Nonparametric Bayesian Meta‐Analysis Model With Change Point Detection: A Case Study on Time‐Varying Temperature–Mortality Associations

Numerous studies have established a U- or J-shaped association between ambient temperature and human mortality by analyzing time-series data collected from multiple locations. However, this association has changed over time owing to climate change and adaptive behaviors, such as the increased use of air conditioning. Temporal changes have been examined using a conventional two-stage modeling framework, which typically assumes a linear change over time. Our preliminary analysis of Japanese data suggests that these temporal changes may not be linear or gradual, challenging the common assumption adopted in the conventional two-stage modeling approach. Moreover, the assumption of normality in the existing second-stage mixed-effects models can make the estimates highly sensitive to outliers. To address these limitations, we propose a two-stage modeling framework with a novel second stage model: a nonparametric Bayesian meta-analysis model with change-point detection. In the first stage, we divide the full study period into non-overlapping one-year sub-periods to capture fine-scale temporal variation and estimate temperature-mortality associations for each location and sub-period using distributed lag nonlinear models. In the second stage, we pool the associations across locations and sub-periods simultaneously applying our novel nonparametric Bayesian meta-analytic model, which is formulated based on the Probit Stick-Breaking Process to facilitate flexible segmentation of time regimes. The model also incorporates a mixture of Gaussian and t-distributed errors to account for potential outliers and ensure robust estimation. The proposed modeling framework is validated through simulation studies and illustrated through an application to the study for time-varying temperature-mortality association in Japan.