Machine learning methods reveal the temporal pattern of dengue incidence using meteorological factors in metropolitan Manila, Philippines

Background Several studies have applied ecological factors such as meteorological variables to develop models and accurately predict the temporal pattern of dengue incidence or occurrence. With the vast amount of studies that investigated this premise, the modeling approaches differ from each study and only use a single statistical technique. It raises the question of whether which technique would be robust and reliable. Hence, our study aims to compare the predictive accuracy of the temporal pattern of Dengue incidence in Metropolitan Manila as influenced by meteorological factors from four modeling techniques, (a) General Additive Modeling, (b) Seasonal Autoregressive Integrated Moving Average with exogenous variables (c) Random Forest and (d) Gradient Boosting. Methods Dengue incidence and meteorological data (flood, precipitation, temperature, southern oscillation index, relative humidity, wind speed and direction) of Metropolitan Manila from January 1, 2009 – December 31, 2013 were obtained from respective government agencies. Two types of datasets were used in the analysis; observed meteorological factors (MF) and its corresponding delayed or lagged effect (LG). After which, these datasets were subjected to the four modeling techniques. The predictive accuracy and variable importance of each modeling technique were calculated and evaluated. Results Among the statistical modeling techniques, Random Forest showed the best predictive accuracy. Moreover, the delayed or lag effects of the meteorological variables was shown to be the best dataset to use for such purpose. Thus, the model of Random Forest with delayed meteorological effects (RF-LG) was deemed the best among all assessed models. Relative humidity was shown to be the top-most important meteorological factor in the best model. Conclusion The study exhibited that there are indeed different predictive outcomes generated from each statistical modeling technique and it further revealed that the Random forest model with delayed meteorological effects to be the best in predicting the temporal pattern of Dengue incidence in Metropolitan Manila. It is also noteworthy that the study also identified relative humidity as an important meteorological factor along with rainfall and temperature that can influence this temporal pattern. Electronic supplementary material The online version of this article (10.1186/s12879-018-3066-0) contains supplementary material, which is available to authorized users.


