\noindent
\textbf{Supplementary Information.} Villena, O.C., A. Arab, C.A. Lippi, S.J. Ryan, and L.R. Johnson. How environmental, geographic, socio-demographic, and epidemiological indicators influence malaria prevalence. Malaria Journal
\bigskip

\noindent
\textbf{Appendix 1:} Supplementary Information
\clearpage

\section{Supplemental Material: Figures}

\begin{figure}[ht!]
\begin{center}
\begin{tabular}{c c}
\includegraphics[trim=0 10 20 50, clip=TRUE, scale=.35]{SuppMat_Maps_PrevData/PfalcAfrica.jpg}
&
\includegraphics[trim=0 10 20 50, clip=TRUE, scale=.35]{SuppMat_Maps_PrevData/PvivaxAfrica.jpg}
\\
\includegraphics[trim=0 10 20 50, clip=TRUE, scale=.35]{SuppMat_Maps_PrevData/PfalcAsia.jpg}
&
\includegraphics[trim=0 10 20 50, clip=TRUE, scale=.35]{SuppMat_Maps_PrevData/PvivaxAsia.jpg}
\end{tabular}
\end{center}
\caption{Survey data in space for:A) {\it P.~falciparum} in Africa, B) {\it P.~vivax} in Africa, C) {\it P.~falciparum} in Asia, and D) {\it P.~vivax} in Asia.}
\label{fg:survey_data}
\end{figure}


\clearpage

\subsection{Marginal predictions for temperature, precipitation, and the basic reproductive number ($R_0$) two quarters prior to the start of the prevalence study for {\it P.~falciparum} and {\it P.~vivax} malaria prevalence in Africa and Asia}


\begin{figure}[ht!]
\begin{center}
\begin{tabular}{c c}
\includegraphics[trim=10 10 10 25, clip=TRUE, scale=.45]{SuppMat_Fig_Pfalc_Africa/qtmean2.jpeg}
&
\includegraphics[trim=10 10 10 25, clip=TRUE, scale=.45]{SuppMat_Fig_Pfalc_Africa/qprecip2.jpeg}
\end{tabular}
\begin{tabular}{c}
\includegraphics[trim=10 10 10 25, clip=TRUE, scale=.45]{SuppMat_Fig_Pfalc_Africa/R02.jpeg}
\end{tabular}
\end{center}
\caption{Marginal predictions based on particular predictors A) Temperature 2nd quarter prior to the start of the study B) Precipitation 2nd quarter prior to the start of the study, and C) The basic reporductive number ($R_0$) 2nd quarter prior to the start of the study for {\it P.~ falciparum} malaria prevalence in Africa}
\label{fg:environmental2_PfalcAfrica}
\end{figure}


\clearpage


\begin{figure}[ht!]
\begin{center}
\begin{tabular}{c c}
\includegraphics[trim=10 10 10 25, clip=TRUE, scale=.45]{SuppMat_Fig_Pfalc_Asia/qtmean2.jpeg}
&
\includegraphics[trim=10 10 10 25, clip=TRUE, scale=.45]{SuppMat_Fig_Pfalc_Asia/qprecip2.jpeg}
\end{tabular}
\begin{tabular}{c}
\includegraphics[trim=10 10 10 25, clip=TRUE, scale=.45]{SuppMat_Fig_Pfalc_Asia/RO2.jpeg}
\end{tabular}
\end{center}
\caption{Marginal predictions based on particular predictors A) Temperature B) Precipitation, and C) The basic reproductive number ($R_0$) for {\it P.~ falciparum} malaria prevalence in Asia}
\label{fg:environmental2_PfalcAsia}
\end{figure}

\clearpage

\begin{figure}[ht!]
\begin{center}
\begin{tabular}{c c}
\includegraphics[trim=10 10 10 25, clip=TRUE, scale=.45]{SuppMat_Fig_Pvivax_Asia/qtmean2.jpeg}
&
\includegraphics[trim=10 10 10 20, clip=TRUE, scale=.45]{SuppMat_Fig_Pvivax_Asia/qprecip2.jpeg}
\end{tabular}
\begin{tabular}{c}
\includegraphics[trim=10 10 10 25, clip=TRUE, scale=.45]{SuppMat_Fig_Pvivax_Asia/R02.jpeg}
\end{tabular}
\end{center}
\caption{Marginal predictions based on particular predictors A) Temperature B) Precipitation, and C) The basic reproductive number ($R_0$) for {\it P.~vivax} malaria prevalence in Asia}
\label{fg:environmental2_PvivAsia}
\end{figure}

