This thesis is concerned with presenting and developing modeling approaches which allow for a time-varying effect of covariates by using time-varying coefficients. The different approaches are compared in simulation studies. Thereby, we investigate how well different components of the simulated models can be identified. The models performing best in the simulation study are then applied to data collected within the study "Improved Air Quality and its Influences on Short-Term Health Effects in Erfurt, Eastern Germany". One specific aspect in this analysis is to assess the necessity of a time-varying estimate compared to a more parsimonious, time-constant fit.

A further topic is the estimation of time-varying coefficient models in the presence of measurement errors in the exposure variable. We specify a measurement error model

and present methods to estimate parameters and measurement error variances of the model in the case of autocorrelated latent exposure as well as measurement errors. Furthermore,

two methods adjusting for measurement errors in the context of time-varying coefficients are developed. The first one is based on a hierarchical Bayesian model and the Bayesian error correction principle. The second method is an extension of the well-known regression calibration approach to the case of autocorrelated data. The obtained estimated true values can then be included into the main model to assess the effect of the variable of interest. Finally, the approaches are again applied to the Erfurt data.