Background
Dengue fever is a mosquito-borne disease transmitted by the bite of a female Aedes aegyti and Ae. albopictus mosquitoes, the primary and secondary mosquito vectors respectively, leading to clinical manifestations of influenza-like symptoms to life-threatening shock syndrome [1]. It had been estimated that 3.9 billion people in 128 countries or 40% of the world population are at risk of contracting the disease [2]. The dynamics of dengue transmission is said to be influenced by three central risk factors that are biological, sociological and environmental in nature [3]. The focus of our study is primarily on the environmental factors such as meteorological patterns that have been attributed to the spread and occurrence of dengue. A list of growing evidence has demonstrated the association between these factors and its epidemiology [4] thus claiming that dengue transmission is sensitive to meteorological variability and change [5][6][7][8]. Moreover, many researchers are asserting the possible future spatial and temporal expansion on the ecology of Ae. aegypti along with its virus in the midst of climate change scenarios [8][9][10][11].
Meteorological factors such as temperature, rainfall and humidity can influence dengue epidemiology by increasing mosquito development, population growth, virus replication and mosquito-human interactions [7]. Rainfall and flood have been shown to be important factors in providing appropriate breeding sites of Ae. aegypti necessary for increasing female mosquito density that may lead to outbreaks [12]. Temperature, on the other hand, has an effect in the reproductive and biting rate of the mosquito vector and the extrinsic incubation of the dengue virus [13]. Humidity tends to influence the vector's longevity and rapid replication of the virus [14,15]. In contrast to the three meteorological factors, wind speed or velocity has been shown to suppress mosquito flight, thus, affecting their oviposition and density [16][17][18][19]. Wind direction, on the other hand, had been explored [18] but there is no mention of how this meteorological variable may influence dengue transmission.
Analyzing the impact of meteorological factors to local dengue disease occurrence has become significant not only because it allows us to understand the role of these factors towards the spread of the disease, but also provides an opportunity to create and adopt an early warning dengue outbreak system [19,20]. Many Southeast Asian countries had studied the role and association of meteorological variables towards its local dengue epidemiology. High dengue epidemics were considered seasonal and coincides the rainy season in Malaysia [21][22][23], Thailand [24,25],Vietnam [26,27] and the Philippines [28]. On the other hand, Singapore has shown that mean temperature, relative humidity [6,29,30] and Southern Oscillation index [31] were important meteorological factors in forecasting or predicting dengue outbreaks. Parts of Indonesia show that both temperature and rainfall are highly associated with high dengue incidence that can lead to epidemics [32]. In the Philippines, changing rainfall patterns [28], temperature and incidence of La Nina contribute varying dengue incidence [33].
The compendium of literature that assessed different meteorological effects on Ae aegypti and dengue incidence featured different statistical modeling techniques and used different dependent variables (e.g. current or lagged meteorological variables). The most commonly used modeling techniques are cross-correlations, Poisson Regression, Generalized Additive Modeling (GAM), Autoregressive Integrated Moving Average (ARIMA) [4] and distributed lag non-linear model (DLNM) [19,34]. Most studies have used GAM and ARIMA models because it became the standard reference for associating environmental factors towards disease outcome and a tool for time series prediction analysis [35][36][37]. Although these statistical modeling techniques are widely used, they suffer certain drawbacks or disadvantages such as handling of missing values, outlier sensitivity, and multicollinearity [38]. More recently, new modeling approaches such as Machine learning methods are gaining popularity and interest because of its flexibility in handling complex and multiple interacting elements [39]. Our study focuses on two popular Machine Learning methods, Random Forest (RF) and Gradient Boosting (GB), because of its wide use in ecology and public health [40][41][42]. These two approaches are designated as tree-based algorithms because of its fundamental process in splitting the dataset into two or more homogeneous sets based on the most significant input variables. The end-result is a tree-like diagram where each node has a partitioning rule [43]. Tree-based learning algorithms are considered to be the best and widely used machine learning methods in generating a model of high and accurate prediction [44,45]. Previous studies which used these modeling approaches (RF and GB) were able to predict the occurrence of dengue using either clinical (e.g. complete blood counts, symptoms) [46][47][48] or land use (e.g. residential, commercial sites) [49] variables. Moreover, it has also been applied to project the spatial extent of the dengue mosquito vector under climate change scenarios [50].
The critical systematic review of Naish et al. [4] outlined methodological issues that modeled dengue occurrence using climate variables such as study design, time periods and scale of analysis. What stands out is the diverse use of different statistical modeling techniques [51]. These studies commonly concentrate towards one statistical technique and produce combinations of meteorological factors in determining the best model for prediction. Although the review paper [4] highlighted each statistical modeling technique used, it wasn't able to emphasize what approach can be robust or reliable in predicting and forecasting dengue incidence. For that reason, our study addresses this gap by evaluating and comparing prediction accuracy of four statistical modeling techniques in forecasting dengue incidence: General Additive Modeling (GAM), seasonal autoregressive integrated moving average (SARIMA), Random Forest (RF) and Gradient Boosting (GB). Moreover, another worth investigating is the type of dependent variables used to predict dengue incidence. Some studies would apply delayed effects or time lags of meteorological variables since it indirectly influence the occurrence of dengue. However, there are still some studies that use current observations of meteorological factors as well. Nevertheless, our study also aims to examine this area and provide basis on what kind of predictors would be well suited for prediction. Lastly, our study also explores the meteorological factors that strongly influences the dengue incidence of Metropolitan Manila based on the best model.