\clearpage

\subsection{CART analysis: Pruned tree for {\it P.~falciparum} malaria prevalence in Africa}

In \Cref{fg:treePfalcAFR}, we show the pruned tree from the CART analysis for {\it P.~falciparum} malaria prevalence in Africa. The tree shows that 12 of the 15 predictors are considered to be predictive of {\it P.~falciparum} malaria prevalence -- only NDVI, population density, $R_0$ from two previous quarters were entirely excluded from the pruned tree. The rest of the variables in the tree appear in (sometimes) surprising combinations to group subsets of the data, suggesting possible interactions that predict prevalence.

We observed that the precipitation of the wettest quarter (BIO 16) is the most important determinant of {\it P.~falciparum} malaria prevalence in Africa, as the initial branching depends on this variable (bio16 $<$ 387 mm). At the second level,  we observed that the year in which the study took place and elevation (left and right child nodes respectively) are correlated with {\it P.~falciparum} malaria prevalence. The left child node has a value of study start year $\geq$ 2009 and the right child node has a value of elevation $\geq$ 1,665 m. At the next level, in the left child node, average temperature of second previous quarter (qtmean $<$ 24) and the precipitation of driest quarter (bio17 $<$ 19) are important variables, and in the right child node the study start year (year\_start $\geq$ 2006) and HDI (hindex $\geq$ 0.5) are important variables. 

At the bottom of the tree, each leaf in the tree diagram shows the probabilities  of {\it P.~falciparum} malaria prevalence. For example, the values at the left-most leaf in \Cref{fg:treePfalcAFR} indicate that the probability of negative (i.e., 0) {\it P.~falciparum} malaria prevalence is 91\% if the precipitation of the wettest quarter is $<$ 387 mm, the year of the study was 2009 or above, and the average temperature two quarters prior the study was $<$ 24$^{\circ}$C. The values at the right-most leaf in \Cref{fg:treePfalcAFR} indicate that the probability of positive (i.e., 1) {\it P.~falciparum} malaria prevalence is 9\% if precipitation of the wettest quarter is $\geq$ 387 mm, the elevation is $<$ 1,665, and the human development index is $<$ 0.5. 

\begin{figure}[ht!]
\centering
\includegraphics[trim=30 35 30 55, clip=TRUE, scale=.63]{SuppMat_Fig_Pfalc_Africa/TreePfalc_AFR.jpeg}
\caption{Pruned tree showing the parameters and values that best predict {\it P.~falciparum} malaria prevalence in Africa. The splits from each node follow the rule left=YES. Each node provides the following information: the predicted class (non-detection (0) or detection (1)), the probability of detection/non-detection which adds to 1, and the percentage of observations in the node. The color scale shows the detection (blue) to non-detection (green), color changes towards white as detection/non-detection approaches 50/50 percent. Bio3: isothermality ($\%$), bio16: precipitation of wettest quarter, bio17: precipitation of driest quarter, elev: elevation (m),  year$\_$start: year at which the study took place, qtmean1 and qtmean2: average temperature one and two quarters prior to the study time, qprecp1 and qprecp2: average precipitation one and two quarters prior to the study time, hindex: human development index, lgdppc: log gross domestic product per capita, and $R_0$q1: basic reproductive number first quarter}.
\label{fg:treePfalcAFR}
\end{figure}

\subsection{CART analysis: Pruned tree for {\it P.~falciparum} malaria prevalence in Asia}

From the CART analysis, we show the pruned tree for {\it P.~falciparum} malaria prevalence in Asia (\Cref{fg:treePfalcAsia}). Of the 15 variables used in the model (\Cref{tb:listvariables}), 6 variables are considered to have an effect on the prediction of {\it P.~falciparum} malaria prevalence in Asia: the year at which the malaria prevalence study took place, isothermality (BIO 3), the human development index, precipitation of driest quarter, average temperature one quarter prior to the study month, and the normalized difference vegetation index (NDVI) (\Cref{fg:treePfalcAsia}).

