In environmental health research there is often interest in the effect of an exposure on a health outcome assessed on the same day and several subsequent days or lags. Distributed lag nonlinear models (DLNM) are a well-established statistical framework for estimating an exposure-lag-response function. We propose methods to allow for prior information to be incorporated into DLNMs. First, we impose a monotonicity constraint in the exposure-response at lagged time periods which matches with knowledge on how biological mechanisms respond to increased levels of exposures. Second, we introduce variable selection into the DLNM to identify lagged periods of susceptibility with respect to the outcome of interest. The variable selection approach allows for direct application of informative priors on which lags have nonzero association with the outcome. We propose a tree-of-trees model that uses two layers of trees: one for splitting the exposure time frame and one for fitting exposure-response functions over different time periods. We introduce a zero-inflated alternative to the tree splitting prior in Bayesian additive regression trees to allow for lag selection and the addition of informative priors. We develop a computational approach for efficient posterior sampling and perform a comprehensive simulation study to compare our method to existing DLNM approaches. We apply our method to estimate time-lagged extreme temperature relationships with mortality during summer or winter in Chicago, IL.

翻译：在环境健康研究中，通常关注暴露对同日及后续若干天（滞后）健康结局的影响。分布滞后非线性模型（DLNM）是用于估计暴露-滞后-反应函数的成熟统计框架。我们提出将先验信息融入DLNM的方法。首先，我们在滞后时间段的暴露-反应关系中施加单调性约束，这符合生物机制对暴露水平升高的响应规律。其次，我们在DLNM中引入变量选择，以识别与结局相关的易感滞后时段。变量选择方法允许直接应用关于哪些滞后与结局存在非零关联的信息性先验。我们提出了一种树中树模型，该模型使用两层树：一层用于划分暴露时间框架，另一层用于拟合不同时间段的暴露-反应函数。我们引入贝叶斯加性回归树中树分裂先验的零膨胀替代方案，以实现滞后选择并添加信息性先验。我们开发了高效后验抽样的计算方法，并通过全面模拟研究将我们的方法与现有DLNM方法进行比较。我们将该方法应用于估计美国伊利诺伊州芝加哥市夏季或冬季死亡率与极端温度之间的时间滞后关系。