Data collection and processing
Reported dengue cases of Metropolitan Manila from January 1, 2009 until December 31, 2013 ( Figure 1) were obtained from the National Epidemiology Center of the Department of Health. Most of the reported dengue cases during this period are suspected or probable cases according to standard definitions and are not laboratory confirmed. The incidence rate of dengue was calculated by dividing the total number of dengue cases by the total population of Metropolitan Manila for a particular year multiplied by a factor of 1000. The factor of 1000 refers to "per 1000 persons" in the population. The population statistics for this region were obtained from the Philippine Statistics Authority agency (www.psa.gov.ph) [52]. Since the Philippine population census was done only for years 2010 and 2015, we used the compounded population growth rate to calculate the population for years 2009, 2011, 2012, and 2013. Dengue incidence was log transformed in order to reduce the skewing of the data and to destabilize the variance which can be useful in the subsequent time series analysis.
Daily meteorological data of Metropolitan Manila from January 1, 2009 until December 31, 2013 ( Figure 1) were obtained from the Philippine Atmospheric Geophysical and Astronomical Services and Administration (PAGASA). The meteorological variables include temperature (maximum, minimum and average), total precipitation, relative humidity, wind speed and wind direction. In this study, we averaged by week the daily meteorological measurements in order to conform to the weekly reported dengue cases. The average, minimum or maximum measurement of the meteorological variable for the week was used in the study for subsequent analysis. It should be noted that the wind direction variable was divided into two observations (Minimum and Maximum) because the reported values represent directionality (0°-360°).
The climate of the Philippines is highly affected by the naturally occurring El Niño/Southern Oscillation (ENSO) phenomenon that develops in the Pacific Ocean. The monitoring of ENSO in the Philippines is relatively significant because of its impact to the various sectors of the society and environment [53]. Thus, we deemed it as an important and relevant factor in the study. The Southern Oscillation Index (SOI) is considered to be the atmospheric representation of ENSO and calculated using Troup's formula [54]. Daily calculation (January 1, 2009 until December 31, 2013) of the Southern Oscillation Index (SOI) were obtained from the Queensland Government Meteorology Bureau (http://www.longpaddock.qld.gov.au) [55] using the National Climate Centre's revised SOI calculation based on Troup's formula. Similar to the meteorological variables, the daily measurements were aggregated into its weekly average for subsequent analysis.
Flood occurrence in Metropolitan Manila was datamined based on real-time public warnings of the Metropolitan Manila Development Authority (MMDA) through their social media platform, Twitter. Since flood may occur in selected parts of Metropolitan Manila because of scattered rain showers, the study considered only a flood occurrence when nearly all major roads of Metropolitan Manila are impassable due to flood. The dates of these reports were recorded and counterchecked from existing news article from credible Philippine news agencies. In the study, the presence or absence of flood during the week was done for subsequent analysis.
The entire dataset consisted of 260 observations of dengue incidence and its meteorological variables. Prior to subjecting the dataset to analysis, the dataset was divided into training and test subsets. The training subset consisted observations from the 1st morbidity week of 2009 until the last morbidity week of 2012 (n = 208) while the test subset consisted observations from all morbidity weeks of year 2013 (n = 52). The training dataset was used to build the model for the different statistical modeling techniques while the test dataset was used to validate the model.
Two types of datasets were used for each statistical modeling technique. The first dataset (MF) consisted of meteorological factors of the appropriate dengue morbidity week while the second dataset (LG) consisted only the delayed time lags of the meteorological factors. To determine the appropriate time lag for each meteorological factor, a cross correlation analysis from 0 to 25 week lags was done and the highest lag association was identified and used for the LG dataset. The number of lag weeks (n = 25) were identified due to crosscorrelation results of past studies [18,37,56] using either monthly or weekly time scales.

Modeling approaches
In our study, the natural log of dengue incidence (y) is the independent or predicted variable while the meteorological factors and its corresponding time lags are the dependent variables or predictors (x 1 , x 2 , x 3 …..

Generalized additive modeling
Generalized additive modeling (GAM) is as one approach to non-parametric regression with multiple predictors. What makes GAM unique is that it applies a "smoothing function" and it helps in capturing the predictive variables which are assumed to be non-linear in nature. GAM is often described as "data-driven" because the smoothing function automatically allows the response curve to fit for each predictor without a priori knowledge, thus generating the estimated parameters [57]. The workflow of GAM starts by first separating the predictors into sections called knots (k) then spline functions are used to fit the data into each section independently [58]. The spline function is a piecewise polynomial curve that joins these independent knots and the commonly used are the natural or B-splines. Afterwards, all functions of k are added to predict the smoothing link function. To avoid overfitting, the smooth terms of the GAM model are represented by penalized regression splines.

