3.1 Epidemiological characteristics of epidemics between 2012 and 2019 in Singapore
Between January 2012 and August 2019, there were a total of five major dengue epidemics with incidence above 100 per 100,000 in Singapore [35]. The time series data shows the trend of dengue cases over the study period, with epidemics in 2013, 2014, 2015, 2016 and 2019 characterised by peaks (Figure 1). The average weekly number of dengue infections was 217.02. There were generally small variations in weekly temperature and wind speed. Weekly rainfall and PSI varies in a wider range (Table 1)
The 2013 epidemic holds the current national record for the highest number of dengue cases recorded in a year, where the dengue incidence was 22,170 cases (404.9 cases per 100,000 population annually) and dengue 1 serotype was the predominant strain (Table S1). Thereafter high incidence levels continued to be seen in the 2014 epidemic, which became Singapore’s second-largest outbreak within a year— the dengue incidence was 18,326 cases (325.6 cases per 100,000 population annually), with dengue 1 serotype as the predominant strain. The 2015 epidemic was comparatively mild with dengue incidence at 11, 294 cases (196.1 cases per 100,000 population annually) and was predominated by strain 2. Subsequently, the 2016 epidemic saw a dengue incidence of 13, 085 cases (229.1 cases per 100,000 population annually) and was predominated by dengue 2 serotype. After low dengue activity levels for a couple of years, the 2019 epidemic became the third-biggest dengue outbreak recorded nationally with a dengue incidence of 16,100 cases (282.3 cases per 100,000 population annually) and dengue 2 and 3 serotypes taking over as the co-predominant strains [30, 36, 37]
3.2 Linear relationship with weather factors in Cross-correlation & ARIMA modelling
Pearson’s cross-correlation coefficients for each climatic factor after pre-whitening are shown in Table 2. In general, pollutant standards index (PSI) and wind speed have an inverse linear relationship associated with dengue incidence while mean, maximum and minimum temperature have a direct linear association with dengue incidence. No significant correlation was observed between rainfall and dengue incidence in Singapore. The maximum lag effect observed across all climatic correlations did not exceed 15 weeks. Both mean and minimum temperature exhibited a lag effect of 1-2 weeks. Additionally, an 11-week lag time for both mean and maximum temperature showed significant correlation with number of dengue cases. Other significant cross-correlations with dengue incidence observed include 5 and 7 weeks lag for PSI, and 5 weeks for wind speed variable. (Table 2)
Moreover, a significant autocorrelation coefficient was found at lag time of 1 week as indicated by the autocorrelation graph (Figure S1). ARIMA (1, 1, 0) was selected as the best model to describe the trend and autoregressive parameters of the dengue time series. Residual diagnostics were conducted to assess model appropriateness, including the use of Ljung-Box tests, which accepted the null hypothesis given a p-value of 0.3686. (Figure S2).
Using univariate ARIMA models with variables derived from significant cross-correlations, the following factors were found to be significantly associated with dengue incidence: PSI with a 5-week and 7-week lag time, mean temperature at 1-week & 11-week lag time, maximum temperature at an 11-week lag time and wind speed at a 5-week lag time (Table 2).
3.3 Non-linear relationship with weather factors in Cross-correlation & DLNM
Using Spearman cross-correlation analysis to explore possible non-linear trends (Figure S3), a positive correlation was found between temperature and dengue cases while PSI and wind speed showed negative correlation. Like the linear cross-correlation analysis, there was no apparent association between rainfall and dengue cases.
For the quasi-Poisson with DLNM association, estimated parameters with optimal fitting performance (the smallest QAIC) were chosen. The choice of df, parameters and corresponding QAIC of each weather factor were shown in Table 3. The models in univariate analysis included the effect of PSI on dengue cases lagged by a maximum of 16 weeks (lag 0-16), total rainfall (lag 0-15), mean temperature (lag 0-16), maximum temperature (lag 0-16) and wind speed (lag 0-5). The best-performing model was that of wind speed with the lowest QAIC of 4842.808, suggesting that wind speed explained dengue incidence the best amongst all climatic factors. Autocorrelation of residuals was tested to ensure absence of autocorrelation and assumption of overdispersion was checked (Figure S4), justifying the use of a Quasi-Poisson regression. The DLNM model output had a fitted number of dengue cases that mirrored the observed trend of dengue cases closely as seen in Figure S5. The graphical output of dengue DLNM modelling for each climatic variable is described in the following subsections.
3.3.1 Effect of PSI
With a median of 48.22 PSI defined as reference, visualisation of DLNM model output with the 3D graph and contour graph (Figure 2(a)(b)) showed that the RR of dengue generally increased up to a PSI level of 100 approximately along with all lags, beyond which the RR falls sharply.
The sliced graph for PSI at lag 7 (Figure 2(c)) indicated that PSI between 15 and 107 increased the RR of dengue, and levels beyond around 107 reduced the RR of dengue. Taking median of PSI 48.22 as reference, the RR of dengue increased 6% (RR: 1.06, 95% CI: 1.03, 1.09) when PSI level is 107 and decreased 25% (RR: 0.75, 95% CI: 0.67, 0.85) when PSI level is 160. From fig. 2(d) different performances of lag-response association at different PSI level were observed. An immediate and inhibiting effect of high level PSI could be easily found.
