Forecasting New Tuberculosis Cases in Malaysia: A Time-Series Study Using the Autoregressive Integrated Moving Average (ARIMA) Model

Abstract

Background The application of the Box-Jenkins autoregressive integrated moving average (ARIMA) model has been widely employed in predicting cases of infectious diseases. It has shown a positive impact on public health early warning surveillance due to its capability in producing reliable forecasting values. This study aimed to develop a prediction model for new tuberculosis (TB) cases using time-series data from January 2013 to December 2018 in Malaysia and to forecast monthly new TB cases for 2019. Materials and methods The ARIMA model was executed using data gathered between January 2013 and December 2018 in Malaysia. Subsequently, the well-fitted model was employed to make projections for new TB cases in the year 2019. To assess the efficacy of the model, two key metrics were utilized: the mean absolute percentage error (MAPE) and stationary R-squared. Furthermore, the sufficiency of the model was validated via the Ljung-Box test. Results The results of this study revealed that the ARIMA (2,1,1)(0,1,0)₁₂ model proved to be the most suitable choice, exhibiting the lowest MAPE value of 6.762. The new TB cases showed a clear seasonality with two peaks occurring in March and December. The proportion of variance explained by the model was 55.8% with a p-value (Ljung-Box test) of 0.356. Conclusions The application of the ARIMA model has developed a simple, precise, and low-cost forecasting model that provides a warning six months in advance for monitoring the TB epidemic in Malaysia, which exhibits a seasonal pattern.

Keywords: early warning surveillance; malaysia; sarima model; time series; tuberculosis.

Figure 1. (a) Geographical distribution of new TB cases in Malaysia from January 2013 to December 2018; (b) trend analysis of new TB cases in Malaysia from January 2013 to December 2018; (c) annual cycle of new TB cases in Malaysia from January 2013 to December 2018.

Figure 1 is the original work of the authors.

Figure 2. Autocorrelation function (ACF) and partial autocorrelation function (PACF) of data and transformed series footnote: (a) ACF without any difference; (b) PACF without any difference; (c) ACF with both seasonal (1, period 12) and nonseasonal difference (1); (d) PACF with both seasonal (1, period 12) and nonseasonal difference (1).

The lag number refers to every 12-month interval (lags 1-12) at lags 12, 24, 36, and 48. With 72 monthly (January 2013-December 2018) values used for the model synthesis, correlations at the first 48 lags were examined. Figure 2 is the original work of the authors.

Figure 3. Observed and forecasted monthly new TB cases in Malaysia for 2013-2019.

The red graph (observed) refers to the actual number of new TB cases for the period of January 2013-December 2018. The light-blue graph (fit) refers to the model-fitted values/number of new TB cases for the period of January 2013-December 2018. The dotted graph (upper confidence level (UCL) and lower confidence level (LCL)) refers to the upper and lower 95% confidence intervals of new TB cases for the period of January 2013-December 2018. The thick blue (forecast) refers to the forecasted number of new TB cases for the period of January-December 2019. Figure 3 is the original work of the authors.