Seasonal autoregressive integrated moving average with exogenous variables (SARIMAX)
The Autoregressive Integrated moving Average (ARIMA) model is considered to be the widely used forecasting model because it can project future values of a series based entirely on its own values. This approach consists of three features the Autoregressive (AR) model, Moving Average (MA) model and an initial differencing step or called Integrated (I). The first step of this approach is to meet the assumption of "stationarity" of the ARIMA model. Stationary means that the time series has no trend and its variations are around the mean and have a constant amplitude. If the original time series values are not considered stationary, then it is either transformed (i.e. natural log) or replaced the time series values with the difference (I) between the actual value and its previous value. The ARIMA model is a linear regression type of equation in which the predictors are the two remaining features, AR and MA. The AR part indicates the variable is regressed on its own lagged values while the MA corresponds to the autocorrelation error. Thus, the ARIMA model is classified as (p,d,q) model where p stands for the number autoregressive (AR) terms, d is the number of differences needed for stationarity while q is the number of lagged error in the prediction equation. Identification of the appropriate number of the AR(p) and MA(q) parameters are determined by analyzing the autocorrelation (ACF) and partial autocorrelation (PACF) function plots. The ARIMA(p,d,q) is considered to be non-seasonal model. However, if the time series has a seasonal component, it can be extended into a Seasonal ARIMA (SARIMA) where the seasonality terms are denoted as (P,D,Q)m. The P,D and Q parameters refer to the autoregressive, differencing, and moving average terms respectively while m denotes the seasonal frequency. Thus a SARIMA consists of both the nonseasonal (p,d,q) and seasonal ((P,D,Q)m) components. The SARIMA model can be further extended to include exogenous variables or regressors (SARIMA-X). The best parameters of SARIMA(p,d,q)(P,D,Q)m with exogenous variables can be selected by choosing the lowest value of Akaike Information Criterion (AIC). This model, then, can be used to forecast the dynamics of the time series.

Random Forest and gradient boosting
Random Forest (RF) and Gradient Boosting (GB) are considered to be tree-based ensemble methods wherein it creates multiple tree sub-models and combine them to produce an improved final model. The difference between the two ensemble methods lies on the process of creating multiple tree models. RF uses the bootstrap aggregation (bagging) ensemble method in generating a large number of independent bootstrapped trees at random from the dataset. The various tree models are then aggregated or combined using the mean [59]. The final tree model estimates the importance of every predictive variable by inspecting how much the prediction error increases [60,61]. In contrast with RF, Gradient Boosting (GB) uses stochastic gradient boosting where the modelbuilding process is a stage-wise procedure. The task of this method is to improve the decision tree by minimizing the loss function (deviance) at each tree split. Hence, this type of ensemble method is considered to be powerful because it can enhance weak predictors by adding a predictor at a time, so that the next predictor is trained to improve the already trained ensemble therefore, improving the predictive accuracy [40].

Implementation
All statistical modeling techniques were performed in R program version 3.3.3 [62]. Initially, Pearson's correlation analysis was done to assess the degree of association of dengue incidence and the meteorological factors. Moreover, the correlation analysis among meteorological factors was also done to determine which meteorological factors are highly correlated with each other.
For GAM, the default parameters specified are family = "Gaussian", link = "identity" and smoothening function using the natural spline was applied to meteorological variables except for flood occurrence. Missing values are excluded from the analysis. GAM analysis was done in a step-wise approach. Model building process was done with independent, combination and all meteorological factors and its corresponding lags. The best model was determined by Akaike Information Criterion (AIC). Determination of predictors important to the model were based on its statistical significance of the p-value. This statistical modeling method and process were performed using the mgcv package version 1.8-17 [58].
In performing SARIMAX, the fpp package version 0.5 [63] was employed. First, the study decided that the seasonal factor of "m" is set at 52 in order to account the annual weekly trend. Next, we applied the xreg function to group together the different predictor variables to be included in the model. We set the parameters for model development to be seasonal (seasonal = TRUE) and used the default parameters such as the AIC as the information criterion (ic = "AIC") and KPSS test (test = "kpss"). Afterwards, the auto.arima function was implemented to determine the model parameters of (p,d,q,)(P,D,Q) with m at 52 along with predictor variables. The best model was chosen based on the lowest AIC. A Kalman filter approach was first employed to the LG dataset which contained missing values. However, the extrapolation of flood, minimum and maximum wind direction were not possible due to the nature of being categorical. Hence, the study still decided to remove the missing values found in the LG dataset similar to GAM. A stepwise approach in SARIMAX modeling building was applied to independent, combination and all meteorological factors and its corresponding lags. Moreover, identification of predictors important to the model was based on the statistical significance of the p-value.
The RF method is performed using randomForest package version 4.6.12 [64] where each model was built based on 1000 trees (n.tree = 1000). The imputation function was applied for missing values where surrogate values are generated based on weighted average of the non-missing observations. Variable importance is selected based on the number of times the variable was used for splitting, then weighted by the squared improvement to the model as a result of each split, and averaged over all trees [40]. RF generates two variable importance measures, the percentage increase of the mean square error (%IncMSE) and increase node purity (IncNodePurity).The %IncMSE is calculated as the average difference of the variables' MSE from the original dataset and the sets of randomly permuted variables. The interpretation of a large %IncMSE value indicates a large difference from randomly permuted variables, thus, making the modeled variables important to the final model. On the other hand, IncNodePurity is a measure of the total decrease in node impurity that results from splits over that variable, averaged over all trees. Since RF shows no significance test towards which variables are important, a randomness threshold [19,65] was used. This is calculated by dividing 100% to the number of predictor variables (MF = 10, LG = 9), hence, the study only considered a randomness threshold of above 10% in MF and 11% in LG datasets as important variables to the model. GB models, on the other hand, comprised the following model parameters that need to be set such as learning or shrinkage rate, tree complexity and bagging factor. Learning or shrinkage rate determines the contribution of each tree to the growing model. Tree complexity determines the degree to which predictors may interact with each other and a higher value is set if more levels of interaction is needed. In the study, the interactions are fitted with a tree complexity of 5 (tree.complexity = 5) and learning or shrinkage rate was set at 0.001 (learning.rate = 0.001). The bagging factor is set at 0.5 (bag.faction = 0.5) as suggested by Freidman [66] and pertains that during the stagewise approach it will randomly select 50% of the training data when the regression tree is fitted to the dependent variable. In contrast with RF, GB can accommodate missing values without the need of imputation. The GB method was performed using the gbm package version 2.1.3 [67]. The process of variable importance in GB is comparable with RF, however, it does not use %IncMSE nor IncNodePurity. It uses the relative contribution (%) where a higher percentage pertains to a strong relative importance of the variable. Similarly with RF that has no test of significance test on important variables, the randomness threshold was used.

