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http://hdl.handle.net/1942/18969Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | NYSEN, Ruth | - |
| dc.contributor.author | FAES, Christel | - |
| dc.contributor.author | Ferrari, Pietro | - |
| dc.contributor.author | Verger, Philippe | - |
| dc.contributor.author | AERTS, Marc | - |
| dc.date.accessioned | 2015-06-22T09:04:30Z | - |
| dc.date.available | 2015-06-22T09:04:30Z | - |
| dc.date.issued | 2016 | - |
| dc.identifier.citation | BIOMETRICAL JOURNAL 58 (2), pag; 331-356 | - |
| dc.identifier.issn | 0323-3847 | - |
| dc.identifier.uri | http://hdl.handle.net/1942/18969 | - |
| dc.description.abstract | In chemical risk assessment, it is important to determine the quantiles of the distribution of concentration data. The selection of an appropriate distribution and the estimation of particular quantiles of interest are largely hindered by the omnipresence of observations below the limit of detection, leading to left-censored data. The log-normal distribution is a common choice, but this distribution is not the only possibility and alternatives should be considered as well. Here, we focus on several distributions that are related to the log-normal distribution or that are seminonparametric extensions of the log-normal distribution. Whereas previous work focused on the estimation of the cumulative distribution function, our interest here goes to the estimation of quantiles, particularly in the left tail of the distribution where most of the left-censored data are located. Two different model averaged quantile estimators are defined and compared for different families of candidate models. The models and methods of selection and averaging are further investigated through simulations and illustrated on data of cadmium concentration in food products. The approach is extended to include covariates and to deal with uncertainty about the values of the limit of detection. These extensions are illustrated with 134-cesium measurements from Fukushima Prefecture, Japan. We can conclude that averaged models do achieve good performance characteristics in case no useful prior knowledge about the true distribution is available; that there is no structural difference in the performance of the direct and indirect method; and that, not surprisingly, only the true or closely approximating model can deal with extremely high percentages of censoring. | - |
| dc.description.sponsorship | We thank the editor and the reviewers for their comments and suggestions leading to an improved presentation of the paper. This research was supported by the IAP research network nr P7/06 of the Belgian Government (Belgian Science Policy). The computational resources and services used in this work were provided by the Hercules Foundation and the Flemish Government, department EWI. The authors are grateful to EFSA for the approval to use the cadmium data (EFSA/DATEX/2007/005). | - |
| dc.language.iso | en | - |
| dc.rights | © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim | - |
| dc.subject.other | left-censoring; limit of detection; model averaging; quantiles | - |
| dc.title | Model averaging quantiles from data censored by a limit of detection | - |
| dc.type | Journal Contribution | - |
| dc.identifier.epage | 356 | - |
| dc.identifier.issue | 2 | - |
| dc.identifier.spage | 331 | - |
| dc.identifier.volume | 58 | - |
| local.format.pages | 26 | - |
| local.bibliographicCitation.jcat | A1 | - |
| dc.description.notes | Nysen, R (reprint author), Hasselt Univ, Interuniv Inst Biostat & Stat Bioinformat, Martelarenlaan 42, B-3500 Hasselt, Belgium. ruth.nysen@uhasselt.be | - |
| dc.relation.references | Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In: Petrov, B. and Csaki, B. (Eds.), 2nd International Symposium on Information Theory, Budapest, HU, pp. 267–281. Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics. Theory and Applications 12, 171–178. Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on amultivariateskewt-distribution. Journal of the Royal Statistical Society. Series B. Statistical Methodology 65, 367–389. Azzalini, A., Dal Cappello, T. and Kotz, S. (2003). Log-skew-normal and log-skew-t distributions as model for family income data. Journal of Income Distribution 11, 12–20. Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715–726. Behl, P., Claeskens, G. and Dette, H. (2014). Focused model selection in quantile regression. Statistica Sinica 24, 601–624. Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Inference: A Practical Information-Theoretical Approach. Springer-Verlag, New York, NY. Claeskens, G. and Carroll, R. J. (2007). An asymptotic theory for model selection inference in general semipara- metric problems. Biometrika 94, 249–265. Claeskens, G. and Hjort, N. L. (2008). Model Selection and Model Averaging. Cambridge University Press, Cambridge, UK. EFSA (2010). Management of left-censored data in dietary exposure assessment of chemical substances. EFSA Journal 8, 96pp. Faes, C., Aerts, M., Geys, H. and Molenberghs, G. (2007). Model averaging using fractional polynomials to estimate a safe level of exposure. Risk Analysis 27, 111–123. Fenton, V. M. and Gallant, A. R. (1996). Qualitative and asymptotic performance of SNP densityestimators. Journal of Econometrics 74, 77–118. Gallant, A. R. and Nychka, D. W. (1987). Semi-nonparametric maximum likelihood estimation. Econometrica 55, 363–390. Gillespie, B. W., Chen, Q., Reichert, H., Franzblau, A., Hedgeman, E., Lepkowski, J., Adriaens, P., Demond, A., Luksemburg, W. and Garabrant, D. H. (2010). Estimating population distributions when some data are below a limit of detection by using a reverse Kaplan-Meier estimator. Epidemiology 21, S64–S70. Hewett, P. and Ganser, G. H. (2007). A Comparison of Several Methods for Analyzing Censored Data. Annals of Occupational Hygiene 51, 611–632. Hoeting, J. A., Madigan, D., Raftery, A. E. and Volinsky, C. T. (1999). Bayesian model averaging: a tutorial. Statistical Science 14, 382–417. Hurvich, C. and Simonoff, J. and Tsai, C.-L. (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. Journal of the Royal Statistical Society B 60, 271–293. Kroll, C. N. and Stedinger, J. (1996). Estimat ion of moments and quantiles using censored data. Water Resources Research 32, 1005–1012. Lin, G. D. and Stoyanov, J. (2009). The logarithmic skew-normal distributions are moment-indeterminate. Journal of Applied Probability 46, 909–916. Morales, K. H., Ibrahim, J. G., Chen, C.-J., and Ryan, L.M. (2006). Model averaging with applications to benchmark dose estimation for arsenic in drinking water. Journal of the American Statistical Association 101, 9–17. Moy, G. G. (2013) Total Diet Studies. Springer-Verlag, New York, NY. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In: Petrov, B. and Csaki, B. (Eds.), 2nd International Symposium on Information Theory, Budapest, HU, pp. 267–281. Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics. Theory and Applications 12, 171–178. Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on amultivariateskewt-distribution. Journal of the Royal Statistical Society. Series B. Statistical Methodology 65, 367–389. Azzalini, A., Dal Cappello, T. and Kotz, S. (2003). Log-skew-normal and log-skew-t distributions as model for family income data. Journal of Income Distribution 11, 12–20. Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715–726. Behl, P., Claeskens, G. and Dette, H. (2014). Focused model selection in quantile regression. Statistica Sinica 24, 601–624. Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Inference: A Practical Information-Theoretical Approach. Springer-Verlag, New York, NY. Claeskens, G. and Carroll, R. J. (2007). An asymptotic theory for model selection inference in general semipara- metric problems. Biometrika 94, 249–265. Claeskens, G. and Hjort, N. L. (2008). Model Selection and Model Averaging. Cambridge University Press, Cambridge, UK. EFSA (2010). Management of left-censored data in dietary exposure assessment of chemical substances. EFSA Journal 8, 96pp. Faes, C., Aerts, M., Geys, H. and Molenberghs, G. (2007). Model averaging using fractional polynomials to estimate a safe level of exposure. Risk Analysis 27, 111–123. Fenton, V. M. and Gallant, A. R. (1996). Qualitative and asymptotic performance of SNP densityestimators. Journal of Econometrics 74, 77–118. Gallant, A. R. and Nychka, D. W. (1987). Semi-nonparametric maximum likelihood estimation. Econometrica 55, 363–390. Gillespie, B. W., Chen, Q., Reichert, H., Franzblau, A., Hedgeman, E., Lepkowski, J., Adriaens, P., Demond, A., Luksemburg, W. and Garabrant, D. H. (2010). Estimating population distributions when some data are below a limit of detection by using a reverse Kaplan-Meier estimator. Epidemiology 21, S64–S70. Hewett, P. and Ganser, G. H. (2007). A Comparison of Several Methods for Analyzing Censored Data. Annals of Occupational Hygiene 51, 611–632. Hoeting, J. A., Madigan, D., Raftery, A. E. and Volinsky, C. T. (1999). Bayesian model averaging: a tutorial. Statistical Science 14, 382–417. Hurvich, C. and Simonoff, J. and Tsai, C.