textsuperscript{3*}
\\
\bigskip
\textbf{1} Jožef Stefan Institute, Department of Intelligent Systems, Jamova cesta 39, SI-1000 Ljubljana, Slovenia
\\
\textbf{2} Executive Office, King Abdullah International Medical Research Center, King Saud bin Abdulaziz University for Health Sciences, Ministry of National Guard -- Health Affairs, Riyadh, Kingdom of Saudi Arabia
\\
\textbf{3} Taipei Medical University, Graduate Institute of Biomedical Informatics, College of Medical Science and Technology, Taipei, Taiwan
\\
\textbf{4} Yashoda Hospitals, Department of  Nephrology, Malakpet, Hyderabad, India
\\
\bigskip

% Use the asterisk to denote corresponding authorship and provide email address in note below.
* erik.dovgan@ijs.si, drshabbir@tmu.edu.tw
\end{flushleft}


\section*{Supporting information}

The tables in this section show:
\begin{itemize}
\item \nameref{tab:Tab1s}-\nameref{tab:Tab5s}: Statistics of AUC for each feature selection approach, data preprocessing and ML algorithm independently when predicting twelve months ahead. 
\item \nameref{tab:Tab6s}-\nameref{tab:Tab7s}: Top 10 algorithms in combination with data processing, when predicting six- and three- months ahead respectively.
\item \nameref{tab:Tab8s}-\nameref{tab:Tab9s}: Confusion matrices for six- and three- months-ahead prediction using Logistic Regression.
\item \nameref{tab:Tab10s}-\nameref{tab:Tab12s}: Confusion matrices for models that are built and tested on data of all patients or of patients with diabetes only. 
\markwithcolor{\item \nameref{tab:Tab13s}: Statistics on the comorbidities in the dataset, including RRT and hazard ratio (HR) for each prediction period.}
\end{itemize}


\paragraph*{Table S1.} {\bf AUCs of approaches for obtaining features.}
\label{tab:Tab1s}
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
  & Mean & Std & Min & 25 \% & 50 \% & 75 \% & Max	\\
\thickhline
Raw & 0.676 & 0.066 & 0.561 & 0.625 & 0.694 & 0.705 & 0.765	\\
\hline
Percentage & 0.642 & 0.137 & 0.321 & 0.575 & 0.686 & 0.746 & 0.769	\\
\hline
Boolean & 0.685 & 0.074 & 0.561 & 0.631 & 0.702 & 0.746 & 0.767	\\
\hline
Time & 0.665 & 0.097 & 0.497 & 0.595 & 0.693 & 0.752 & \textbf{0.773}	\\
\hline
\end{tabular}
\end{center}

\paragraph*{Table S2.} {\bf AUCs of feature selection approaches.}
\label{tab:Tab2s}
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
  & Mean & Std & Min & 25 \% & 50 \% & 75 \% & Max	\\
\thickhline
None & 0.676 & 0.066 & 0.561 & 0.625 & 0.694 & 0.705 & \textbf{0.765}	\\
\hline
Correlations & 0.573 & 0.014 & 0.549 & 0.560 & 0.576 & 0.586 & 0.587	\\
\hline
Comorbidities & 0.568 & 0.056 & 0.498 & 0.527 & 0.557 & 0.619 & 0.657	\\
\hline
SHL & 0.552 & 0.023 & 0.509 & 0.535 & 0.563 & 0.568 & 0.569	\\
\hline
\end{tabular}
\end{center}

\paragraph*{Table S3.} {\bf AUCs of filtering approaches.}
\label{tab:Tab3s}
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
  & Mean & Std & Min & 25 \% & 50 \% & 75 \% & Max	\\
\thickhline
None & 0.676 & 0.066 & 0.561 & 0.625 & 0.694 & 0.705 & \textbf{0.765}	\\
\hline
Diabetes & 0.650 & 0.059 & 0.544 & 0.616 & 0.656 & 0.689 & 0.732	\\
\hline
\end{tabular}
\end{center}

\paragraph*{Table S4.} {\bf AUCs of dimensionality reduction approaches.}
\label{tab:Tab4s}
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
  & Mean & Std & Min & 25 \% & 50 \% & 75 \% & Max	\\
\thickhline
None & 0.676 & 0.066 & 0.561 & 0.625 & 0.694 & 0.705 & \textbf{0.765}	\\
\hline
PCA & 0.649 & 0.057 & 0.548 & 0.626 & 0.644 & 0.681 & 0.729	\\
\hline
\end{tabular}
\end{center}

