Short term association between ozone and mortality: global two stage time series study in 406 locations in 20 countries

Dear Editor
I re-calculated the mortality data for Toronto, Canada, which are a part of the data used in the recently published results of a multi-city multi-country study [1]. In my calculations I considered all mortality daily counts as health outcomes. In the main model I used lag0-1 of ozone concentration (O3, maximum eight hour average) and weather factors. Temperature and relative humidity in the statistical models were represented in the form of natural splines with 3 degrees of freedom. Two approaches were realized {(A) and (B)}. Let Z=ozone (O3).
(A) Case-crossover (CC) method implemented as conditional Poisson regression [2-6].
(B) The same as in (A), but the concentration Z was transformed (T(Z)) and the relative risk (RR) was represented as RR(Z)=exp( β*T(Z) ) .
The scalar β is estimated by the statistical model, in this case by the CC method. The parameters of the transformation were determined by applying the Akaike information criterion (AIC) [7,8]. In the final step, the models were re-calculated with the option “family=quasipoisson” (“gnm” in R).
The CC method (point (A)) gives AIC= 78707.7. The method used for point (B) gives AIC= 78699.3.
I calculated RR and the 95% confidence interval (95%CI) for both approaches at 75th percentile of Z (=55 mig/m3). The two methods resulted in the following different estimations:

(A) RR= 1.01947 (95%CI: 1.00295 - 1.03627).
(B) RR= 1.00391 (95%CI: 1.00181 - 1.00601).

The results (RR) are reported to relatively high increase in ozone exposure (third quartile of Z). The CC method gives larger estimates than method (B). Since the methods used by Vicedo-Cabrera et al. [1] also use Z in a linear form (log-linear model), this may suggest that their estimates (RR) are also too high. In the Supplementary Materials of [8] are presented the results for mortality in relation to ambient ozone in London (UK). Applying method (B) allowed to determine the threshold.
References
1. Vicedo-Cabrera AM, Sera F, Liu C et al. Short term association between ozone and mortality: global two stage time series study in 406 locations in 20 countries. BMJ. 2020;368:m108. doi:10.1136/bmj.m108.
2. Janes H, Sheppard L, Lumley T. Case-crossover analyses of air pollution exposure data: referent selection strategies and their implications for bias. Epidemiology 2005;16: 717- 726. https://doi.org/10.1097/01.ede.0000181315.18836.9d
3. Szyszkowicz M. Use of generalized linear mixed models to examine the association between air pollution and health outcomes. Int. J. Occup. Med. Environ. Health 2006;19: 224–227.
4. Armstrong BG, Gasparrini A, Tobias A. Conditional Poisson models: A flexible alternative to conditional logistic case cross-over analysis. BMC Med. Res. Methodol 2014,14, 122.
5. Szyszkowicz M. Case-Crossover Method with a Short Time-Window. Int J Environ Res Public Health. 2019 Dec 27;17(1). pii: E202. doi: 10.3390/ijerph17010202.
6. Szyszkowicz M. Use of two-point models in “Model choice in time-series studies of air pollution and mortality”. Air Qual Atmos Health 13, 225–232 (2020). https://doi.org/10.1007/s11869-019-00787-5
7. Nasari MM, Szyszkowicz M, Chen H et al. A class of non-linear exposure-response models suitable for health impact assessment applicable to large cohort studies of ambient air pollution. Air Qual Atmos Health 2016;9: 961-972. https://doi.org/10.1007/s11869-016-0398-z
8. Szyszkowicz M. Concentration-response functions for short-term exposure and air pollution health effects. Environ Epidemiol 2018: e011. https://doi.org/10.1097/EE9.0000000000000011