-L. (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. Journal of the Royal Statistical Society B 60, 271–293. Kroll, C. N. and Stedinger, J. (1996). Estimat ion of moments and quantiles using censored data. Water Resources Research 32, 1005–1012. Lin, G. D. and Stoyanov, J. (2009). The logarithmic skew-normal distributions are moment-indeterminate. Journal of Applied Probability 46, 909–916. Morales, K. H., Ibrahim, J. G., Chen, C.-J., and Ryan, L.M. (2006). Model averaging with applications to benchmark dose estimation for arsenic in drinking water. Journal of the American Statistical Association 101, 9–17. Moy, G. G. (2013) Total Diet Studies. Springer-Verlag, New York, NY. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In: Petrov, B. and Csaki, B. (Eds.), 2nd International Symposium on Information Theory, Budapest, HU, pp. 267–281. Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics. Theory and Applications 12, 171–178. Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on amultivariateskewt-distribution. Journal of the Royal Statistical Society. Series B. Statistical Methodology 65, 367–389. Azzalini, A., Dal Cappello, T. and Kotz, S. (2003). Log-skew-normal and log-skew-t distributions as model for family income data. Journal of Income Distribution 11, 12–20. Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715–726. Behl, P., Claeskens, G. and Dette, H. (2014). Focused model selection in quantile regression. Statistica Sinica 24, 601–624. Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Inference: A Practical Information-Theoretical Approach. Springer-Verlag, New York, NY. Claeskens, G. and Carroll, R. J. (2007). An asymptotic theory for model selection inference in general semipara- metric problems. Biometrika 94, 249–265. Claeskens, G. and Hjort, N. L. (2008). Model Selection and Model Averaging. Cambridge University Press, Cambridge, UK. EFSA (2010). Management of left-censored data in dietary exposure assessment of chemical substances. EFSA Journal 8, 96pp. Faes, C., Aerts, M., Geys, H. and Molenberghs, G. (2007). Model averaging using fractional polynomials to estimate a safe level of exposure. Risk Analysis 27, 111–123. Fenton, V. M. and Gallant, A. R. (1996). Qualitative and asymptotic performance of SNP densityestimators. Journal of Econometrics 74, 77–118. Gallant, A. R. and Nychka, D. W. (1987). Semi-nonparametric maximum likelihood estimation. Econometrica 55, 363–390. Gillespie, B. W., Chen, Q., Reichert, H., Franzblau, A., Hedgeman, E., Lepkowski, J., Adriaens, P., Demond, A., Luksemburg, W. and Garabrant, D. H. (2010). Estimating population distributions when some data are below a limit of detection by using a reverse Kaplan-Meier estimator. Epidemiology 21, S64–S70. Hewett, P. and Ganser, G. H. (2007). A Comparison of Several Methods for Analyzing Censored Data. Annals of Occupational Hygiene 51, 611–632. Hoeting, J. A., Madigan, D., Raftery, A. E. and Volinsky, C. T. (1999). Bayesian model averaging: a tutorial. Statistical Science 14, 382–417. Hurvich, C. and Simonoff, J. and Tsai, C.-L. (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. Journal of the Royal Statistical Society B 60, 271–293. Kroll, C. N. and Stedinger, J. (1996). Estimat ion of moments and quantiles using censored data. Water Resources Research 32, 1005–1012. Lin, G. D. and Stoyanov, J. (2009). The logarithmic skew-normal distributions are moment-indeterminate. Journal of Applied Probability 46, 909–916. Morales, K. H., Ibrahim, J. G., Chen, C.-J., and Ryan, L.M. (2006). Model averaging with applications to benchmark dose estimation for arsenic in drinking water. Journal of the American Statistical Association 101, 9–17. Moy, G. G. (2013) Total Diet Studies. Springer-Verlag, New York, NY. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In: Petrov, B. and Csaki, B. (Eds.), 2nd International Symposium on Information Theory, Budapest, HU, pp. 267–281. Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics. Theory and Applications 12, 171–178. Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on amultivariateskewt-distribution. Journal of the Royal Statistical Society. Series B. Statistical Methodology 65, 367–389. Azzalini, A., Dal Cappello, T. and Kotz, S. (2003). Log-skew-normal and log-skew-t distributions as model for family income data. Journal of Income Distribution 11, 12–20. Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715–726. Behl, P., Claeskens, G. and Dette, H. (2014). Focused model selection in quantile regression. Statistica Sinica 24, 601–624. Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Inference: A Practical Information-Theoretical Approach. Springer-Verlag, New York, NY. Claeskens, G. and Carroll, R. J. (2007). An asymptotic theory for model selection inference in general semipara- metric problems. Biometrika 94, 249–265. Claeskens, G. and Hjort, N. L. (2008). Model Selection and Model Averaging. Cambridge University Press, Cambridge, UK. EFSA (2010). Management of left-censored data in dietary exposure assessment of chemical substances. EFSA Journal 8, 96pp. Faes, C., Aerts, M., Geys, H. and Molenberghs, G. (2007). Model averaging using fractional polynomials to estimate a safe level of exposure. Risk Analysis 27, 111–123. Fenton, V. M. and Gallant, A. R. (1996). Qualitative and asymptotic performance of SNP densityestimators. Journal of Econometrics 74, 77–118. Gallant, A. R. and Nychka, D. W. (1987). Semi-nonparametric maximum likelihood estimation. Econometrica 55, 363–390. Gillespie, B. W., Chen, Q., Reichert, H., Franzblau, A., Hedgeman, E., Lepkowski, J., Adriaens, P., Demond, A., Luksemburg, W. and Garabrant, D. H. (2010). Estimating population distributions when some data are below a limit of detection by using a reverse Kaplan-Meier estimator. Epidemiology 21, S64–S70. Hewett, P. and Ganser, G. H. (2007). A Comparison of Several Methods for Analyzing Censored Data. Annals of Occupational Hygiene 51, 611–632. Hoeting, J. A., Madigan, D., Raftery, A. E. and Volinsky, C. T. (1999). Bayesian model averaging: a tutorial. Statistical Science 14, 382–417. Hurvich, C. and Simonoff, J. and Tsai, C.-L. (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. Journal of the Royal Statistical Society B 60, 271–293. Kroll, C. N. and Stedinger, J. (1996). Estimat ion of moments and quantiles using censored data. Water Resources Research 32, 1005–1012. Lin, G. D. and Stoyanov, J. (2009). The logarithmic skew-normal distributions are moment-indeterminate. Journal of Applied Probability 46, 909–916. Morales, K. H., Ibrahim, J. G., Chen, C.-J., and Ryan, L.M. (2006). Model averaging with applications to benchmark dose estimation for arsenic in drinking water. Journal of the American Statistical Association 101, 9–17. Moy, G. G. (2013) Total Diet Studies. Springer-Verlag, New York, NY. References Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In: Petrov, B. and Csaki, B. (Eds.), 2nd International Symposium on Information Theory, Budapest, HU, pp. 267–281. Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics. Theory and Applications 12, 171–178. Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on amultivariateskewt-distribution. Journal of the Royal Statistical Society. Series B. Statistical Methodology 65, 367–389. Azzalini, A., Dal Cappello, T. and Kotz, S. (2003). Log-skew-normal and log-skew-t distributions as model for family income data. Journal of Income Distribution 11, 12–20. Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715–726. Behl, P., Claeskens, G. and Dette, H. (2014). Focused model selection in quantile regression. Statistica Sinica 24, 601–624. Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Inference: A Practical Information-Theoretical Approach. Springer-Verlag, New York, NY. Claeskens, G. and Carroll, R. J. (2007). An asymptotic theory for model selection inference in general semipara- metric problems. Biometrika 94, 249–265. Claeskens, G. and Hjort, N. L. (2008). Model Selection and Model Averaging. Cambridge University Press, Cambridge, UK. EFSA (2010). Management of left-censored data in dietary exposure assessment of chemical substances. EFSA Journal 8, 96pp. Faes, C., Aerts, M., Geys, H. and Molenberghs, G. (2007). Model averaging using fractional polynomials to estimate a safe level of Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In: Petrov, B. and Csaki, B. (Eds.), 2nd International Symposium on Information Theory, Budapest, HU, pp. 267–281. Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics. Theory and Applications 12, 171–178. Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. Journal of the Royal Statistical Society. Series B. Statistical Methodology 65, 367–389. Azzalini, A., Dal Cappello, T. and Kotz, S. (2003). Log-skew-normal and log-skew-t distributions as model for family income data. Journal of Income Distribution 11, 12–20. Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715–726. Behl, P., Claeskens, G. and Dette, H. (2014). Focused model selection in quantile regression. Statistica Sinica 24, 601–624. Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Inference: A Practical Information-Theoretical Approach. Springer-Verlag, New York, NY. Claeskens, G. and Carroll, R. J. (2007). An asymptotic theory for model selection inference in general semiparametric problems. Biometrika 94, 249–265. Claeskens, G. and Hjort, N. L. (2008). Model Selection and Model Averaging. Cambridge University Press, Cambridge, UK. EFSA (2010). Management of left-censored data in dietary exposure assessment of chemical substances. EFSA Journal 8, 96pp. Faes, C., Aerts, M., Geys, H. and Molenberghs, G. (2007). Model averaging using fractional polynomials to estimate a safe level of exposure. Risk Analysis 27, 111–123. Fenton, V. M. and Gallant, A. R. (1996). Qualitative and asymptotic performance of SNP densityestimators. Journal of Econometrics 74, 77–118. Gallant, A. R. and Nychka, D. W. (1987). Semi-nonparametric maximum likelihood estimation. Econometrica 55, 363–390. Gillespie, B. W., Chen, Q., Reichert, H., Franzblau, A., Hedgeman, E., Lepkowski, J., Adriaens, P., Demond, A., Luksemburg, W. and Garabrant, D. H. (2010). Estimating population distributions when some data are below a limit of detection by using a reverse Kaplan-Meier estimator. Epidemiology 21, S64–S70. Hewett, P. and Ganser, G. H. (2007). A Comparison of Several Methods for Analyzing Censored Data. Annals of Occupational Hygiene 51, 611–632. Hoeting, J. A., Madigan, D., Raftery, A. E. and Volinsky, C. T. (1999). Bayesian model averaging: a tutorial. Statistical Science 14, 382–417. Hurvich, C. and Simonoff, J. and Tsai, C.-L. (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. Journal of the Royal Statistical Society B 60, 271–293. Kroll, C. N. and Stedinger, J. (1996). Estimation of moments and quantiles using censored data. Water Resources Research 32, 1005–1012. Lin, G. D. and Stoyanov, J. (2009). The logarithmic skew-normal distributions are moment-indeterminate. Journal of Applied Probability 46, 909–916. Morales, K. H., Ibrahim, J. G., Chen, C.-J., and Ryan, L.M. (2006). Model averaging with applications to benchmark dose estimation for arsenic in drinking water. Journal of the American Statistical Association 101, 9–17. Moy, G. G. (2013) Total Diet Studies. Springer-Verlag, New York, NY. Nysen, R. (2016). 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(1978). Estimating the dimension of a model. The Annals of Statistics 6, 461–464. Stacy, E. (1962). A generalization of the gamma distribution. The Annals of Mathematical Statistics, 1187–1192. Wheeler, M. W. and Bailer, A. J. (2007). Properties of model-averaged BMDLs: a study of model averaging in dichotomous response risk estimation. Risk analysis 27, 659–670. Wheeler, M. W. and Bailer, A. J. (2009). Comparing model averaging with other model selection strategies for benchmark dose estimation. Environmental and Ecological Statistics 16, 37–51. Zhang, M. and Davidian, M. (2008). “Smooth” semiparametric regression analysis for arbitrarily censored timeto-event data. Biometrics 64, 567–669. | - |
| local.type.refereed | Refereed | - |
| local.type.specified | Article | - |
| dc.identifier.doi | 10.1002/bimj.201400108 | - |
| dc.identifier.isi | 000372174400006 | - |
| item.validation | ecoom 2017 | - |
| item.contributor | NYSEN, Ruth | - |
| item.contributor | FAES, Christel | - |
| item.contributor | Ferrari, Pietro | - |
| item.contributor | Verger, Philippe | - |
| item.contributor | AERTS, Marc | - |
| item.accessRights | Restricted Access | - |
| item.fullcitation | NYSEN, Ruth; FAES, Christel; Ferrari, Pietro; Verger, Philippe & AERTS, Marc (2016) Model averaging quantiles from data censored by a limit of detection. In: BIOMETRICAL JOURNAL 58 (2), pag; 331-356. | - |
| item.fulltext | With Fulltext | - |
| crisitem.journal.issn | 0323-3847 | - |
| crisitem.journal.eissn | 1521-4036 | - |
| Appears in Collections: | Research publications | |
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