The variable that best split this dataset is the year at which the malaria prevelance study took place (year\_start $\geq$ 2006). The second most important determinants of {\it P.~falciparum} malaria prevalence are isothermality (bio3 $<$ 46) at the left child node, and the human development index (hindex $<$ 0.38) at the right child node. At the third level, the most important determinants are human index (hindex $\geq$ 0.45 and 0.65) at the left child nodes and precipitation of the driest quarter (BIO 17 $\geq$ 542) and isothermality  (BIO 3 $<$ 33) at the right child nodes. We continue in a similar way in the next levels until branches terminate in leaves (\Cref{fg:treePfalcAsia}).

Each leaf in the tree diagram shows the probabilities of {\it P.~falciparum} malaria prevalence in Asia. For example, the values at the left-most leave in (\Cref{fg:treePfalcAsia}) indicate a 88\% probability of  no {\it P.~falciparum} malaria prevalence and 12\% probability of detecting {\it P.~falciparum} malaria prevalence in Asia if the year at which the malaria prevalence study took place is $\geq$ 2006, isothermality is $<$ 46, and human development index $\geq$ 0.43.

\begin{figure}[ht!]
\centering
\includegraphics[trim=15 20 15 20, clip=TRUE, scale=.65]{SuppMat_Fig_Pfalc_Asia/treePfalc_Asia.jpeg}
\caption{Pruned tree showing the parameters and values that most explain {\it P.~falciparum} malaria prevalence in Asia. The splits from each node follow the rule left=YES. year$\_$start: year at which the study took place, bio3: isothermality ($\%$), hindex: the human development index, bio17: precipitation of driest quarter, qtmean1: average temperature one quarter prior to the study time, NDVI: the normalized difference vegetation index.}
\label{fg:treePfalcAsia}
\end{figure}

\subsection{CART analysis: Pruned tree for {\it P.~vivax} malaria prevalence in Asia}

From the CART analysis, we show the pruned tree for the full data set for {\it P.~vivax} malaria prevalence in Asia (\Cref{fg:treePvivaxAsia}). In the final model, 8 variables are considered to have an effect on the prediction of {\it P.~vivax} malaria prevalence in Asia, with the exception of isothermality, mean temperature of the 2nd quarter prior to the study date, mean precipitation of the 1st quarter prior to the study date, the basic reproductive number ($R_0$) for the 1st quarter, elevation, population density, and NDVI (\Cref{fg:treePvivaxAsia}).

The variable that best split this dataset is the year in which the study took place. This is the most important determinant of {\it P.~vivax} malaria prevalence, as the initial branching depends on this variable (study start year $\geq$ 2005). The second most important determinants of {\it P.~vivax} malaria prevalence are the GDPPC in the left child node (lGDP $<$ 9.1) and the precipitation of the driest quarter in the right child node (bio17 $\geq$ 636). At the next level, the precipitation of the wettest quarter (bio16 $\geq$ 1221) in the left child node and GDPPC (lGDP $<$ 7.7) and the human development index (hindex $\geq$ 0.73) in the right child node are the most important.

Each leaf in the tree diagram is labeled with the probability that the response variable ({\it P.~vivax} malaria prevalence) is true. For example, the values at the left-most leave in figure \Cref{fg:treePvivaxAsia} indicate that the probability of non-detecting {\it P.~vivax} malaria prevalence is 91\% if the year at which the study took place is $\geq$ 2005, log(gdppc) $<$ 9.1, and  precipitation of the wettest quarter is $\geq$ 1221 mm (\Cref{fg:treePvivaxAsia}).

\begin{figure}[ht!]
\centering
\includegraphics[trim=50 30 40 50, clip=TRUE, scale=.6]{SuppMat_Fig_Pvivax_Asia/tree_PvivAsia.jpeg}
\caption{Pruned tree showing the parameters and values that most explain {\it P.~vivax} malaria prevalence in Asia. The splits from each node follow the rule left=YES. year$\_$start: year at which the study took place, lGDPPC: log of the gross domestic product per capita, bio17: precipitation of the driest quarter, bio16: precipitation of the wettest quarter, hindex: the human development index, qprecp2: average precipitation two quarters prior to the study time, qtmean1: average temperature one quarter prior to the study time, Roq2: the basic reproductive number two quarters prior to the study time.}
\label{fg:treePvivaxAsia}
\end{figure}

