Environmental and Clinical Predictors Forecast Malaria
Environmental and Clinical Predictors Forecast Malaria
There were slightly more females than males with confirmed malaria at each site and the mean annual temperatures were relatively similar with a 2°C difference across the sites (Table 2). Nagongera had the youngest malaria cases in age and generally, there were slightly more female than male confirmed malaria cases at each site. On average, Nagongera had the highest daytime temperatures (29.8°C) and received the most rain in 2012 (1.66 m).
The predictors included in the final models varied by sentinel site (Table 3). A commonly included category of predictor was drug treatment, with at least one treatment predictor series included in every model. Appropriate treatment and the number of courses of ACT were the most frequently included treatment predictors. Total rainfall was the most commonly retained environmental predictor. Kamwezi's models contained the smallest number of predictors, four, whereas Walukuba contained the most, fourteen. Approximately half the predictor series were lagged, ranging from lags of 1 to 52 weeks. A table of the predictors, parameters, and lags are included in an appendix (See Additional file 1: Table S1 http://www.malariajournal.com/content/14/1/245/additional).
Seasonality was visually assessed for each model using the ACF and PACF, although none of the models included seasonal terms as non-seasonal parameters and predictors were sufficient to capture any seasonal variation. All models had one order of differencing and a moving average term of one order. However, the orders of the autoregressive (AR) terms ranged from 1 to 43.
The short-term horizons (e.g., 1- to 4-weeks ahead) were better at predicting high-frequency variation in malaria cases compared to longer-term horizons although the short-term horizons predicted the peaks 1 to 4 weeks after they were observed (Figure 2). Kamwezi had the highest error with an average of 128% across all 52 forecast horizons and Nagongera had the lowest average error at 27% (Table 4). When examining the forecasting accuracy by forecast horizon, horizon one forecasts (i.e., 1-week ahead forecasts), typically resulted in the smallest error. The weekly SMAPE error was highest when the observed counts were low or zero which occurred most often with the Kamwezi site (Figure 3). When examining the ability of models to predict the total number of cases during the forecasting period, Nagongera had the lowest percent error at 2% (Figure 4). The Kihihi model had the largest error with an overprediction of 22% and the average error was 9% for the 52-week forecasted malaria burden across all six sites.
(Enlarge Image)
Figure 2.
Plot of weekly observed and forecasted malaria counts (horizon 1 forecasts) for each UMSP site from 1 June 2012 to 31 May 2013.
(Enlarge Image)
Figure 3.
Plot of weekly-observed malaria counts sized by SMAPE error for forecast horizon 1 for each UMSP site from 1 June 2012 to 31 May 2013. Each weekly observed count of malaria is sized proportionally to the forecasting error associated with that particular observation.
(Enlarge Image)
Figure 4.
Bar chart of the total observed malaria burden versus burden prediction by UMSP site from 1 June 2012 to 31 May 2013.
Results
There were slightly more females than males with confirmed malaria at each site and the mean annual temperatures were relatively similar with a 2°C difference across the sites (Table 2). Nagongera had the youngest malaria cases in age and generally, there were slightly more female than male confirmed malaria cases at each site. On average, Nagongera had the highest daytime temperatures (29.8°C) and received the most rain in 2012 (1.66 m).
The predictors included in the final models varied by sentinel site (Table 3). A commonly included category of predictor was drug treatment, with at least one treatment predictor series included in every model. Appropriate treatment and the number of courses of ACT were the most frequently included treatment predictors. Total rainfall was the most commonly retained environmental predictor. Kamwezi's models contained the smallest number of predictors, four, whereas Walukuba contained the most, fourteen. Approximately half the predictor series were lagged, ranging from lags of 1 to 52 weeks. A table of the predictors, parameters, and lags are included in an appendix (See Additional file 1: Table S1 http://www.malariajournal.com/content/14/1/245/additional).
Seasonality was visually assessed for each model using the ACF and PACF, although none of the models included seasonal terms as non-seasonal parameters and predictors were sufficient to capture any seasonal variation. All models had one order of differencing and a moving average term of one order. However, the orders of the autoregressive (AR) terms ranged from 1 to 43.
The short-term horizons (e.g., 1- to 4-weeks ahead) were better at predicting high-frequency variation in malaria cases compared to longer-term horizons although the short-term horizons predicted the peaks 1 to 4 weeks after they were observed (Figure 2). Kamwezi had the highest error with an average of 128% across all 52 forecast horizons and Nagongera had the lowest average error at 27% (Table 4). When examining the forecasting accuracy by forecast horizon, horizon one forecasts (i.e., 1-week ahead forecasts), typically resulted in the smallest error. The weekly SMAPE error was highest when the observed counts were low or zero which occurred most often with the Kamwezi site (Figure 3). When examining the ability of models to predict the total number of cases during the forecasting period, Nagongera had the lowest percent error at 2% (Figure 4). The Kihihi model had the largest error with an overprediction of 22% and the average error was 9% for the 52-week forecasted malaria burden across all six sites.
(Enlarge Image)
Figure 2.
Plot of weekly observed and forecasted malaria counts (horizon 1 forecasts) for each UMSP site from 1 June 2012 to 31 May 2013.
(Enlarge Image)
Figure 3.
Plot of weekly-observed malaria counts sized by SMAPE error for forecast horizon 1 for each UMSP site from 1 June 2012 to 31 May 2013. Each weekly observed count of malaria is sized proportionally to the forecasting error associated with that particular observation.
(Enlarge Image)
Figure 4.
Bar chart of the total observed malaria burden versus burden prediction by UMSP site from 1 June 2012 to 31 May 2013.
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