Accurate trend forecasting in healthcare time series is essential for planning and resource allocation. This paper proposes a Bayesian framework for predicting oncology demand trends, modeling weekly appointments as a Poisson process with a Gamma prior to the demand rate. To enhance adaptability and capture persistent directional patterns, we incorporate a residual-based boosting mechanism grounded in a Gamma-Log-Normal conjugate structure. This boosting approach allows the model to track both short- and long-term trend shifts while maintaining the analytical tractability of conjugate Bayesian updating. The methodology was evaluated on real oncology service data from Cariri, Ceara, Brazil, and compared against established baselines, including linear regression, ARIMA, naive forecasting, LSTM neural networks, and XGBoost. Results showed that the proposed model outperforms competing methods in trend detection accuracy, with gains in terms of percentage of correct direction of 38.25% in relation to the second best approach in some cases.
Public health forecasts must respond to abrupt changes in surveillance data without over-extrapolating noise, reporting artifacts, or temporary trends. We evaluated autoregressive integrated moving average (ARIMA), random forest, and extreme gradient boosting (XGBoost) models using 190 weekly observations of publicly available Ontario COVID-19 case counts from January 2020 to October 2023. Rolling-origin time-series cross-validation preserved temporal order during model tuning and evaluation. Performance was assessed across three operating dimensions: responsiveness following selected turning points, forecast horizons of one to six weeks, and the amount of historical training data. We also developed Machine Learning and ARIMA Model Averaging (MLAMA), a non-negative performance-weighted ensemble with weights that vary by forecast horizon and responsiveness setting. Retrospective comparisons showed that ARIMA adapted rapidly after turning points but its normalized error increased at longer horizons. Random forest and XGBoost were less responsive initially but maintained more stable normalized error over longer horizons. For two-week forecasts at the end of the study period, training on the most recent data outperformed using longer historical periods, particularly for XGBoost. MLAMA achieved the lowest normalized mean absolute percentage error across most forecast horizons and ranked among the best-performing methods across responsiveness settings. These findings support selecting forecasting models according to operating conditions rather than relying on a single universally preferred approach. MLAMA provides a practical framework for combining complementary statistical and machine-learning forecasts. The accompanying Python package is currently maintained in a private repository while software validation and reproducibility testing are completed.
This work studies lung tumor growth prediction from sparse and irregular longitudinal computed tomography (CT) observations with measurement variability. A Bayesian physics-informed neural network is developed by combining Gompertz growth dynamics with low-dimensional Bayesian inference in the log-volume domain. The framework employs a two-stage inference strategy combining maximum a posteriori (MAP) estimation and Hamiltonian Monte Carlo (HMC) sampling to estimate posterior predictive distributions and uncertainty intervals. The method was evaluated on longitudinal data from the National Lung Screening Trial (30 patients). Results show that the model captures heterogeneous tumor growth patterns while maintaining reasonable prediction accuracy under limited observations. Compared with deterministic modeling approaches, the proposed approach additionally provides calibrated uncertainty estimates. The inferred posterior parameter correlations were consistent with expected biological growth behavior. The proposed framework achieved a cohort-level log-space RMSE of approximately 0.20 together with well-calibrated 95% credible interval coverage across 30 patients. These findings suggest that Bayesian physics-informed modeling may be useful for uncertainty-aware tumor growth assessment when only limited longitudinal follow-up scans are available.
Medical and public health experts must make real-time resource decisions, such as expanding hospital bed capacity, based on projected hospitalization trends during large-scale healthcare disruptions (e.g., operational failures or pandemics). Forecasting models can assist in this task by analyzing large volumes of resource-related data at the facility level, but they must be reliable for decision-making under real-world data conditions. Recent work shows that large language models (LLMs) can incorporate richer forms of context into numerical forecasting. Whereas traditional models rely primarily on temporal context (i.e., past observations), LLMs can also leverage non-temporal public health context such as demographic, geographic, and population-level features. However, it remains unclear how these models should be used to produce stable or decision-relevant predictions in real-world healthcare settings. To evaluate how LLMs can be effectively used in this setting, we evaluate three approaches across 60 counties with low-,mid-, and high-hospitalization intensities in the United States: direct LLM-based forecasting, classical time-series models, and a context-augmented hybrid pipeline (HybridARX) that incorporates LLM-derived signals into structured models. Because the goal is operational decision-making rather than error minimization alone, we evaluate performance with bias and lead-lag alignment in addition to standard forecasting metrics. Our results show that HybridARX improves over classical ARX by yielding more stable and better-calibrated forecasts, particularly when incorporating noisy contextual signals into structured time-series models. These findings suggest that, in non-stationary healthcare resource forecasting, LLMs are most useful when embedded within structured hybrid models.