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.

翻译：医疗时间序列的精确趋势预测对于规划和资源分配至关重要。本文提出了一种贝叶斯框架，用于预测肿瘤学需求趋势，将每周预约建模为泊松过程，并为需求率设置伽马先验。为增强适应性并捕捉持续的方向性模式，我们引入了一种基于残差的提升机制，该机制基于伽马-对数正态共轭结构。这种提升方法使模型能够追踪短期和长期趋势变化，同时保持共轭贝叶斯更新的分析可处理性。该方法在巴西塞阿拉州卡里里地区的真实肿瘤学服务数据上进行了评估，并与包括线性回归、ARIMA、朴素预测、LSTM神经网络和XGBoost在内的基准方法进行了比较。结果表明，所提出模型在趋势检测准确性上优于竞争方法，在某些情况下，正确方向百分比相比次优方法提升了38.25%。