# Analysing radon accumulation in the home by flexible M-quantile mixed effect regression

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## Abstract

Radon is a noble gas that occurs in nature as a decay product of uranium. Radon is the principal contributor to natural background radiation and is considered to be one of the major leading causes of lung cancer. The main concern revolves around indoor environments where radon accumulates and reaches high concentrations. In this paper, a semiparametric random-effect M-quantile model is introduced to model radon concentration inside a building, and a way to estimate the model within the framework of robust maximum likelihood is presented. Using data collected in a monitoring survey carried out in the Lombardy Region (Italy) in 2003–2004, we investigate the impact of a number of factors, such as geological typologies of the soil and building characteristics, on indoor concentration. The proposed methodology permits the identification of building typologies prone to a high concentration of the pollutant. It is shown how these effects are largely not constant across the entire distribution of indoor radon concentration, making the suggested approach preferable to ordinary regression techniques since high concentrations are usually of concern. Furthermore, we demonstrate how our model provides a natural way of identifying those areas more prone to high concentration, displaying them by thematic maps. Understanding how buildings’ characteristics affect indoor concentration is fundamental both for preventing the gas from accumulating in new buildings and for mitigating those situations where the amount of radon detected inside a building is too high and has to be reduced.

## Keywords

Environmental radioactivity Building factors Radon-prone areas Hierarchical mixed models Penalised splines Lombardy region## Notes

### Acknowledgements

The work of Nicola Salvati has been carried out with the support of the project InGRID 2Grant Agreement No 730998, EU) and of project PRA_2018_9 (‘From survey-based to register-based statistics: a paradigm shift using latent variable models’). The authors were further supported by the MIUR-DAAD Joint Mobility Program (57265468).

