Nonlinear Responses of Marathon Performance to Heat Stress: Evidence from 18 U.S. Cities (2011–2019)

Marathon heat stress is an increasing public health concern under climate change, particularly for mass participation endurance events. Using 967,878 runners from 18 U.S. marathon events between 2011 and 2019, this study examined the nonlinear association between race-day thermal exposure and marathon performance. A two-way fixed effects framework was used to account for race- and year-specific heterogeneity, demographic characteristics, race-day maximum air temperature, relative humidity, their interaction, and non-stationary exposure proxies. The results identified a humidity-dependent thermal optimal zone (TOZ). At the sample mean humidity level of 77.7%, the estimated the TOZ based on the race-day maximum air temperature was 13.0 °C, with a low-penalty range of 8.5–17.4 °C for predicted losses below 60 s. In the main specification, the temperature–humidity interaction was positive, suggesting that humidity-related penalties may increase under warmer conditions; however, race-year-level sensitivity analyses indicated that this interaction should be interpreted cautiously. Under 28.0 °C and 80% relative humidity, the model predicted a finish-time penalty of approximately 737.5 s. Stratified analyses showed that mass participation runners experienced larger high-temperature penalties than elite runners, and male runners aged 35–49 years showed the highest estimated thermal sensitivity at 28.0 °C. The UTCI modestly improved model calibration but produced unstable optimum estimates, supporting its use as a complementary biometeorological benchmark rather than as the primary basis for defining a marathon-specific TOZ. These findings suggest that a marathon heat-risk assessment should jointly consider air temperature, humidity, integrated biometeorological exposure, and subgroup-specific vulnerability.