\paragraph*{Table S5.} {\bf AUCs of ML algorithms.}
\label{tab:Tab5s}
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
  & Mean & Std & Min & 25 \% & 50 \% & 75 \% & Max	\\
\thickhline
Decision tree & 0.577 & 0.037 & 0.512 & 0.549 & 0.580 & 0.602 & 0.660	\\
\hline
Bagging Decision Tree & 0.629 & 0.065 & 0.526 & 0.560 & 0.641 & 0.690 & 0.707	\\
\hline
Random Forest & 0.620 & 0.056 & 0.527 & 0.561 & 0.627 & 0.670 & 0.697	\\
\hline
XGBoost & 0.691 & 0.060 & 0.568 & 0.654 & 0.698 & 0.736 & 0.767	\\
\hline
SVM & 0.613 & 0.135 & 0.269 & 0.594 & 0.635 & 0.691 & 0.762	\\
\hline
SGD & 0.673 & 0.064 & 0.527 & 0.643 & 0.671 & 0.731 & 0.768	\\
\hline
Nearest Neighbors & 0.582 & 0.029 & 0.512 & 0.566 & 0.581 & 0.602 & 0.632	\\
\hline
Naive Bayes & 0.574 & 0.070 & 0.498 & 0.511 & 0.554 & 0.651 & 0.696	\\
\hline
Logistic Regression & 0.687 & 0.059 & 0.569 & 0.649 & 0.675 & 0.739 & \textbf{0.773}	\\
\hline
Neural Network & 0.639 & 0.053 & 0.538 & 0.596 & 0.662 & 0.672 & 0.706	\\
\hline
\end{tabular}
\end{center}

\paragraph*{Table S6.} {\bf Top 10 algorithms in combination with data processing, when predicting six months ahead. Results are sorted with respect to AUC.}
\label{tab:Tab6s}
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
Model & Features & Balance & AUC & Sensitivity & Specificity	\\
\thickhline
Logistic Regression & time & no & 0.791 & 0.059 & 0.995	\\
    \hline
SGD Classifier & time & no & 0.790 & 0.055 & 0.995	\\
    \hline
XGBoost & raw & no & 0.785 & 0.021 & 0.999	\\
    \hline
XGBoost & boolean & no & 0.782 & 0.018 & 0.999	\\
    \hline
XGBoost & percentage & no & 0.781 & 0.016 & 0.999	\\
    \hline
SGD Classifier & time & yes & 0.780 & 0.630 & 0.794	\\
    \hline
XGBoost & time & no & 0.778 & 0.017 & 0.999	\\
    \hline
Logistic Regression & time & yes & 0.778 & 0.568 & 0.832	\\
    \hline
XGBoost & raw & yes & 0.778 & 0.562 & 0.834	\\
    \hline
Logistic Regression & percentage & no & 0.777 & 0.020 & 0.998	\\
    \hline
\end{tabular}
\end{center}

\paragraph*{Table S7.} {\bf Top 10 algorithms in combination with data processing, when predicting three months ahead. Results are sorted with respect to AUC.}
\label{tab:Tab7s}
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
Model & Features & Balance & AUC & Sensitivity & Specificity	\\
\thickhline
SGD & time & no & 0.801 & 0.017 & 0.999	\\
    \hline
Logistic Regression & time & no & 0.798 & 0.031 & 0.998	\\
    \hline
XGBoost & time & no & 0.793 & 0.008 & 1.000	\\
    \hline
XGBoost & raw & no & 0.792 & 0.008 & 0.999	\\
    \hline
XGBoost & boolean & no & 0.789 & 0.012 & 1.000	\\
    \hline
XGBoost & percentage & no & 0.788 & 0.004 & 1.000	\\
    \hline
Logistic Regression & percentage & no & 0.784 & 0.002 & 0.999	\\
    \hline
SGD & percentage & no & 0.784 & 0.002 & 0.999	\\
    \hline
XGBoost & boolean & yes & 0.782 & 0.548 & 0.847	\\
    \hline
SGD & percentage & yes & 0.781 & 0.514 & 0.838	\\
    \hline
\end{tabular}
\end{center}

\paragraph*{Table S8.} {\bf Confusion matrix for six-months-ahead prediction.}
\label{tab:Tab8s}
\begin{center}
\begin{tabular}{|c|c|c|c|}
\cline{3-4}
\multicolumn{1}{c}{} & & \multicolumn{2}{|c|}{Predicted} \\
\cline{3-4}
\multicolumn{1}{c}{} &  & No & Yes \\ 
\hline
\multirow{2}{*}{True} & No & 10351 & 2087	\\
\cline{2-4}
 & Yes & 328 & 432	\\
\hline
\end{tabular}
\end{center}