## References

- Alfó M, Ranalli M, Salvati N (2017) Finite mixtures of quantiles and m-quantile models. Stat Comput 27:547–570CrossRefGoogle Scholar
- Apte M, Price P, Nero A, Revzan K (1999) Predicting new hampshire indoor radon concentrations from geologic information and other covariates. Environ Geol 37:181–194CrossRefGoogle Scholar
- Bianchi A, Fabrizi E, Salvati N, Tzavidis N (2018) Estimation and testing in M-quantile regression with applications to small area estimation. Int Stat Rev 86(3):1–30CrossRefGoogle Scholar
- Borgoni R (2011) A quantile regression approach to evaluate factors influencing residential indoor radon concentration. Environ Model Assess 16:239–250CrossRefGoogle Scholar
- Borgoni R, Bianco PD, Salvati N, Schmid T, Tzavidis N (2018) Modelling the distribution of health-related quality of life of advanced melanoma patients in a longitudinal multi-centre clinical trial using m-quantile random effects regression. Stat Methods Med Res 27:549–563CrossRefGoogle Scholar
- Borgoni R, Quatto P, Soma G, de Bartolo D (2010) A geostatistical approach to define guidelines for radon prone area identification. Stat Methods Appl 19:255–276CrossRefGoogle Scholar
- Borgoni R, Tritto V, Bigliotto C, de Bartolo D (2011) A geostatistical approach to assess the spatial association between indoor radon concentration, geological features and building characteristics: the Lombardy case, Northern Italy. Int J Environ Res Public Health 8:1420–1440CrossRefGoogle Scholar
- Bosch RJ, Ye Y, Woodworth GG (1995) A convergent algorithm for quantile regression with smoothing splines. Comput Stat Data Anal 19(6):613–630CrossRefGoogle Scholar
- Breckling J, Chambers R (1988) M-quantiles. Biometrika 75(4):761–771CrossRefGoogle Scholar
- Cade B, Noon BR, Flather CH (2005) Quantile regression reveals hidden bias and uncertainty in habitat models. Ecology 86:786–800CrossRefGoogle Scholar
- Chaudhuri P (1991) Global nonparametric estimation of conditional quantile functions and their derivatives. J Multivar Anal 39(2):246–269CrossRefGoogle Scholar
- Cinelli G, Tondeur F, Dehandschutter B (2011) Development of an indoor radon risk map of the Walloon region of Belgium, integrating geological information. Environ Earth Sci 62:809–819CrossRefGoogle Scholar
- Darby S, Hill D, Auvinen A, Barros-Dios J, Baysson J, Bochicchio F, Deo H, Falk R, Forastiere F, Hakama M, Heid I, Kreienbrock L, Kreuzer M, Lagarde F, MSkelSinen I, Muirhead C, Oberaigner W, Pershagen G, Ruano-Ravina A, Ruosteenoja E, Rosario AS, Tirmarche T, Tomsek L, Whitley E, Wichmann H, Doll R (2005) Radon in homes and risk of lung cancer: collaborative analysis of individual data from 13 European case–control studies. Br Med J 330(6485):223–226CrossRefGoogle Scholar
- Fellner WH (1986) Robust estimation of variance components. Technometrics 28(1):51–60CrossRefGoogle Scholar
- Fontanella L, Ippoliti L, Sarra A, Valentini P, Palermi S (2015) Hierarchical generalised latent spatial quantile regression models with applications to indoor radon concentration. Stoch Environ Res Risk Assess 29:357–367CrossRefGoogle Scholar
- Foxall R, Baddeley A (2002) Nonparametric measures of association between a spatial point process and a random set, with geological applications. J R Stat Soc Ser C 51(2):165–182CrossRefGoogle Scholar
- Gates A, Gundersen L (1992) Geologic controls on radon. Geological Society of America, Washington, DC (Special Paper 271)Google Scholar
- Geraci M (2018) Additive quantile regression for clustered data with an application to children’s physical activity. arXiv:1803.05403
- Geraci M, Bottai M (2014) Linear quantile mixed models. Stat Comput 24(3):461–479CrossRefGoogle Scholar
- Green B, Miles J, Bradley E, Rees D (2002) Radon atlas of England and Wales. Report nrpb-w26, Chilton NRPBGoogle Scholar
- Gunby J, Darby S, Miles J, Green B, Cox D (1993) Indoor radon concentrations in the United Kingdom. Health Phys 64:2–12CrossRefGoogle Scholar
- Huber P (1981) Robust statistics. Wiley, New YorkCrossRefGoogle Scholar
- Huggins RM (1993) A robust approach to the analysis of repeated measures. Biometrics 49(3):715–720CrossRefGoogle Scholar
- Huggins RM, Loesch DZ (1998) On the analysis of mixed longitudinal growth data. Biometrics 54(2):583–595CrossRefGoogle Scholar
- Hunter N, Muirhead C, Miles J, Appleton JD (2009) Uncertainties in radon related to house-specific factors and proximity to geological boundaries in England. Radiat Prot Dosim 136:17–22CrossRefGoogle Scholar
- Jacobi W (1993) The history of the radon problem in mines and homes. Ann ICRP 23(2):39–45CrossRefGoogle Scholar
- Jones M (1994) Expectiles and m-quantiles are quantiles. Stat Probab Lett 20:149–153CrossRefGoogle Scholar
- Kaufman L, Rousseeuw P (1990) Finding groups in data: an introduction to cluster analysis. Wiley, New YorkCrossRefGoogle Scholar
