Age-disaggregated health data is crucial for effective public health planning and monitoring. Monitoring under-five mortality, for example, requires highly detailed age data since the distribution of potential causes of death varies substantially within the first few years of life. Comparative researchers often have to rely on multiple data sources yet, these sources often have ages aggregated at different levels, making it difficult to combine the data into a single, coherent picture. To address this challenge in the context of under-five cause-specific mortality, we propose a Bayesian approach, that calibrates data with different age structures to produce unified and accurate estimates of the standardized age group distributions. We consider age-disaggregated death counts as fully-classified multinomial data and show that by incorporating partially-classified aggregated data, we can construct an improved Bayes estimator of the multinomial parameters under the Kullback-Leibler (KL) loss. We illustrate the method using both synthetic and real data, demonstrating that the proposed method achieves adequate performance in imputing incomplete classification. Finally, we present the results of numerical studies examining the conditions necessary for obtaining improved estimators. These studies provide insights and interpretations that can be used to aid future research and inform guidance for practitioners on appropriate levels of age disaggregation, with the aim of improving the accuracy and reliability of under-five cause-specific mortality estimates.

翻译：年龄分层的健康数据对于有效的公共卫生规划和监测至关重要。例如，监测五岁以下儿童死亡率需要高度细化的年龄数据，因为潜在死因的分布在其出生后最初几年内有显著差异。比较研究者往往依赖多种数据源，但这些数据源的年龄聚合层次不一，导致难以将其整合成单一、连贯的完整图景。为应对五岁以下儿童分病因死亡率估算中的这一挑战，我们提出了一种贝叶斯方法，该方法能校准具有不同年龄结构的数据，从而生成标准化年龄组分布的统一且精确估计。我们将年龄分层的死亡计数视为完全分类的多项式数据，并证明通过纳入部分分类的聚合数据，可以在Kullback-Leibler（KL）损失下构建改进的多项式参数贝叶斯估计量。我们利用合成数据和真实数据展示了该方法，证明其在填补不完全分类方面能达到令人满意的性能。最后，我们展示了数值研究结果，探讨了获得改进估计量所需的条件。这些研究提供了洞察和解释，可用于指导未来研究，并为从业者选择适当的年龄细分水平提供实践建议，旨在提高五岁以下儿童分病因死亡率估计的准确性和可靠性。