Prediction of HIV incidence in Xinjiang Uygur autonomous region, China: a time series study

ObjectiveIn China, Xinjiang Uygur Autonomous Region has a high incidence of HIV, and the situation regarding its prevention and control remains challenging. This study aimed to compare the predictive performance of three time series models, SARIMAX (Seasonal Autoregressive Integrated Moving Average with Exogenous Regressors), Prophet with exogenous variables, and random forest, using rolling validation, and to provide references for HIV prevention and control in Xinjiang.MethodsWe collected 168 months of HIV incidence data in Xinjiang from 2012 to 2025. SARIMAX, Prophet, and random forest were developed with COVID-19 as an exogenous intervention variable. Prophet was tuned via grid search (optimal changepoint.prior.scale=0.1, seasonality.prior.scale=1); random forest was optimized with mtry=3 and 12-month lags selected by PACF. Rolling validation used RMSE, MAE, MAPE, sMAPE, and MASE with Bootstrap 95% CI. SARIMAX failed to converge in the first four windows; therefore, models were compared on windows 5–9 (2021–2025).ResultsThe optimal SARIMAX model was SARIMAX(0, 1, 4)(1, 0, 0)(1) with an exogenous COVID-19 intervention variable; its residuals passed the Ljung-Box test (Q = 8.8, p = 0.7199). The Prophet model incorporated seasonal and periodic components and included COVID-19 as an exogenous variable; Bayesian MCMC inference gave a posterior mean of −0.1064. The random forest model used 12 lagged values, month, and COVID-19 as features, achieving a permutation importance (%IncMSE) of 4.31% for the COVID-19 variable, ranking 10th among 14 features. SHapley Additive exPlanations (SHAP) analysis further showed that COVID-19 ranked 14th (last) with a mean absolute SHAP value of 0.00135. Within windows 5–9 (2021–2025), random forest had the lowest RMSE (0.2211), MAE (0.1722), and MAPE (85.83%); (sMAPE 41.11%, MASE 0.8745). However, Diebold–Mariano tests with Bonferroni correction showed no significant differences among models (all p > 0.0167), with small RMSE differences (0.0047–0.0225).ConclusionsAll three models are applicable. Although random forest had the lowest numerical errors, it was statistically indistinguishable from the other models; therefore, model selection should consider interpretability, data-updating frequency, and resource constraints rather than marginal accuracy differences. These findings support HIV surveillance and resource allocation in Xinjiang.