\clearpage

\subsection{Magnitude and uncertainty of the effects for each variable of the GLM models}

\begin{figure}[ht!]
\centering
\includegraphics[trim=20 0 0 0, clip=TRUE, scale=.90]{SuppMat_Fig_Pfalc_Africa/glm_PfalcAFR.png}
\caption{Magnitude and uncertainty of the effects for each variable of the glm model for {\it P. falciparum} malaria prevalence in Africa.}
\label{fg:plotcoeff_PfalcAF}
\end{figure}

\clearpage

\begin{figure}[ht!]
\centering
\includegraphics[trim=20 0 0 0, clip=TRUE, scale=.90]{SuppMat_Fig_Pfalc_Asia/glm_PfalASIA.png}
\caption{Magnitude and uncertainty of the effects for each variable of the glm model on {\it P. falciparum} malaria prevalence in Asia.}
\label{fg:plotcoeff_PfalcASIA}
\end{figure}

\clearpage

\begin{figure}[ht!]
\centering
\includegraphics[trim=20 0 0 0, clip=TRUE, scale=.90]{SuppMat_Fig_Pvivax_Asia/glm_PvivASIA.png}
\caption{Magnitude and uncertainty of the effects for each variable of the glm model on {\it P. vivax} malaria prevalence in Asia.}
\label{fg:plotcoeff_PvivASIA}
\end{figure}

\clearpage


\section{Supplemental Material: Tables}


\subsection{Summary glm models for {\it P. falciparum} and {\it P. vivax} malaria prevalence in Africa and Asia}


\begin{table}[ht!]
\begin{tabular}{@{} l *{3}{d{5}} @{}}
\toprule
& \mc{Estimate} & \mc{S.E.} \\
\midrule
Intercept                     & 1.55  & (0.05)^{***}  \\
precipitation of the wettest quarter & 6.26 & (0.39)^{***} \\
start year of the study           & -211.42 & (13.34)^{***} \\
mean temperature - 2nd quarter   & 2.94 & (0.72)^{***} \\
isothermality  & 4.72 & (0.38)^{***} \\
mean precipitation - 1st quarter (sq) & -8.53 & (0.82)^{***} \\
basic reproductive number (RO) - 1st quarter & 0.43 & (0.14)^{**} \\
isothermality (sq)  & 20.57 & (2.93)^{***} \\
mean precipitation - 2nd quarter & 2.29 & (0.32)^{***} \\
mean temperature - 1st quarter & 4.62 & (0.68)^{***} \\
gross domestic product per capita & 5.42 & (1.29)^{***} \\
human development index & -1.43 & (0.42)^{***} \\
mean temperature - 1st quarter (sq) & -7.55 & (3.22)^{*} \\
population density & 2.06 & (1.01)^{*} \\
\bottomrule
\hline
\multicolumn{2}{l}{\scriptsize{$^{***}p<0.001$; $^{**}p<0.01$; $^{*}p<0.05$};$^{\cdotp}p<0.1$}
\end{tabular}
\caption{Summary of the glm model for {\it Plasmodium falciparum} prevalence in Africa. Squared terms (sq)}
\label{tb:outputglm Pfalc_Africa}
\end{table}



\begin{table}[ht!]
\begin{tabular}{@{} l *{3}{d{5}} @{}}
\toprule
& \mc{Estimate} & \mc{S.E.} \\
\midrule
Intercept                & 0.69  & (0.09)^{***}  \\
isothermality (sq) & -12.89 & (1.95)^{***} \\
mean precipitation - 2nd quarter & -5.32 & (0.41)^{***} \\
start year of the study           & -163.94 & (21.16)^{***} \\
isothermality & 2.78 & (0.44)^{***} \\
precipitation of the driest quarter & -3.44 & (0.37)^{***} \\
elevation & -1.92 & (0.64)^{**} \\
normalized difference vegetation index & 1.50 & (0.31)^{***} \\
gross domestic product per capita & 2.50 & (0.58)^{***} \\
human development index & -1.58 & (0.68)^{*} \\
mean precipitation - 1st quarter (sq) & -0.69 & (0.31)^{*} \\
population density & -3.08 & (1.36)^{*} \\
basic reproductive number (RO)- 1st qtr & -0.84 & (0.28)^{**} \\
mean temperature - 2nd quarter   & 1.64 & (0.56)^{**} \\
\bottomrule
\hline
\multicolumn{2}{l}{\scriptsize{$^{***}p<0.001$; $^{**}p<0.01$; $^{*}p<0.05$};$^{\cdotp}p<0.1$}
\end{tabular}
\caption{Summary of the glm model for {\it Plasmodium falciparum} prevalence in Asia. Squared terms (sq)}
\label{tb:outputglm Pfalc_Asia}
\end{table}

