Investigating the association between indoor radon concentrations and some potential influencing factors through a profile regression approach

Abstract

Radon-222 is a naturally occurring radioactive gas arising from the decay of Uranium-238 present in the earth’s crust. The knowledge of the radon effects on human health is generating a growing attention by national and international authorities aimed at assessing the exposure of people to this radioactive gas and identifying building types and geographic areas where high indoor radon concentrations (IRCs) are likely to be found. However, given its multi-factorial dependence and the substantial regional variation, the analysis of IRC is not a simple task. There have been several efforts to evaluate the impact of the major influencing factors on IRCs. In this paper we illustrate how the complex relationships between the IRCs and a set of associated variables can be analysed using profile regression, a Bayesian non-parametric model for clustering responses and regressors simultaneously. Analyzing a geo-referenced database of annual IRCs for the Abruzzo region (Central Italy), we show that the proposed methodology allows to identify clusters of buildings according to their proneness to IRCs and that, through cluster assignment, it is possible to disentangle the effect of regressors on IRC and predict its levels for specific combinations of the explanatory variables.

Appendices

Appendices

Appendix A: Model parametrization

This Section provides details about the values chosen for the hyperparameters of the BPR model to obtain results discussed in Sect. 4. The setting follows suggestions given in Liverani et al. (2016).

Distinctively, for the stick-breaking process we have set $s_{\alpha }=2$ and $r_{\alpha }=1$ which refer to the shape and rate parameter for the Gamma prior on $\alpha$, respectively. Further, each element of the vector of the parameters for the Dirichlet prior on $\phi _{p}$, $(a_{1}, \ldots a_{P},)$ is set to 1. For each cluster c, following Liverani et al. (2016), we adopt a t location-scale distribution on $\theta _{c}$, with hyperparameters $\mu _\theta$ and $\sigma _\theta$ with 7 degrees of freedom. The location parameter ($\mu _{\theta }$) and the scale parameter ($\sigma _{\theta }$) are equal to 0 and 2.5, respectively. We adopt the same prior for the $\varvec{\beta }_2$, with hyperparameters $\mu _\beta =0$ and $\sigma _\beta =2.5$. Finally, for the precision parameter $\sigma ^{-2}_\epsilon$ we consider a Gamma distribution with shape and rate (inverse scale) parameters both fixed at 2.5.

Appendix B: Model predictive accuracy and residual analysis

See Figs. 6, 7.

Fig. 6

Root mean squared prediction errors (RMSE) computed for the test set and the associated number of estimated clusters (in boxes) as a function of of the number of principal splines, i.e. $\varvec{\gamma }_v, v=1, \ldots , q=15$

Fig. 7

Empirical variogram of the estimated model residuals using the first 7 eigenfunctions, $\varvec{\gamma }_v, \ v=1, \ldots ,7$

Appendix C: Posterior distribution of all cluster specific parameters

See Figs. 8, 9, 10 and 11.

Fig. 8

Summary plot of the posterior distribution of parameter $\phi _{c}$, for $\; c=1, \ldots , 11$—explanatory variables: Year of construction, Materials, Windows quality, Soil connection

Fig. 9

Summary plot of the posterior distribution of parameter $\phi _{c}$, for $\; c=1, \ldots , 11$—explanatory variables: Floor, Type of building, Altitude

Fig. 10

Summary plot of the posterior distribution of parameter $\phi _{c}$, for $\; c=1, \ldots , 11$—explanatory variables: Karst, Fracturation, Permeability

Fig. 11

Summary plot of the posterior distribution of parameter $\phi _{c}$, for $\; c=1, \ldots , 11$—explanatory variables: Porosity, Thickness, Lithology