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：环境健康研究中，常关注同一天及随后若干天（滞后）内暴露因素对健康结局的影响。分布式滞后非线性模型是估计暴露-滞后-反应函数的成熟统计框架。我们提出将先验信息纳入DLNM的方法。首先，在滞后时间段的暴露-反应关系中施加单调性约束，这与生物机制对暴露水平升高的响应规律相符。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。该变量选择方法可直接应用有信息先验，指定哪些滞后与结局存在非零关联。我们提出"树中树"模型，采用双层树结构：一层用于划分暴露时间框架，另一层用于拟合不同时间段上的暴露-反应函数。在贝叶斯加性回归树中引入零膨胀替代树分裂先验，实现滞后选择与有信息先验的添加。我们开发了高效后验采样计算方法，并通过全面模拟研究将本方法与现有DLNM方法进行比较。以伊利诺伊州芝加哥市夏季或冬季极端温度与死亡率的时滞关系为例，应用本方法进行估计。