\clearpage

\begin{table}[ht!]
\begin{tabular}{@{} l *{3}{d{5}} @{}}
\toprule
& \mc{Estimate} & \mc{S.E.} \\
\midrule
Intercept                & 0.43  & (0.11)^{***}  \\
start year of the study  & -213.21 & (20.16)^{***} \\
mean precipitation - 2nd qtr & -6.89 & (0.54)^{***} \\
human development index & 0.68 & (0.55) \\
normalized difference vegetation index & 1.63 & (0.26)^{***} \\
isothermality (sq) & -5.75 & (1.96)^{**} \\
mean precipitation - 1st quarter (sq) & -10.09 & (1.55)^{***} \\
precipitation of the driest quarter & -1.97 & (0.35)^{***} \\
basic reproductive number (RO)- 1st qtr & 0.79 & (0.25)^{**} \\
mean temperature - 1st qtr  & -3.65 & (0.66)^{***} \\
square mean temperature - 1st qtr  & -6.05 & (2.01)^{**} \\
elevation & -1.46 & (0.62)^{*} \\
gross domestic product per capita & 1.67 & (0.58)^{**} \\
precipitation of the wettest quarter & 1.26 & (0.57)^{*} \\
isothermality & 0.84 & (0.39)^{*} \\
\bottomrule
\hline
\multicolumn{2}{l}{\scriptsize{$^{***}p<0.001$; $^{**}p<0.01$; $^{*}p<0.05$};$^{\cdotp}p<0.1$}
\end{tabular}
\caption{Summary of the glm model for {\it Plasmodium vivax} prevalence in Asia. Squared terms (sq)}
\label{tb:outputglm Pviv_Asia}
\end{table}

\clearpage

\subsubsection{Model performance assessment: CART and GLM models }

We assessed the performance of the CART and glm model for {\it Plasmodium falciparum} malaria prevalence in Africa and {\it Plasmodium vivax} in Asia which are the two most rich data sets in our study (\Cref{tb:prevcases}). To assess the prediction performance we use a validation data set (30\% of the total amount of data) to estimate the classification ability of these two models, We use four different metrics: accuracy, precision, recall, and the F1 score based on each model's confusion matrix \citep{irmanita2021classification,goutte2005probabilistic}.

The confusion matrix is a table that summarizes how successful classification models are at predicting samples belonging to various classes as summarized at \Cref{tb:confmatrix}. To build the confusion matrix, a set of predictions are calculated based on the model so that they can be compared to the actual targets. To do this, we used the function {\it predict} in the software R which computes the predictions on the validation data set (0.3 of each data set). In the confusion matrix, each row represent a calculated, also called actual, target, while each column represents a predicted target where it is count the number of times "TRUE" instances are classified either as "TRUE" or "FALSE" following the next design. (\Cref{tb:confmatrix}).

\begin{table}[ht!]
\begin{center}
\begin{tabular}{c c c c } 
\hline
 &  & \multicolumn{2}{c}{Predicted} \\
 \hline
 &      &   FALSE & TRUE  \\ 
\hline
\multirow{2}{5em}{Calculated} &  FALSE & True Negative (TN) & False Positive (FP) \\ 
& TRUE & False Negative (FN) & True Positive (TP) \\
\hline
\end{tabular}
\end{center}
\caption{Confusion matrix}
\label{tb:confmatrix}
\end{table} 

Using the information of the confusion matrix, we estimated the model accuracy. Model accuracy is defined as the total correctly classified samples divided by the total number of classified samples. The accuracy equation in terms of the confusion matrix is express as:

\begin{equation}\label{eq:accuracy}
    Accuracy =  \frac{TP + TN} {TP + TN + FP + FN}
\end{equation} \\

