S1 Appendix -

<p>Table A: Summary of acronyms used throughout the analysis. Table B: Summary statistics for the studied Peruvian departments. Population refers to the last mid-year population estimate of a department’s population within the studied period, as of 30 June 2021, whilst Population Density is the corresponding estimated population per km2. DIR is the mean dengue incidence rate per 100,000 across the studied period of 2010 to 2021. Maximum Temperature and Minimum Temperature similarly relate to the mean average observed value of the monthly means of maximum daily temperatures and of the monthly means of minimum daily temperatures. Total Precipitation is the mean of monthly observed total precipitations. Table C: Summary statistics for LOOCV outbreak detection performance. Out-of-sample observations (<i>n</i> = 417), across 2010 to 2021, were classified as being predicted true outbreaks such that DIR exceeded 50 (or 150) per 100,000 if the posterior probability of DIR exceeding 50 (or 150) per 100,000 was greater than a calibrated cut-off probability of 0.16 (or 0.13). True Positive measures the hit rate, or equivalently the proportion of true outbreaks correctly detected, whilst False Positive measures the proportion of non-outbreaks incorrectly classified as outbreaks. Accuracy represents the proportion of observations whose outbreak classification matched the true observed state (such as a predicted outbreak coinciding with an outbreak). Precision measures the proportion of predicted outbreaks which were true outbreaks. Finally, the AUC is the area under the Receiver Operating Characteristic (ROC) curve, is used as a measure of our model’s skill for distinguishing between outbreaks and non-outbreaks, and here, represents an upper bound on the model’s retrospective performance (due to calibration of our cut-off probability for outbreak classification). 95% confidence intervals (CIs) for summary statistics were derived using exact binomial confidence limits, with the exception of the 95% CI for AUC being calculated using 2,000 bootstrap replicates. Table D: Summary statistics for non-model-based forecasting outbreak detection across 2018 to 2021. DIR (Dengue Incidence Rate) observations (<i>n</i> = 180) were classified one month ahead of time as being predicted true outbreaks with DIR exceeding 50 (or 150) per 100,000 only if the previous month’s DIR had exceeded 50 (or 150) per 100,000. The performance metrics below, and associated 95% confidence intervals (CIs), each have the same interpretation as defined in Table C. Classification of outbreaks below can be compared to our model-based classification of future outbreaks in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0012596#pntd.0012596.t001" target="_blank">Table 1</a>, where 100Fig A: Exploratory analysis of climate-dengue relationships. Cross-correlation plots for monthly lags of six climatic variables and the monthly dengue incidence rate (DIR) per 100,000 in each of the three studied departments. The plots depict a strong degree of shared similarity across departments in the timing and nature of relationship between the climate exposure and DIR. Negative lags correspond to lead times in months. Fig B: Omitting RSI and seasonality effects, exposure-lag-response relationships between climatic variables and dengue incidence. Plots of relative risk (RR), on a logarithm scale, for the included DLNMs (Distributed Lag Non-linear Models) in a climate-based Bayesian hierarchical model for dengue incidence fitted to the entire period of 140 months, where RR is defined relative to the risk induced by the mean observed value of each climate variable. Log RR values greater than 0 (pink to purple) correspond to heightened relative risk of dengue incidence, whilst values less than 0 (green) correspond to reduced RR. The four climatic variables were included in the model via DLNM specifications alongside spatial random effects, temporal random effects, and spatiotemporal random effects, but not including our usual fixed effects (of momentum and seasonality). Fig C: Omitting maximum temperature effects, exposure-lag-response relationships between climatic variables and dengue incidence. Plots of relative risk (RR), on a logarithm scale, for the included DLNMs (Distributed Lag Non-linear Models) in a climate-based Bayesian hierarchical model for dengue incidence fitted to the entire period of 140 months, where RR is defined relative to the risk induced by the mean observed value of each climate variable. Log RR values greater than 0 (pink to purple) correspond to heightened relative risk of dengue incidence, whilst values less than 0 (green) correspond to reduced RR. The three climatic variables were included in the model via DLNM specifications alongside spatial random effects, temporal random effects, and spatiotemporal random effects, and fixed effects (of momentum and seasonality). Fig D: Omitting precipitation