Comparing Classical Time-Series and Recurrent Neural Network Models for Univariate and Multivariate Cardiovascular Mortality Forecasting in Shiraz, Iran

Abstract

Background: Daily forecasting of cardiovascular mortality can support short-term public health surveillance and planning, particularly in urban settings where mortality is monitored along with air pollution and meteorological conditions. Shiraz, Iran, is an arid urban setting in which daily cardiovascular mortality and environmental records provide a useful case for comparing classical and recurrent forecasting models. Objectives: This study compared autoregressive integrated moving average (ARIMA), ARIMA with exogenous variables (ARIMAX), recurrent neural network (RNN), long short-term memory (LSTM), and gated recurrent unit (GRU) models for forecasting daily cardiovascular mortality in Shiraz under univariate, cross-correlation function (CCF)-selected multivariate, and manual 7-day multivariate input designs. Methods: We analyzed daily cardiovascular mortality and environmental records from 21 March 2010 to 19 March 2020. Candidate environmental predictors included carbon monoxide (CO), ozone (O3), nitrogen dioxide (NO2), sulfur dioxide (SO2), particulate matter with an aerodynamic diameter of less than 10 μm (PM10), temperature, and humidity. Models were evaluated using a primary 80/20 chronological train–test split and a 70/30 chronological sensitivity split. Neural models were trained with five random seeds per setting. Seed-level losses were aggregated by model and forecast date before computing accuracy metrics and conducting statistical tests; thus, repeated seeds were not treated as independent test observations. Models were ranked by root mean square error (RMSE); mean absolute error (MAE) and symmetric mean absolute percentage error (SMAPE) were also reported, with lower values indicating better forecast accuracy. Statistical evidence was assessed using model confidence set (MCS) analysis, Diebold–Mariano comparisons with Newey–West adjustment and Holm correction, and Friedman omnibus sensitivity testing. Results: Under the primary 80/20 split, the univariate GRU yielded the lowest overall RMSE (RMSE = 0.407, MAE = 0.322, SMAPE = 2.061%). Under the 70/30 sensitivity split, the univariate GRU again yielded the lowest overall RMSE (RMSE = 0.399, MAE = 0.308, SMAPE = 2.014%). The MCS retained multiple close competitors in both splits, indicating that the MCS did not support unique statistical superiority of any single model. Thus, the univariate GRU was the model most consistently ranked first by RMSE, although it was not uniquely statistically superior. Conclusions: Recent mortality history contained most of the short-term forecasting signal. The univariate GRU most consistently had the lowest RMSE, although several classical and recurrent alternatives remained statistically similar. Environmental variables provided limited independent forecasting value beyond recent mortality history under the evaluated input designs and should therefore be assessed as operational extensions rather than assumed to improve forecasts.