The model precision, also called positive predictive value, refers at the accuracy of the positive predictions (False and True positive). Precision is calculated using the following equation:

\begin{equation}\label{eq:precision}
    Precision =  \frac{TP} {TP + FP}
\end{equation} \\

the model recall, also called sensitivity, is the ratio of positive instances that are correctly detected by the classifier and it is calculated using the following equation:

\begin{equation}\label{eq:recall}
    Recall =  \frac{TP} {TP + FN}
\end{equation} \\

The F1-score is based on the precision and recall. The F1-score is a weighted mean of these two metrics, meaning it gives more weight to the lower values and it is calculated using the following equation:

\begin{equation}\label{eq:f1}
    F1-score =  2 * \frac{Precision * Recall} {Precision + Recall}
\end{equation} \\

\vspace{5mm}
\noindent
\textbf{Model performance assessment for {\it Plasmodium falciparum} malaria prevalence in Africa}
\vspace{5mm}


We build confusion matrices for the CART (\Cref{tb:matrixCART}) and glm ({\Cref{tb:matrixGLM}) models . The first row of the CART confusion matrix shows the Non-detection (0) of {\it P. falciparum} malaria prevalence. Of the 585 cases, 198 were correctly classified as non-detection of {\it P. falciparum} malaria prevalence, while the remaining (387) was wrongly classified as detection (1) of {\it P. falciparum} malaria prevalence when {\it P. falciparum} malaria prevalence should be non-detected. The second row, considers the detection (1) of {\it P. falciparum} malaria prevalence. Of the 1729 cases, 1615 were correctly classified as detection of {\it P. falciparum} malaria prevalence, while the remaining (114) was wrongly classified as non-detection of {\it P. falciparum} malaria prevalence when {\it P. falciparum} malaria prevalence should be detected (Table 6). 

\begin{table}[ht!]
\begin{center}
\begin{tabular}{c c c c c } 
\hline
 &  & \multicolumn{3}{c}{Prediction} \\
 \hline
 &      &   Non-detection (0) & Detection (1)  & Row total \\ 
\hline
\multirow{2}{5em}{Calculated} &  Non-detection (0) & 198 &  387 & 585 \\ 
 & Detection (1) & 114 & 1615 & 1729 \\
 \hline
 & Colum total &  312  &  2002   &  2314  \\
\hline
\end{tabular}
\end{center}
\caption{Confusion matrix for the CART model for {\it Plasmodium falciparum} malaria prevalence in Africa.}
\label{tb:matrixCART}
\end{table} 


For the glm model, the confusion matrix shows that of the 585 cases, 149 were correctly classified as non-detection of {\it P. falciparum} malaria prevalence, while the remaining (436) was wrongly classified as detection of {\it P. falciparum} malaria prevalence when {\it P. falciparum} malaria prevalence should be no detected. For the detection (1) of {\it P. falciparum} malaria prevalence, of the 1729 cases, 1637 were correctly classified as detection of {\it P. falciparum} malaria prevalence, while the remaining (92) was wrongly classified as non-detection of {\it P. falciparum} malaria prevalence when {\it P. falciparum} malaria prevalence should be detected (Table 7). 

\begin{table}[ht!]
\begin{center}
\begin{tabular}{c c c c c }
\hline
 &  &  \multicolumn{3}{c}{Prediction} \\ 
 \hline
 &  & Non-detection (0) & Detection (1)  & Row total \\ 
\hline
 \multirow{2}{5em}{Calculated} & Non-detection (0) & 149 &  436 & 585 \\ 
 & Detection (1) & 92 & 1637 & 1729 \\
 \hline
 & Colum total &  241  &  2073   &  2314  \\
\hline
\end{tabular}
\end{center}
\caption{Confusion matrix for the glm model for {\it Plasmodium falciparum} malaria prevalence in Africa.}
\label{tb:matrixGLM}
\end{table}

\begin{table}[ht!]
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
 & \multicolumn{2}{|c|}{Model} \\
 \hline
Metric & CART & GLM \\
\hline
Accuracy & 78.4 & 77 \\
\hline
Precision & 81 & 79 \\
\hline
Recall & 93 & 95 \\
\hline
F1-score & 87 & 86 \\
\hline
\end{tabular}
\end{center}
\caption{Accuracy, precision, recall, and F1-score results from the performance assessment to the CART and glm models for {\it Plasmodium falciparum} prevalence in Africa. Values are expressed in percentages.}
\label{tb:model_performance_PfalcAF}
\end{table}

Even though our models show high accuracy, both of them overestimated the number of false negatives, especially the glm model. This is very common when there is a dominant class which in this case is the true negatives (Non-detection) which in our data set represent the high number of zeros. In this situations,  it is recommended to perform further test such as the calculation of the model precision, the model recall, and the F1-score. 