Performance evaluation
All the best models generated from each statistical modeling technique were employed to predict the dengue incidence of 2013 from the meteorological factors and its time lag of the test dataset. Afterwards, the predicted and observed values were used to calculate the root mean square error (RMSE) and mean absolute error (MAE). These two measures are commonly used to evaluate the performance of a model and determine the accuracy of regression type analysis with a continuous outcome variable [68]. The RMSE is calculated by the square root of the average of squared differences while MAE is the average over the absolute differences between predicted and actual observations. The difference between the two lies on the calculation of the error. RMSE uses the square root of the average squared errors in order to give relatively high weight to large errors. Thus, RMSE value tends to increase along with the variance of the frequency distribution of error magnitudes. On the other hand, MAE relies only to the variance of the errors without considering its magnitude. As such, MAE is considered to be an unbiased estimator while RMSE is a biased estimator due to this difference. Nevertheless, we adhere to the recommendation of the study by Chai and Draxler [68] where both measures should be used in assessing the different modeling approaches.

Association and cross-correlation analysis
Pearson's correlation analysis showed that 7 meteorological variables are found to be significantly associated with dengue Incidence (Table 1). These are from highest to lowest correlation; [1] relative humidity, [2] maximum temperature, [3] total rainfall, [4] mean temperature, [5] flood, [6] minimum wind direction and [7] southern oscillation index. Moreover, all climatic variables except for average wind speed, average and maximum temperature were found to have a positive association towards dengue incidence. Also, Table 1 shows the identified highest associated time lags each meteorological factor to dengue incidence. Relative humidity, rainfall and flood showed the highest association from lag weeks 4-6 respectively. Minimum, average and maximum temperatures showed the highest association from lag weeks 13-18. Lag weeks 10 and 25 were identified in minimum and maximum wind direction respectively while SOI showed highest association in lag week 20. Wind speed had correlation coefficients near zero and found to be not statistically significant, thus, this lag meteorological factor was not included in subsequent analysis.
Correlation analysis among meteorological factors (MF) (Additional file 1: Table S1a) showed that Average and Maximum Temperatures are highly correlated (r > 0.8) but not in the case of their corresponding lags (LG) (r < 0.8) (Additional file 1: Table S1b). We still decided to include Average Temperature for both datasets in the model development for comparative purposes and also assess in the subsequent sections if its exclusion may considerably affect the robustness of the final model (Additional file 4: Table S4).

