hisprwanda/sarimax-xgboost-malaria-model-comoros

# Ensemble S+X — Climate-Health Probabilistic Forecasting A CHAP-compatible probabilistic forecasting model that combines two structurally distinct learners — **SARIMAX** for temporal autocorrelation and **XGBoost** for non-linear covariate response — into a single ensemble. Originally developed and benchmarked on weekly malaria case data from the **Ngazidja (Grande Comore)** island, Union of the Comoros. Validated on **5 districts** using ground-truth local station climate data, where it outperformed SARIMAX, Prophet, and XGBoost as standalone models, as well as a three-component (S+P+X) ensemble. --- ## What it does For each spatial unit (district, region, etc.) and each forecast week, the model produces a probabilistic forecast represented as a sample distribution. This lets downstream tools compute any statistic — median, mean, prediction intervals, exceedance probabilities for outbreak alerts, etc. Two component models are fit independently per location and combined by **sample concatenation** (50 SARIMAX samples + 50 XGBoost samples = 100 samples per location/week): | Component | Role | Key technique | |---|---|---| | **SARIMAX(1,0,1) tuned** | Captures temporal autocorrelation and lagged climate signal | Per-location informed feature selection at \|r\| > 0.10 | | **XGBoost calibrated** | Captures non-linear climate-response interactions | Native multi-quantile objective (25 quantile levels) | The two are structurally orthogonal — SARIMAX models *temporal* dependence, XGBoost models *covariate-conditional* response — which is what makes their combination genuinely additive. --- ## Benchmark performance (Comoros, 5 districts — local station data) Evaluated on weeks 79–104 (26-week test horizon), trained on weeks 1–78. Climate data sourced from **ground-truth local meteorological stations** (not satellite proxy). | District | CRPS | RMSE | 80% PI coverage | 95% PI coverage | |---|---|---|---|---| | Hamahamet-Mboinkou | 22.23 | 38.00 | 69 % | 88 % | …