\vspace{5mm}
\noindent
\textbf{Model performance assessment for {\it Plasmodium vivax} malaria prevalence in Asia}
\vspace{5mm}


We build confusion matrices for our CART model (\Cref{tb:matrixCART_PvASIA}) and for our glm model ({\Cref{tb:matrixGLM_PvASIA}). The first row of the CART confusion matrix shows the Non-detection (0) of {\it P. vivax} malaria prevalence. Of the 489 cases, 366 were correctly classified as non-detection of {\it P. vivax} malaria prevalence, while the remaining (123) was wrongly classified as detection of {\it P. vivax} malaria prevalence. The second row, considers the detection (1) of {\it P. vivax} malaria prevalence. Of the 375 cases, 287 were correctly classified as detection of {\it P. vivax} malaria prevalence, while the remaining (88) was wrongly classified as non-detection of {\it P. vivax} malaria prevalence (\Cref{tb:matrixCART_PvASIA}). 

\begin{table}[ht!]
\begin{center}
\begin{tabular}{c c c c c } 
\hline
 &  & \multicolumn{3}{c}{Prediction} \\
 \hline
 &      &   Non-detection (0) & Detection (1)  & Row total \\ 
\hline
\multirow{2}{5em}{Calculated} &  Non-detection (0) & 366 &  123 & 489 \\ 
 & Detection (1) & 88 & 287 & 375 \\
 \hline
 & Colum total &  454  &  410   &  864  \\
\hline
\end{tabular}
\end{center}
\caption{Confusion matrix for CART model for the prediction of {\it Plasmodium vivax} prevalence in Asia. The confusion matrix is based in 864 observations}
\label{tb:matrixCART_PvASIA}
\end{table} 


For the glm model, the confusion matrix shows that of the 489 cases, 397 were correctly classified as non-detection of {\it P. vivax} malaria prevalence, while the remaining (92) was wrongly classified as detection of {\it P. vivax} malaria prevalence when {\it P. vivax} malaria prevalence should be no detected. For the detection (1) of {\it P. vivax} malaria prevalence, of the 375 cases, 236 were correctly classified as detection of {\it P. vivax} malaria prevalence, while the remaining (139) was wrongly classified as non-detection of {\it P. vivax} malaria prevalence when {\it P. vivax} malaria prevalence should be detected (\Cref{tb:matrixGLM_PvASIA}). 

\begin{table}[ht!]
\begin{center}
\begin{tabular}{c c c c c }
\hline
 &  &  \multicolumn{3}{c}{Prediction} \\ 
 \hline
 &  & Non-detection (0) & Detection (1)  & Row total \\ 
\hline
 \multirow{2}{5em}{Calculated} & Non-detection (0) & 397 &  92 & 489 \\ 
 & Detection (1) & 139 & 236 & 375 \\
 \hline
 & Colum total &  536  &  328   &  864  \\
\hline
\end{tabular}
\end{center}
\caption{Confusion matrix for GLM model for the prediction of {\it Plasmodium vivax} malaria prevalence in Asia. The confusion matrix is based in 864 observations}
\label{tb:matrixGLM_PvASIA}
\end{table}

\begin{table}[ht!]
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
 & \multicolumn{2}{|c|}{Model} \\
 \hline
Metric & CART & GLM \\
\hline
Accuracy & 76 & 73 \\
\hline
Precision & 70 & 72 \\
\hline
Recall & 76.5 & 63 \\
\hline
F1-score & 73 & 67 \\
\hline
\end{tabular}
\end{center}
\caption{Accuracy, precision, recall, and F1-score results from the performance assessment for {\it Plasmodium vivax} prevalence in Asia. Values are expresed in percentages.}
\label{tb:model_performance_PvivAsia}
\end{table}