General additive model
Additional file 2: Table S2a 81). The allmeteorological model (GAM-LG) was shown to be the best model with an adjusted R 2 of 0.65 and variables that were statistically significant for the model are flood occurrence, rainfall, relative humidity, maximum temperature and SOI (Table 3) (Additional file 3: Table S3a). Since Average and Maximum Temperature were highly correlated, we examine their model quality when either one of them are excluded in model development for both datasets (MF and LG). In both MF and LG datasets, exclusion of maximum or average temperatures in the model development resulted to higher AIC values as compared to all-meteorological models (Additional file 4: Table S4a). Moreover, with the direct dependence of relative humidity with rainfall and temperature, we also explored the exclusion of this meteorological factor in model development and compared the model quality in  ). Similarly, the excluded relative humidity models were shown to generate higher AIC values than GAM-MF and GAM-LG models. Table 2 and Figure 2a show the prediction performance of the GAM-MF and GAM-LG models when using the test subset for model validation. Although both models were able to capture the dengue trend pattern, some forecast points are either overestimated or underestimated. Furthermore, the GAM-LG appears to be the better model than GAM-MF since it generated a lower RMSE and MAE values.

SARIMAX
Additional file 2  Table S3a). Furthermore, exclusion of average, maximum temperatures and relative humidity did not improve the model quality and performance (Additional file 4: Tables S4a and b). SARIMA-DI, SARIMA-MF and SARIMA-LG models were used to forecast the dengue incidence from the test dataset. Figure 2b shows the dengue pattern produced by the different models. It can be observed that the point forecasts are considerably away from the observed values and the dengue trend pattern is not discernable. Among the three models, SARIMA-LG model generated lowest RMSE and MAE values ( Table 2).   Table 2). Figure 2c shows that that two models were able to capture the dengue trend pattern of 2013. However, majority of the predictive values of RF-MF were either overestimated or underestimated. Figure 3b and Additional file 3: Table S3b shows the important variables of each GB model. In the GB   meteorological factors model (GB-MF), four factors were only considered above the 10% threshold; relative humidity, rainfall, average and maximum temperature. On the other hand, the GB lagged meteorological (GB-LG) model determined 5 lagged meteorological factors above the 11% threshold; relative humidity, rainfall, southern oscillation index, average and maximum temperatures. GB-MF and GB-LG are still considered the suitable models even though maximum, average temperatures and relative humidity are excluded in the model development (Additional file 4: Tables S4a and b). Furthermore, the prediction accuracy of the GB-LG model generated lower RMSE and MAE values than the GB-MF model ( Table 2). All models were able to capture the dengue trend pattern of 2013 however majority of the predictive values were either overestimated or underestimated (Fig. 2d).

Comparison and evaluation of model performance across all statistical modeling techniques
Among the statistical modeling techniques, RF showed the lowest RMSE and MAE values across all types of datasets (Table 2). Moreover, it was also shown that LG datasets provided the lowest values across the different statistical modeling techniques. The RF-LG model showed to be the best model as evidence from the performance measures and the pattern of the predictive values against the observed values. Table 3 shows the variable importance of the four statistical modeling technique from each type of dataset. It is clear that no factor is commonly found in all techniques except for relative humidity and maximum temperature. The two factors are determined important by GAM, RF and GB in both datasets (MF and LG). Furthermore, rainfall and average temperature appears to be also mutually important too in the LG datasets.

