Time Series Modeling and Forecasting the Number of Patients with Cancer at Benghazi Medical Center Using Box-Jenkins Methodology (2022–2025)

Abstract

Cancer represents one of the most prominent health challenges of the modern era, given the continuous rise in the incidence and mortality rates associated with malignant tumors, and it is classified among the leading causes of death in Libya. Given the importance of analyzing and forecasting the temporal trends of new cases, Utilizing the Box–Jenkins (ARIMA) approach, a statistical model was developed to examine monthly records of newly identified malignant tumors at the Benghazi Medical Center spanning from January 2022 through December 2025, providing future case estimates for the subsequent two-year period (2026–2027). The study relied on monthly data comprising 48 observations, analyzed using the statistical software EViews 13.0, with a mean of 115.75 cases and a standard deviation of 16.64. The methodology included applying the Augmented Dickey-Fuller (ADF) unit root test to verify the stationarity of the series. The ADF test indicated that the series was non-stationary at the level, while stationarity was achieved after taking the first difference (d = 1). Using the autocorrelation function (ACF) and the partial autocorrelation function (PACF), and by comparing the candidate models according to the Akaike Information Criterion (AIC), the Schwarz Bayesian Criterion (SBC), and the lowest standard error of estimate, it was found that the ARIMA (0,1,1) model was the most appropriate and efficient for representing the series. The model passed the diagnostic tests (randomness of residuals and their normality according to the Jarque-Bera test) before proceeding to the forecasting stage. The forecast results indicated a continued upward trend in the number of new cases, with a projected total of 1,624 cases in 2026 and 1,712 cases in 2027, with monthly forecasts concentrated within a balanced range between 102 and 108 cases per month as a minimum and 132 and 175 cases as a maximum within 95% confidence intervals. The study recommends strengthening the capacity of Benghazi Medical Center and ensuring the availability of medicines and diagnostic supplies. It also recommends establishing a unified, comprehensive national registry to document patient data accurately and systematically. Furthermore, it emphasizes the adoption of ARIMA models as an official statistical tool for the periodic forecasting of future patient numbers to anticipate future health needs and support health planning. This would advance scientific research and improving the quality of health services in the public interest.