  Cookstove replacement trials have found mixed results on their impact on
respiratory health. The limited range of concentrations and small sample sizes
of individual studies are important factors that may be limiting their
statistical power. We present a hierarchical approach to modeling exposure
concentrations and pooling data from multiple studies in order to estimate a
common exposure-response curve. The exposure concentration model accommodates
temporally sparse, clustered longitudinal observations. The exposure-response
curve model provides a flexible, semi-parametric estimate of the
exposure-response relationship while accommodating heterogeneous clustered
data. We apply this model to data from three studies of cookstoves and
respiratory infections in children in Nepal, which represent three study types:
crossover trial, parallel trial, and case-control study. We find evidence of
increased odds of disease for particulate matter concentrations between 50 and
200 $\mu$g/m$^3$ and a flattening of the exposure-response curve for higher
exposure concentrations. The model we present can incorporate additional
studies and be applied to other settings.
