The standard approach to estimating the short-term effects of air pollution on health is to apply a Poisson generalized linear or additive model to daily measurements of population health, air pollution and meteorology for an extended urban area such as a city. For simplicity, the majority of studies estimate a linear relationship between air pollution and health. However, there are a number which estimate a non-linear dose-response curve. Typically, this is done using a smoothing or penalized spline but these curves are otherwise left unconstrained. This can result in non-biologically plausible curves being estimated. For example, for some levels of pollution the estimated health effects may decrease for increasing concentrations. This project proposed a method for estimating biologically plausible dose-response curves for air pollution and health studies. To achieve this we implemented the three constraints. We then applied our methods to the city of Glasgow, focusing on ozone concentrations and respiratory related hospital admissions.