Comparison of the statistical modeling techniques and datasets
Overall, the two machine learning methods (MLMs), Random Forest and Gradient Boosting outperformed the two conventional statistical modeling techniques in predicting the temporal dengue incidence of Metro Manila in 2013. The findings of our study are consistent with other literature in showing the exceptional performance of these methods over classical methods [45,69,70]. MLMs have several advantages as compared to conventional statistical techniques. One such case is the robustness towards outliers. Parametric statistics such as means, standard deviation and correlations are highly sensitive to outliers. Thus, conventional statistical procedures that are based on these parametric statistics may severely influence the final model especially on the predicted responses. The reason why tree-based ensemble methods are robust to outliers because of its fundamental process of splitting and partitioning the dataset. The split can occur based on the proportion of samples within a certain range. Therefore, it is known that outliers would not affect the splitting rule at each node of the tree model. GB was the only method to handle and accommodate missing values. Moreover, imputation of missing values was needed for RF in order to implement model development. This goes the same with SARIMA however, during the imputation process using Kalman filter approach, extrapolation of categorical meteorological factors (e.g. Flood) were not possible. GAM, on the other hand, may only use complete datasets, thus the removal of observations with incomplete entries was needed. Thus, only selected MLMs may have the capability to accommodate missing values. Among all statistical methods used in our study, Random Forest has shown to be the best method in predicting the temporal dengue incidence of Metropolitan Manila. This is consistent with other studies where they find this method as robust and accurate [71][72][73]. Although there are studies which shows GB to be superior from RF, the use of these methods may generate mixed results [74] when applied to different types of dataset. It is highly recommended that applying these methods should compare both results in order to select the best model for prediction as demonstrated by this study. The observed lower RMSE and MAE values in RF can be explained towards how both algorithmic models tackles the bias-variance dilemma [75]. Generally, GB's algorithm is tasked to reduce bias by producing shallow trees while RF reduces variance by generating fully grown decision trees. Moreover, the GB process uses each tree model as its basis to correct errors in its stage-wise approach, thus, producing a higher variance as compared to RF.
Our study has clearly demonstrated that the use of delayed effects or time lags is suitable towards the prediction of dengue incidence. These time lags account for the potential delays in the time which weather affects both the mosquito vector and virus. Since our analysis explored the influence of meteorological factors towards the disease occurrence, the observed time lags may potentially explain the dengue temporal variability in Metropolitan Manila. Time lags are appropriate in model development for dengue due to the nature of its disease dynamics where it starts with mosquito development, mosquito acquisition and amplification of the virus, seeking host behavior of mosquitoes and virus incubation in humans leading to disease outbreak [76,77]. The impact of time lag effect on dengue incidence has been investigated by numerous studies [16,37,78,79] (with varying lags observed for each meteorological factor. With this, it is clearly appropriate and applicable the use of time lags in predicting dengue incidence especially when using meteorological factors. It should be known that our study is inherent with certain limitations. First, the study specifies only one location in the Philippines which is Metropolitan Manila. The application of the results may only be good for this area but may change to some extent when applied to other regions in the Philippines. Different regions may possess diverse types of landscapes (i.e. urban or rural) or experience atypical ENSO effects that can feature different annual climatological cycles as well as meteorological profiles. Thus, leading to other meteorological factors or teleconnections besides ENSO to be important as compared to the results of this study. Another that needs to be considered is the multifacet nature of dengue disease dynamics where the study limited itself to a selected ecological factor. Other factors such as biological (e.g. mosquito surveillance and serological surveys) and sociological (human movement, health services) aspects may be added in the future along with meteorological variables. It is noteworthy to mention that the Philippines had started to use the approved dengue vaccine (Dengvaxia®) [80] in high dengue endemic areas such as Metropolitan Manila. It is expected that dengue morbidity will lower as compared to previous years, thus, affecting the prediction nature of the models used in the study. It is essential that such event should be included in future endeavors of dengue risk modeling. Nonetheless, the results of the study provide valuable insights when employing different modeling approaches. This may serve as a guide especially for those who are embarking to model factors that are linked with dengue disease using recent modeling techniques such as MLMs.