A similar trend was observed in the overall effects graph (Figure 2(e)). The overall effect of PSI on RR of dengue increased around 63% (RR: 1.63, 95% CI: 1.20, 2.20) when PSI level was 100, and reduced by around 84% (RR: 0.16, 95% CI: 0.06, 0.41) when PSI level was 150. This further illustrates that moderate escalation of PSI would increase risk of dengue while extremely high PSI level would inhibit dengue. However, in the sensitivity analysis, CI around 100 expanded dramatically, corresponding to reduced statistical significance.
3.3.2 Effect of rainfall
Reference of rainfall level was 5.54 mm. In the 3D graph and Contour graph (Figure 3(a)(b)), it can be observed that associations between exposure and response across all the lags was identical -- positive and negative effect appeared alternately along with lags. From sliced graph at lag 4 and lag 11, we can observe similar curve but slightly different confidence interval, which may indicate that rainfall at lag 11 had more significant effect on dengue infections (Figure 3(c)). A similar trend was observed in the overall effect graph (Figure 3(d)). The interval of rainfall between 0 and 7 (mm) promoted the dengue infections (Rainfall: 7 (mm), RR: 1.16, 95%: 1.01, 1.34). On the contrary, heavy rainfall had a ‘protective’ effect on dengue, with RR: 0.44 (0.28-0.70) at rainfall level 12 (mm) and RR: 0.19 (0.06, 0.58) at rainfall level 21(mm). The positive effect on RR observed between rainfall levels of 13-17 mm and 24-25 mm were, however, insignificant.
3.3.3 Effect of temperature
Median of mean, maximum and minimum temperature were 28.01 °C, 31.84 °C and 25.14 °C respectively. From the 3D and contour graphs of each temperature (Figure 4(a)(b)) three types of temperature showcased similar behaviour in exposure-lag-response relationship – eachpresented a different temperature-dengue correlation at each lag. Specific to one certain lag, lag 1 and lag 5 were selected as the benchmark to illustrate the variation of association at different lags. RR increased once the mean, maximum and minimum temperature escalated at lag 1 while RR decreased when temperature reached up to a high level at lag 5 (Figure 4(c)(d)(e)). On the other hand, lag-response association, holding the temperature constant, behaved similarly in 3 types of temperature (Figure 4(c)(d)(e)). A relatively cold temperature showed an inhibitive effect at lag 0 whereas a relatively hot temperature showed an inhibitive effect at lag 4 and a positive effect at lag 1. In terms of overall effect (Figure 4(f)), mean temperature was observed to have no significant association with the relative risk of dengue. Maximum and minimum temperature were found to have positive association within the relatively cold temperature interval (27-32 °C and 23-25 °C). The RR of maximum temperature model at 28 °C was 0.46 (Ref. 31.84 °C), with 95% CI (0.22, 0.94). while the RR of minimum temperature model at 24 °C was 0.76 (Ref. 25.14 °C), with 95% CI (0.65, 0.88). Moreover, a relatively hot temperature was always found to exert a negative influence on dengue infections, especially significant in minimum temperature situation (27°C, Ref. 25.14 °C; RR: 0.74, 95% CI: 0.58, 0.93).
3.3.4 Effect of wind speed
In terms of wind speed at a reference value of 7.52km/h, the 3D and contour graph showed different curves at marginal lags and middle lags (Figure 5(a)(b)). At lag 2 and lag 5 (Figure 5(c)), RR at lag 2 was consistently stagnant as wind speed increased.. However, wind speed-dengue association graph at lag 5 clearly illustrated a reduction in RR of dengue as wind speed increased.. Meanwhile, wind speed at 10 km/h, compared with 6 km/h, suggested stronger negative effect along the lags. From figure 5(d), an evident downward trend of RR related to overall effect along with wind speed was observed. Wind speed at 12 km/h was associated with a 38% (RR: 0.62, 95% CI: 0.50, 0.76, Ref : 7.52km/h) overall reduction in risk of dengue.
3.3.5 Multivariate analysis
Utilising the forward selection methodology, wind speed was first selected for the model based on its smallest QAIC of 4842.808. The model was introduced with a second variable PSI, which had a QAIC of 4523.012, as wind speed was kept constant. Subsequent selection of remaining variables failed to reduce QAIC further, which implied that only cross basis of wind speed and PSI would be considered for the final model. To check the robustness of our model, overall effect graphs of both of PSI and wind speed were redrawn and similar performances in univariate model were found (Figure S6).
3.3.6 Sensitivity analysis
In general, varying the df of time trend and seasonality did not change the direction of effect to a large degree (Figure S7). However, some statistical significance was lost when df per year increased, such as PSI around 100, rainfall around 20 mm, minimum temperature under median value, wind speed beyond median value. This reduction in significance was likely due to the far fewer counts at these levels or collinearity introduced by more df of time trend and seasonality. Figure S8 displayed overall effect of weather factors when df of exposure ranging from 2-6 (Exclude the number used in previous sections). The general features of overall effect remain the same despite occurrence of some wider CI intervals. Figure S9 also illustrated the robustness while knots placement varied. Among all of above sensitivity analysis, an alert was proposed that at the marginal level of weather or interval where the level of weather rarely reached, the statistical significance of RR would expand dramatically when model parameters varied.
3.4 Evaluation of Model Prediction Performance
To exploit the predictive power of this model, data from 2012-2018 was used as the training set while data from 2019 was used for testing purposes. Among all models, mean temperature was the best variable to forecast the future number of dengue cases, with a mean absolute error 43.15 and root mean square error 51.39 (Table S2).