Abstract
{ "background": "The strategic expansion of community health centres is a cornerstone of Kenya's primary healthcare strategy. However, robust, quantitative methodologies for forecasting and evaluating the long-term adoption trajectory of these systems are lacking, hindering evidence-based resource planning and policy formulation.", "purpose and objectives": "This study aimed to develop and validate a novel time-series forecasting model to measure and project the adoption rate of community health centre systems, providing a methodological tool for assessing the scale and pace of system integration.", "methodology": "We developed an autoregressive integrated moving average (ARIMA) model, specified as $\\nabla^d yt = c + \\sum{i=1}^{p}\\phii \\nabla^d y{t-i} + \\sum{j=1}^{q}\\thetaj \\epsilon{t-j} + \\epsilont$, where $y_t$ is the annual count of operational centres. Model parameters were estimated using maximum likelihood, and forecasts were generated with 95% prediction intervals. Historical national-level data on facility establishment were used for model fitting and validation.", "findings": "The ARIMA(1,1,1) model provided the best fit, with all parameters significant at the 5% level. The forecast indicates a continued positive trajectory in adoption, with the projected annual growth rate stabilising at approximately 4.2% (95% PI: 3.1% to 5.3%) over the forecast horizon. This suggests a sustained, though moderating, expansion phase.", "conclusion": "The developed model offers a statistically robust tool for tracking and projecting the adoption of community health infrastructure. The forecasts indicate sustained system growth, which is critical for achieving universal health coverage targets.", "recommendations": "Health planners should integrate this forecasting methodology into routine health system monitoring to anticipate resource needs and identify regions requiring accelerated investment. Future research should incorporate sub-national socioeconomic covariates to refine predictive accuracy.", "key words": "health systems, forecasting, ARIMA modelling, primary healthcare