Important meteorological factors in predicting dengue incidence
The impact of meteorological factors towards dengue incidence has been widely studied. The most common meteorological factors associated with dengue incidence are rain, temperature and relative humidity [81][82][83][84]. Following the factors deemed important by the best model, RF-LG, rainfall, relative humidity, temperature, and SOI were selected. These findings are consistent with previous results [28,33] except for relative humidity. In our study, we find that a positive correlation of rainfall to dengue incidence. Moreover, the annual increasing trend of dengue cases in the Philippines, especially in the study area, happens during the rainy season (June -October) of the Philippines. The presence of water bodies plays a big role in the abundance and development of the dengue vector mosquito. Aedes aegypti mosquitoes are holometabolous insects wherein it relies on water bodies to complete its general life cycle of about two weeks under ideal conditions [85]. Hence, the presence of rainfall provides breeding habitats and opportunities for these mosquito vectors to proliferate or become abundant in the environment [86]. However, there is still a debate on whether this factor is considered as the sole basis of explaining the weekly occurrence of dengue. In Singapore, for example, rainfall was determined not highly influential towards the temporal pattern of dengue cases [87]. The likely impact of rainfall may be restricted due to the fact that majority of the breeding sites of Ae aegpyti are found indoors. This may possibly be one of the reasons why dengue is incessant in Metropolitan Manila especially during the non-rainy months throughout the year.
With the Philippines being a tropical country, Metropolitan Manila's temperature annual do not vary as much. The study area has an average annual temperature of 27.91°C with an average minimum temperature of 22.51°C and an average maximum temperature of 33.60°C during 2009-2013. Our correlation analysis found a positive association in minimum temperature while a negative association in average and maximum temperature. Thus pertaining that high dengue occurrence may occur in temperatures between 23°C -28°C in Metropolitan Manila. The role of temperature has been considered to be the driving factor for mosquito development, thus leading to its abundance.
Several studies [88][89][90][91] have conducted experiments to ascertain the optimal temperature for the development and survival of the vector. Because of such, this had led to the basis that these mosquitoes can spatially expand their habitat under climate-based scenarios. Additionally, temperature regulation in breeding containers was determined to be a factor towards the developmental rate of the dengue mosquito [92]. Changes in temperature not only affect the biology and ecology of the mosquito but also the dengue virus. There is compelling evidence that changes in temperature is associated in the replication, maturation and infective periods of the virus in mosquitoes [37,93].
What is noteworthy in our findings is the importance of relative humidity. In our correlation analysis, it was ranked with the highest association among all meteorological variables. Furthermore, relative humidity appears to be an important meteorological factor in most of the statistical techniques employed in the study. Although there is a direct dependence of relative humidity towards temperature and rainfall, our study demonstrated that the omission of such affect the model quality and performance of the different models. Thus, indicating its non-dependency towards rainfall or temperature. Relative humidity was neither emphasized nor highlighted by previous Philippine studies [28,33]. There is a great deal of emphasis of this meteorological factor linking the biology and population dynamics of Ae. aegypti. Relative humidity had been claimed to be a consistent and substantial factor that provides a suitable condition for the development and survival of the mosquito vector [94]. In Thailand, relative humidity is deemed to be a determinant in the egg development and adult population size of the mosquito vector [95]. It was also observed in Texas that there was an increase in the hatching rate of Ae. aegypti eggs whenever there is an increase in relative humidity [96]. Moreover, relative humidity is highlighted to be a crucial factor in affecting the life patterns of the mosquito dengue vectors such as mating, oviposition, and seeking host pattern [97] which are necessary for increasing dengue transmission.
Another notable observation in the results is that no single factor was found to be important across all models. However, relative humidity and maximum temperature appear to be the common important factors found in the models of GAM, RF and GB in both datasets.
Additionally, it appears that conventional modeling techniques (e.g. SARIMAX) tend to obtain different statistical significant factors when a different dataset is applied. Unlike MLMs, the important factors identified were nearly the same in MF and LG datasets. It is the intention of the study to capture common meteorological factor/s when different statistical modeling techniques are applied. This pertains that the factor is really robust amidst on how it is used in model development. Therefore, our study may only infer the importance of the two meteorological factors because of its frequent occurrence across modeling techniques. Moreover, our study would also like to emphasize that it does not challenge nor invalidate the importance of other meteorological factors such as rainfall or flood. We acknowledge these meteorological factors to be highly important due to its link in dengue disease dynamics. The importance of relative humidity was indeed a remarkable outcome in the study, thus broadening our current perspective and understanding on its influence in dengue disease dynamics of Metropolitan Manila. Lastly, our study is a clear demonstration of how different modeling approaches may tend to yield diverse meteorological factors as important predictors. Thus, it is imperative to be mindful on what kind of datasets to use (e.g. lag factors) or the application of a modeling approach in order to present a meaningful interpretation. It is recommended to future researchers to apply the same approach employed by the study in order to gain valuable insights not only in its methodological aspect but to other potential effects of meteorological factors to dengue occurrence.

Conclusion
Our study has revealed that Tree-based Machine Learning methods (RF and GB) performed well in predicting the temporal pattern of dengue Incidence of Metropolitan Manila as compared to conventional statistical modeling techniques (GAM and SARIMAX). Our study also highlighted that the use of delayed effects or time lags (LG) of each meteorological factor are more appropriate in predicting dengue incidence. With this, our approach may serve as a basis towards choosing an appropriate modeling technique to be used in adopting an early outbreak warning system. It is further recommended that other factors such as temporal vector abundance and virus epidemiology should be included in order to broaden the scope of understanding and perspective of dengue disease.
Relative humidity was deemed by our study to be also an important variable in the RF-LG model along with rainfall and temperature. This meteorological factor was not only found from the best model but from other models as well either on the top two or three most important variable. Such finding is noteworthy because it provides a broader perspective and understanding on how meteorological variables tend to influence the temporal pattern of disease occurrence in Metropolitan Manila. This is worth investigating for future endeavors since no study has ever been conducted yet in exploring this meteorological factor to dengue disease in the Philippines.