Exposure to ambient pollutants at concentrations above defined standards is a risk factor for respiratory symptoms, especially in sensitive children. 
Many studies have been undertaken to monitor air quality and to assess its association with respiratory symptoms. We propose a joint mixed effects 
regression model of time series measures and recurrent events to analyze the air quality and respiratory symptom data from the Yale Mothers and Infants 
Health Study. Three mothers' symptoms (runny nose, cough, and sore throat) and three infants' symptoms (runny nose, cough, and general sickness) 
were investigated. To alleviate the computational complexity, a two-stage maximum likelihood based  estimation procedure is introduced to estimate the 
parameters, and simulation studies are conducted to assess the validity of this estimation procedure. Our analysis reveals differences in the etiology of 
respiratory symptoms between mothers and infants. Most notably, coarse particles of mass between 2.5 and 10  microns in diameter increased the risks 
of mothers' runny nose and cough symptoms, but had no significant impact on any of the three infants' symptoms. The sulfate level was negatively associated 
with the risk of infants' runny nose and cough symptoms, but had no significant effects on any of the three mothers' symptoms. High level of humidity is 
negatively associated with the mothers' cough incidence, but had no significant association on any of the three infants' symptoms. Such differences reveal 
not only the sensitivity of the mothers and infants to the air quality, but also call for further understanding of the differences. It is possible that actions taken 
to overcome humidity by mothers may inadvertently affect the infants.

This is a joint work with Yuanqing Ye, Peter Diggle, and Jian Shi.