{ "background": "Community health centres are critical for primary care delivery, yet systematic evaluations of their operational efficiency and yield forecasting in low-resource settings are limited. Methodological rigour in assessing these systems directly influences policy and resource allocation for sustainable healthcare.", "purpose and objectives": "This meta-analysis aims to methodologically evaluate studies on community health centre systems and to develop a robust time-series forecasting model for predicting service yield improvements, with a focus on methodological strengths and limitations.", "methodology": "A systematic review and meta-analysis of published and grey literature was conducted. Quantitative synthesis employed a random-effects model. The core forecasting methodology utilised an autoregressive integrated moving average (ARIMA) model, specified as $Yt = \\mu + \\phi1 Y{t-1} + \\theta1 \\epsilon{t-1} + \\epsilont$, where $Y_t$ is the yield metric at time $t$. Model diagnostics included checks for stationarity and residual autocorrelation.", "findings": "The methodological appraisal revealed that over 60% of included studies lacked longitudinal design or sufficient power for detecting system-level changes. The forecasting model, applied to antenatal care coverage, projected a mean increase of 15.2% (95% CI: 11.8, 18.6) in yield over a five-year horizon, with forecasts remaining robust to different volatility assumptions.", "conclusion": "Current evidence on health centre performance exhibits significant methodological heterogeneity, constraining comparative analysis. The proposed ARIMA framework provides a validated tool for predicting service yield, offering a more standardised approach for strategic planning.", "recommendations": "Future research should adopt longitudinal, mixed-methods designs with clearly defined outcome metrics. Health programme planners should integrate formal time-series forecasting into monitoring and evaluation frameworks to anticipate capacity requirements.", "key words": "health systems research, forecasting models, primary health care, operational research, programme evaluation", "contribution statement": "This study provides the first consolidated methodological critique of the evidence