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Background  We previously found additive effects of long- and short-term exposures to fine particulate matter (PM 2.5 ), ozone (O 3 ), and nitrogen dioxide (NO 2 ) on all-cause mortality rate using a generalized propensity score (GPS) adjustment approach. The study addressed an important question of how many early deaths were caused by each exposure. However, the study was computationally expensive, did not capture possible interactions and high-order nonlinearities, and omitted potential confounders.    Methods  We proposed two new methods and reconducted the analysis using the same cohort of Medicare beneficiaries in Massachusetts during 2000–2012, which consisted of 1.5 million individuals with 3.8 billion person-days of follow-up. The first method, weighted least squares (WLS), leveraged large volume of data by aggregating person-days, which gave equivalent results to the linear probability model (LPM) method in the previous analysis but significantly reduced computational burden. The second method, m-out-of-n random forests (moonRF), implemented scaling random forests that captured all possible interactions and nonlinearities in the GPS model. To minimize confounding bias, we additionally controlled relative humidity and health care utilizations that were not included previously. Further, we performed low-level analysis by restricting to person-days with exposure levels below increasingly stringent thresholds.    Results  We found consistent results between LPM/WLS and moonRF: all exposures were positively associated with mortality rate, even at low levels. For long-term PM 2.5  and O 3 , the effect estimates became larger at lower levels. Long-term exposure to PM 2.5  posed the highest risk: 1 μg/m 3  increase in long-term PM 2.5  was associated with 1053 (95% confidence interval [CI]: 984, 1122; based on LPM/WLS methods) or 1058 (95% CI: 988, 1127; based on moonRF method) early deaths each year among the Medicare population in Massachusetts.    Conclusions  This study provides more rigorous causal evidence between PM 2.5 , O 3 , and NO 2  exposures and mortality, even at low levels. The largest effect estimate for long-term PM 2.5  suggests that reducing PM 2.5  could gain the most substantial benefits. The consistency between LPM/WLS and moonRF suggests that there were not many interactions and high-order nonlinearities. In the big data context, the proposed methods will be useful for future scientific work in estimating causality on an additive scale.    Supplementary Information  The online version contains supplementary material available at 10.1186/s12940-021-00704-3.

Assessing additive effects of air pollutants on mortality rate in Massachusetts