\paragraph*{Table S9.} {\bf Confusion matrix for three-months-ahead prediction.}
\label{tab:Tab9s}
\begin{center}
\begin{tabular}{|c|c|c|c|}
\cline{3-4}
\multicolumn{1}{c}{} & & \multicolumn{2}{|c|}{Predicted} \\
\cline{3-4}
\multicolumn{1}{c}{} &  & No & Yes \\ 
\hline
\multirow{2}{*}{True} & No & 13639 & 2170	\\
\cline{2-4}
 & Yes & 256 & 260	\\
\hline
\end{tabular}
\end{center}

\paragraph*{Table S10.} {\bf Confusion matrix for the model that was built on data of all patients and tested on data of all patients.}
\label{tab:Tab10s}
\begin{center}
\begin{tabular}{|c|c|c|c|}
\cline{3-4}
\multicolumn{1}{c}{} & & \multicolumn{2}{|c|}{Predicted} \\
\cline{3-4}
\multicolumn{1}{c}{} &  & No & Yes \\ 
\hline
\multirow{2}{*}{True} & No & 5819 & 1628	\\
\cline{2-4}
 & Yes & 394 & 651	\\
\hline
\end{tabular}
\end{center}

\paragraph*{Table S11.} {\bf Confusion matrix for the model that was built on data of patients with diabetes and tested on data of patients with diabetes.}
\label{tab:Tab11s}
\begin{center}
\begin{tabular}{|c|c|c|c|}
\cline{3-4}
\multicolumn{1}{c}{} & & \multicolumn{2}{|c|}{Predicted} \\
\cline{3-4}
\multicolumn{1}{c}{} &  & No & Yes \\ 
\hline
\multirow{2}{*}{True} & No & 2028 & 570	\\
\cline{2-4}
 & Yes & 225 & 281	\\
\hline
\end{tabular}
\end{center}

\paragraph*{Table S12.} {\bf Confusion matrix for the model that was built on data of all patients and tested on data of patients with diabetes.}
\label{tab:Tab12s}
\begin{center}
\begin{tabular}{|c|c|c|c|}
\cline{3-4}
\multicolumn{1}{c}{} & & \multicolumn{2}{|c|}{Predicted} \\
\cline{3-4}
\multicolumn{1}{c}{} &  & No & Yes \\ 
\hline
\multirow{2}{*}{True} & No & 1789 & 809	\\
\cline{2-4}
 & Yes & 154 & 352	\\
\hline
\end{tabular}
\end{center}