effects, exposure-lag-response relationships between climatic variables and dengue incidence. Plots of relative risk (RR), on a logarithm scale, for the included DLNMs (Distributed Lag Non-linear Models) in a climate-based Bayesian hierarchical model for dengue incidence fitted to the entire period of 140 months, where RR is defined relative to the risk induced by the mean observed value of each climate variable. Log RR values greater than 0 (pink to purple) correspond to heightened relative risk of dengue incidence, whilst values less than 0 (green) correspond to reduced RR. The three climatic variables were included in the model via DLNM specifications alongside spatial random effects, temporal random effects, and spatiotemporal random effects, and fixed effects (of momentum and seasonality). Fig E: Omitting the drought indicator, exposure-lag-response relationships between climatic variables and dengue incidence. Plots of relative risk (RR), on a logarithm scale, for the included DLNMs (Distributed Lag Non-linear Models) in a climate-based Bayesian hierarchical model for dengue incidence fitted to the entire period of 140 months, where RR is defined relative to the risk induced by the mean observed value of each climate variable. Log RR values greater than 0 (pink to purple) correspond to heightened relative risk of dengue incidence, whilst values less than 0 (green) correspond to reduced RR. The three climatic variables were included in the model via DLNM specifications alongside spatial random effects, temporal random effects, and spatiotemporal random effects, and fixed effects (of momentum and seasonality). Fig F: Omitting El Niño effects, exposure-lag-response relationships between climatic variables and dengue incidence. Plots of relative risk (RR), on a logarithm scale, for the included DLNMs (Distributed Lag Non-linear Models) in a climate-based Bayesian hierarchical model for dengue incidence fitted to the entire period of 140 months, where RR is defined relative to the risk induced by the mean observed value of each climate variable. Log RR values greater than 0 (pink to purple) correspond to heightened relative risk of dengue incidence, whilst values less than 0 (green) correspond to reduced RR. The three climatic variables were included in the model via DLNM specifications alongside spatial random effects, temporal random effects, and spatiotemporal random effects, and fixed effects (of momentum and seasonality). Fig G: Historical climatic time series. Exploratory plots which depict the monthly climatic data in Piura, Tumbes and Lambayeque over 140 months from May 2010 to December 2021. Both indicators for El Niño events (ICEN and ONI) are common across the three departments. Fig H: Department-specific seasonality. A decomposition of the seasonality component in dengue incidence rates in each of the departments, calculated using the bfast package in R, which iteratively decomposes a time series into trend and seasonality components whilst detecting abrupt changes within the components. The results of the bfast algorithm indicate similarity in the seasonal trends in dengue incidence rates across each of the three departments. Fig I: Cumulative association between climatic variables and DIR. Plots of cumulative risk for the included DLNMs in climate-based Bayesian hierarchical model for dengue incidence, where cumulative risk is defined relative to the cumulative risk induced by the mean observed value of each climate variable. Cumulative risk values greater than 1 correspond to heightened cumulative risk of dengue incidence, whilst values less than 1 correspond to reduced cumulative risk. For example, as cumulative risk was negative for a monthly precipitation of 1mm at the current lag, then exposure over one month to dry conditions was associated with reduced risk, whilst positive values of cumulative risk at two months indicates that the exposure over two months resulted in a increased cumulative risk in dengue incidence. Note that in each sub-plot, we define a high and low value of the climatic variable, and the cumulative risk at each lag is defined relative to the cumulative risk induced by the mean value of the climatic variable. Fig J: In-sample predictive performance of our Bayesian spatiotemporal model. The DIR (Dengue Incidence Rate) time series (gold) for each department is plotted alongside the posterior median estimate (forest green) for each observation and the corresponding estimated 95% credible intervals (shaded grey). <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0012596#pntd.0012596.g004" target="_blank">Fig 4</a> is the corresponding figure for the cross-validation setting which display the estimated out-of-sample predictive performance and thus, approximates the model’s generalisability. Fig K: Estimated posterior distributions of department-specific yearly random effects. The visualization displays the posterior median est