Point-wise estimation of non-linear effects of airborne pollen levels on asthma emergency room admissions A. Tobías*, M. Sµez, I. Galµn, J. R. Banegas Key words: air pollution; asthma; generalized additive models; pollen; relative risk. Airborne pollen levels have been associated with an increase in asthma morbidity (1). This relationship has usu- ally been formu- lated in terms of a linear form. However, effects of environmental exposures on health could also be nonlinear (2). Approximations based on linear modals present limitations mak- ing arbitrary assumptions about shape of the relationship; also, categorical analy- ses usually have low efficiency and cut-off points are in most cases opportunistic (3). To solve these limitations, a nonpara- metric method to compute point-wise estimation of non-linear exposures has recently been proposed (4). Under a Generalized Additive Model (GAM) a nonparametric estimate of the relative risk (RR) can be defined as RRðx; x ref Þ¼ exp f ðxÞ f ðx ref Þ ð Þ, where x ref is the reference value of the continuous exposure and f(x) any of usual smoothers. Asymptotic variance of ln(RR(x,x ref )) can be expressed in terms of the covariance matrix of the smoother f(x) as V lnðRRðx; x ref ÞÞ ½ ¼ var fðxÞ ½ þ var fðx ref Þ ½  2 cov fðxÞ; fðx ref Þ ½ : Figueiras and Cadarso-Sua´ rez (4) provide exact formulae estimation. We applied this method to derive GAM-based risk estimates for the effects of airborne pollen levels on asthma emergency room (ER) admissions in Madrid, Spain. Daily number of asthma ER admissions from Gregorio Maran˜o´n Hospital was studied for 1995–1998. Pol- len types collected were those with the highest allergenic capacity in Madrid (Olea, Plantago, Poaceae, and Urticaceae). Data on air pollutants (PM 10 , SO 2 , NO 2 and O 3 ), temperature and relative humidity were also collected. Additional information has been de- scribed elsewhere (5). Trend and season- ality were fitted using a cubic smoothing spline with 72 degrees of freedom (df). Cubic smoothing splines with 2 and 4 df were included to adjust for humidity and temperature, respectively. Dummy vari- ables for day of the week and holidays were also fitted. Air pollutants were adjusted using cubic smoothing splines with 2 df for PM 10 (lag 3) and SO 2 (lag 3), 3 df for NO 2 (lag 3), and 1 df for O 3 (lag 1). Finally, all airborne pollen levels were adjusted using cubic smoothing splines with 3 df: Olea (lag 1), Plantago (lag 2), Poaceae (lag 2) and Urticaceae (lag 1). Figure 1 shows evident non-linear rela- tionships between airborne pollen levels and risk of asthma ER admissions. Refer- ence values were taken as the 90th percen- tile, as it is a minimum risk value (5) (Olea: 6.3 grains/m 3 , Plantago: 15.3 grains/m 3 , Poaceae: 27.8 grains/m 3 , and Urticaceae: 6 grains/m 3 ). Airborne pollen levels with statistically significant (P < 0.05) risk were those placed between 30 and ALLERGY 2009: 64: 961–967 • ª 2009 THE AUTHORS • JOURNAL COMPILATION ª 2009 BLACKWELL MUNKSGAARD • CONTRIBUTIONS TO THIS SECTION WILL NOT UNDERGO PEER REVIEW, BUT WILL BE REVIEWED BY THE ASSOCIATE EDITORS • Relationships between the risk of asthma emergency room admissions and pollen levels were clearly non-linear. Thus, the use of non-parametric methods provided more informative estimations than the traditional approaches. Figure 1. Relationship between airborne pollen levels and risk of asthma emergency admissions [log relative risk, ln(RR)] in Madrid, Spain (1995–1998). Vertical lines represent the reference value placed at the 90th percentile of type of pollen. ALLERGY Net 961