The purpose of this application is to develop semiparametric regression methods for the design and analysis of environmental health studies. The primary areas of investigations are (1) extension of generalized additive modeling methodology for aiding several environmental health studies, particularly those involving geographical and missing data; (2) extension of conditional panel designs to allow for incorporation of nonparametric relationships; (3) combination of distributed lag and varying coefficient models to aid air pollution research. The first aim is the most involved and is driven by a number of studies that involve geographical, clustered, missing and time-ordered data; but also benefit from additive modeling. These studies include disease mapping, cardiac vulnerability and air pollution, pollen forecasting and diabetes research. Extensions of the additive model to handle geostatistical methods ('kriging'), mixed effects and autoregression are proposed. Some of the data sets are quite large so the development of more computationally efficient models is another key component. The second aim concerns a low-cost design that has been developed recently to assess time-varying covariate effects in a longitudinal study on aeroallergens and asthma. It is important to be able to control for covariates such as seasonality and temperature in a flexible fashion so the extension to smooth functions of covariates is proposed. The third aim is motivated by several air pollution studies where the effect of a stimulus is distributed across time lags, as well as being subjected to modification by an auxiliary variable. The proposed research will involve empirical data analysis with real data as well as theory and methodology. One purpose of the grant is to provide support for methodological research on ideas that arise out of the work of the three main investigators as director and co-directors of the Kresge Center Grant.