- Kemski J, Klingel R, Siehl A, Valdivia-Manchego M (2009) From radon hazard to risk prediction-based on geological maps, soil gas and indoor measurements in Germany. Environ Geol 56:1269–1279CrossRefGoogle Scholar
- Koenker R (2005) Quantile regression. Cambridge University Press, New YorkCrossRefGoogle Scholar
- Koenker R, Bassett G (1978) Regression quantiles. Econometrica 46:33–50CrossRefGoogle Scholar
- Koenker R, Mizera I (2004) Penalized triograms: total variation regularization for bivariate smoothing. J R Stat Soc Ser B 66(1):145–163CrossRefGoogle Scholar
- Koenker R, Ng P, Portnoy S (1994) Quantile smoothing splines. Biometrika 81(4):673–680CrossRefGoogle Scholar
- Kreienbrock L, Kreuzer M, Gerken M, Dingerkus M, Wellmann J, Keller G, Wichmann H (2001) Case-control study on lungcancer and residential radon in western Germany. Am J Epidemiol 89(4):339–348Google Scholar
- Krewski D, Lubin MAJH, Zielinski JM, Catalan V, Field R, Klotz J, Letourneau E, Lynch C, Lyon J, Sandler D, Schoenberg D, Steck J, Stolwijk C, Weinberg C, Wilcox H (2005) Residential radon and risk of lung cancer: a combined analysis of seven North American case-control studies. Epidemiology 16(4):137–145CrossRefGoogle Scholar
- Levesque B, Gauvin D, McGregor R, Martel R, Gingras S, Dontigny A, Walker W, Lajoie P, Levesque E (1997) Radon in residences: influences of geological and housing characteristics. Health Phys 72:907–914CrossRefGoogle Scholar
- Lubin J, Boice J (1997) Lung cancer risk from residential radon: a meta-analysis of eight epidemiological studies. J Natl Cancer Inst 89(1):49–57CrossRefGoogle Scholar
- Nero A, Schwehr M, Nazaroff W, Revzan K (1986) Distribution of airborne radon-222 concentrations in US homes. Science 234:992–997CrossRefGoogle Scholar
- Newey WK, Powell JL (1987) Asymmetric least squares estimation and testing. Econometrica 55(4):819–847CrossRefGoogle Scholar
- Opsomer J, Claeskens G, Ranalli M, Kauermann G, Breidt F (2008) Nonparametric small area estimation using penalized spline regression. J R Stat Soc Ser B 70(1):265–283CrossRefGoogle Scholar
- Organization WH (2009) WHO handbook on indoor radon: a public health perspective. WHO Library Cataloguing-in-Publication DataGoogle Scholar
- Pratesi M, Ranalli M, Salvati N (2009) Nonparametric m-quantile regression using penalized splines. J Nonparametr Stat 21:287–304CrossRefGoogle Scholar
- Price P, Nero A, Gelman A (1996) Bayesian prediction of mean indoor radon concentrations for Minnesota counties. Health Phys 71:922–936CrossRefGoogle Scholar
- R Core Team (2017) R: a language and environment for statistical computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
- Rowe J, Kelly M, Price L (2002) Weather system scale variation in radon-222 concentration of indoor air. Sci Total Environ 284:157–166CrossRefGoogle Scholar
- Ruppert D, Wand M, Carroll R (2003) Semiparametric regression. Cambridge University Press, CambridgeCrossRefGoogle Scholar
- Sarra A, Fontanella L, Ippoliti L, Valentini P, Palermi S (2016) Quantile regression and Bayesian cluster detection to identify radon prone areas. J Environ Radioact 164:354–364CrossRefGoogle Scholar
- Shi X, Hoftiezer D, Duell E, Onega T (2006) Spatial association between residential radon concentration and bedrock types in New Hampshire. Environ Geol 51:65–71CrossRefGoogle Scholar
- Smith B, Field R (2007) Effect of housing factor and surficial uranium on the spatial prediction of residential radon in Iowa. Environmetrics 18:481–497CrossRefGoogle Scholar
- Smith B, Zhang L, Field R (2007) Iowa radon leukemia study: a hierarchical population risk model. Stat Med 10:4619–4642CrossRefGoogle Scholar
- Sundal A, Henriksen H, Soldal O, Strand T (2004) The influence of geological factors on indoor radon concentrations in Norway. Sci Total Environ 328:41–53CrossRefGoogle Scholar
- Tiefelsdorf M (2007) Controlling for migration effects in ecological disease mapping of prostate cancer. Stoch Environ Res Risk Assess 21:615–624CrossRefGoogle Scholar
- Tzavidis N, Salvati N, Schmid T, Flouri E, Midouhas E (2016) Longitudinal analysis of the strengths and difficulties questionnaire scores of the millennium cohort study children in England using m-quantile random effects regression. J R Stat Soc Ser A 179(2):427–452CrossRefGoogle Scholar
- USEPA (1992) National residential radon survey: summary report. Technical Report EPA/402/R-92/011, United States Environmental Protection Agency, Washington, DCGoogle Scholar
- Wang Y, Lin X, Zhu M, Bai Z (2007) Robust estimation using the Huber funtion with a data dependent tuning constant. J Comput Graph Stat 16(2):468–481CrossRefGoogle Scholar
- Yu K, Lu Z, Stander J (2003) Quantile regression: applications and current research areas. Statistician 52(3):331–350Google Scholar