\begin{sidewaystable}[!ht]
\centering
\color{\markedcolor}
\paragraph*{Table S13.} {\bf Statistics on the comorbidities in the dataset, including RRT and hazard ratio (HR) for each prediction period.}
\label{tab:Tab13s}
\begin{adjustbox}{max width=1.1\textwidth,max height=0.8\textheight,center}
\begin{tabular}{|p{3cm}|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline		
\multirow{2}{*}{Comorbidity}	& \multirow{2}{*}{No.\ cases}	& \multicolumn{4}{c|}{One year} &	\multicolumn{4}{c|}{Six months} &	\multicolumn{4}{c|}{Three months}\\
\cline{3-14}
 & & No.\ ca\-ses	& With RRT	& Without RRT	& HR	& No.\ cases	& With RRT	& Without RRT	& HR	& No.\ cases	& With RRT	& Without RRT	& HR\\
\thickhline
All patients&19954&8492&1045&7447&&13198&760&12438&&16325&516&15809&\\ 
\hline
Diabetes&6506 (33\%)&3123 (37\%)&508 (49\%)&2615 (35\%)&1.4&4545 (34\%)&357 (47\%)&4188 (34\%)&1.4&5479 (34\%)&231 (45\%)&5248 (33\%)&1.3\\ 
\hline
Diabetic Type I&198 (1\%)&108 (1\%)&27 (3\%)&81 (1\%)&2.4&149 (1\%)&22 (3\%)&127 (1\%)&2.8&173 (1\%)&12 (2\%)&161 (1\%)&2.3\\ 
\hline
Diabetic Type II&5928 (30\%)&2863 (34\%)&480 (46\%)&2383 (32\%)&1.4&4132 (31\%)&338 (44\%)&3794 (31\%)&1.5&5001 (31\%)&222 (43\%)&4779 (30\%)&1.4\\ 
\hline
Diabetic Type II unspecified&6468 (32\%)&3104 (37\%)&506 (48\%)&2598 (35\%)&1.4&4515 (34\%)&356 (47\%)&4159 (33\%)&1.4&5446 (33\%)&230 (45\%)&5216 (33\%)&1.4\\ 
\hline
Essential hypertension&9052 (45\%)&4622 (54\%)&633 (61\%)&3989 (54\%)&1.1&6370 (48\%)&452 (59\%)&5918 (48\%)&1.2&7640 (47\%)&300 (58\%)&7340 (46\%)&1.3\\ 
\hline
Hypertensive heart disease&3938 (20\%)&2124 (25\%)&271 (26\%)&1853 (25\%)&1.0&2844 (22\%)&195 (26\%)&2649 (21\%)&1.2&3350 (21\%)&128 (25\%)&3222 (20\%)&1.2\\ 
\hline
Hypertensive chronic kidney disease&250 (1\%)&139 (2\%)&27 (3\%)&112 (2\%)&1.7&181 (1\%)&18 (2\%)&163 (1\%)&1.8&211 (1\%)&10 (2\%)&201 (1\%)&1.5\\ 
\hline
Hypertensive heart and chronic kidney disease&175 (1\%)&112 (1\%)&17 (2\%)&95 (1\%)&1.3&136 (1\%)&13 (2\%)&123 (1\%)&1.7&155 (1\%)&12 (2\%)&143 (1\%)&2.6\\ 
\hline
Secondary hypertension&159 (1\%)&101 (1\%)&23 (2\%)&78 (1\%)&2.1&120 (1\%)&16 (2\%)&104 (1\%)&2.5&138 (1\%)&12 (2\%)&126 (1\%)&2.9\\
\hline 
Acute glomerulonephritis&110 (1\%)&61 (1\%)&16 (2\%)&45 (1\%)&2.5&81 (1\%)&10 (1\%)&71 (1\%)&2.3&95 (1\%)&9 (2\%)&86 (1\%)&3.2\\ 
\hline
Chronic glomerulonephritis&1727 (9\%)&1120 (13\%)&232 (22\%)&888 (12\%)&1.9&1351 (10\%)&177 (23\%)&1174 (9\%)&2.5&1522 (9\%)&118 (23\%)&1404 (9\%)&2.6\\ 
\hline
Acute and chronic glomerulonephritis&1811 (9\%)&1159 (14\%)&241 (23\%)&918 (12\%)&1.9&1408 (11\%)&182 (24\%)&1226 (10\%)&2.4&1591 (10\%)&123 (24\%)&1468 (9\%)&2.6\\ 
\hline
Polycystic kidney&65 (0\%)&43 (1\%)&12 (1\%)&31 (0\%)&2.8&51 (0\%)&7 (1\%)&44 (0\%)&2.6&59 (0\%)&3 (1\%)&56 (0\%)&1.6\\ 
\hline
Nephritis NEC&16 (0\%)&11 (0\%)&4 (0\%)&7 (0\%)&4.1&15 (0\%)&2 (0\%)&13 (0\%)&2.5&16 (0\%)&2 (0\%)&14 (0\%)&4.4\\ 
\hline
Calculus of kidney and ureter&1228 (6\%)&486 (6\%)&32 (3\%)&454 (6\%)&0.5&726 (6\%)&26 (3\%)&700 (6\%)&0.6&951 (6\%)&12 (2\%)&939 (6\%)&0.4\\ 
\hline
Calculus of lower urinary tract&70 (0\%)&23 (0\%)&0 (0\%)&23 (0\%)&0.0&34 (0\%)&0 (0\%)&34 (0\%)&0.0&51 (0\%)&0 (0\%)&51 (0\%)&0.0\\ 
\hline
Urinary obstruction&19 (0\%)&8 (0\%)&1 (0\%)&7 (0\%)&1.0&13 (0\%)&1 (0\%)&12 (0\%)&1.4&14 (0\%)&0 (0\%)&14 (0\%)&0.0\\ 
\hline
Vesicoureteral reflux&5 (0\%)&1 (0\%)&0 (0\%)&1 (0\%)&0.0&2 (0\%)&0 (0\%)&2 (0\%)&0.0&2 (0\%)&0 (0\%)&2 (0\%)&0.0\\ 
\hline
Infections of kidney&455 (2\%)&209 (2\%)&27 (3\%)&182 (2\%)&1.1&284 (2\%)&23 (3\%)&261 (2\%)&1.4&362 (2\%)&16 (3\%)&346 (2\%)&1.4\\ 
\hline
\end{tabular}
\end{adjustbox}
\end{sidewaystable}


\end{document}