Modelling Cumulative Effects of Air Pollution on Respiratory Illnesses by Performing Spline Estimation of Constrained, Additive Single-Index Model

It is widely recognised that air pollutants including sulphur dioxide (SO₂), respirable suspended particulates (PM10), nitrogen oxides (NOx), nitrogen dioxide (NO₂), and ozone (O₃), as well as weather conditions such as temperature (Temp) and relative humidity (RH), are major causes of respiratory illnesses. To quantify the unknown and highly nonlinear relationships between these factors and respiratory illness, and the cumulative effect from exposure to symptoms, in this paper, we propose a semiparametric index model with constraints to capture the cumulative effect additively and the nonlinearity nonparametrically. As a case study, the model is applied to a dataset from the Hong Kong SAR. As the data period includes the SARS (severe acute respiratory syndrome) epidemic in 2003, we further construct a growth curve model to account for the extra impact of public health measures. The results show that the effects of SO₂, NO₂, and PM10 decay quickly, while the other pollutants have a period of stable accumulation (18-38 days for O₃, 2-30 days for NOx, 1-13 days for RH, and 4-12 days for temperature). The results also show that the proposed model has a better fitting performance than previous models and hence has potential applications in health monitoring programs.