Modelling Hepatitis B virus related hospital discharges in Spain: ARIMAX based liver disease forecasting tool for hospital workload and mortality progression

Introduction: Chronic hepatitis B (CHB) virus infection leads to severe complications, cirrhosis and hepatocellular carcinoma (HCC). The main objective of this study was to develop an ARIMA-based model to forecast the progression of global hospital discharges, due to cirrhosis and HCC related to chronic hepatitis B. Methods: Retrospective observational study of monthly incidence of CHB related hospitalization discharges from 2005 to 2021 in Spain. Data were obtained through the Spanish Minimum dataset of hospital discharge registry (CMBDH) of the Health Ministry. Main diagnosis of CHB, liver cirrhosis and HCC encoded by International Medical codes (ICM–9 and ICM-10) were used. Descriptive and time series analysis was performed with forecasts made for 2022 using seasonal ARIMA and ARIMAX models. Data stationarity was achieved via a square root Box-Cox transformations and differencing. Model selection used was AIC, BIC, MAPE, and forecasting precision. Analysis was performed in R (version 4.5.0). Results: The total number of discharges related to hepatitis B was 6743, 58% were due to HCC and 42% to cirrhosis diagnosis. Median age was 59 years (range: 7 to > 100), being 83.4% men. The global chronic hepatitis B (CHB) related workload values range from 10 to 55 monthly discharges, while hepatitis B related to HCC and cirrhosis range from 4 to 34 and 1–29 discharges, respectively. The best fit and 2022 forecasts found for CHB and HCC time series was obtained with the approximate Gaussian Y-ARIMAX (6,0,0) (0,1,1) _12 model. This model after treating outliers, removes seasonal patterns and captures the series’ autoregressive dynamics with an AR(6) and seasonal MA(1) noise with expression: (1 − ϕ1B − ϕ2B2 − ... − ϕ6B6)(yt −yt−12) = εt + Θ1 εt−12 with ε ~ N(0, σ²) and in the square root scale. Conclusion: Both ARIMA and ARIMAX models play critical roles in forecasting CHB-related HCC and cirrhosis, enabling better disease monitoring, healthcare resources, and intervention assessment. ARIMAX provided more accurate context-aware predictions, making it especially valuable for public health decision-making.