Temperature-mortality relationships are nonlinear, time-lagged, and can vary depending on the time of year and geographic location, all of which limits the applicability of simple regression models in describing these associations. This research demonstrates the utility of an alternative method for modeling such complex relationships that has gained recent traction in other environmental fields: nonlinear autoregressive models with exogenous input (NARX models). All-cause mortality data and multiple temperature-based data sets were gathered from 41 different US cities, for the period 1975–2010, and subjected to ensemble NARX modeling. Models generally performed better in larger cities and during the winter season. Across the US, median absolute percentage errors were 10% (ranging from 4% to 15% in various cities), the average improvement in the r-squared over that of a simple persistence model was 17% (6–24%), and the hit rate for modeling spike days in mortality (>80th percentile) was 54% (34–71%). Mortality responded acutely to hot summer days, peaking at 0–2 days of lag before dropping precipitously, and there was an extended mortality response to cold winter days, peaking at 2–4 days of lag and dropping slowly and continuing for multiple weeks. Spring and autumn showed both of the aforementioned temperature-mortality relationships, but generally to a lesser magnitude than what was seen in summer or winter. When compared to distributed lag nonlinear models, NARX model output was nearly identical. These results highlight the applicability of NARX models for use in modeling complex and time-dependent relationships for various applications in epidemiology and environmental sciences.

温度与死亡率的关系是非线性的，有时间滞后的，并且可以根据一年中的时间和地理位置而变化，所有这些都限制了简单回归模型在描述这些关联时的适用性。这项研究证明了一种用于建模这种复杂关系的替代方法的实用性，该方法最近在其他环境领域也受到关注：带有外源输入的非线性自回归模型（NARX模型）。从1975年至2010年期间，从美国41个不同的城市收集了全因死亡率数据和多个基于温度的数据集，并对它们进行了整体NARX建模。在较大的城市和冬季，模型的效果通常更好。在整个美国，中位数绝对百分比误差为10％（各个城市从4％到15％不等），与简单的持久性模型相比，r平方的平均改善率为17％（6–24％），对死亡率高峰期进行建模的命中率（> 80％）为54％（34–71％）。死亡率对炎热的夏季有敏锐的反应，在滞后的0–2天达到峰值，然后急剧下降，而在寒冷的冬日则出现了延长的死亡率响应，在滞后的2-4天达到峰值，然后缓慢下降并持续数周。春季和秋季显示了上述两种温度-死亡率关系，但通常程度不如夏季或冬季。与分布式滞后非线性模型相比，NARX模型的输出几乎相同。