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打ち切りデータのベイズ推定 




Stochastic models are used to express pathogen density in environmental samples for performing microbial risk assessment with quantitative uncertainty. However, enteric virus density in water often falls below the quantification limit (nondetect) of the analytical methods employed, and it is always difficult to apply stochastic models to a dataset with a substantially high number of nondetects, i.e., leftcensored data. We applied a Bayesian model that is able to model both the detected data (detects) and nondetects to simulated leftcensored datasets of enteric virus density in wastewater. One hundred paired datasets were generated for each of the 39 combinations of a sample size and the number of detects, in which three sample sizes (12, 24, and 48) and the number of detects from 1 to 12, 24 and 48 were employed. The simulated observation data were assigned to one of two groups, i.e., detects and nondetects, by setting values on the limit of quantification to obtain the assumed number of detects for creating censored datasets. Then, the Bayesian model was applied to the censored datasets, and the estimated mean and standard deviation were compared to the true values by root mean square deviation. The difference between the true distribution and posterior predictive distribution was evaluated by Kullback–Leibler (KL) divergence, and it was found that the estimation accuracy was strongly affected by the number of detects. It is difficult to describe universal criteria to decide which level of accuracy is enough, but eight or more detects are required to accurately estimate the posterior predictive distributions when the sample size is 12, 24, or 48. The posterior predictive distribution of virus removal efficiency with a wastewater treatment unit process was obtained as the log ratio posterior distributions between the posterior predictive distributions of enteric viruses in untreated wastewater and treated wastewater. The KL divergence between the true distribution and posterior predictive distribution of virus removal efficiency also depends on the number of detects, and eight or more detects in a dataset of treated wastewater are required for its accurate estimation.









本研究では打ち切りデータを扱う．赤い曲線で描いた確率分布に従って１２個のデータ点を生成したが，赤点５個しか検出限界を超えなかった．よって，青点７個のデータ点の値は分布の推定に使うことができない．黒い曲線は本研究で用いた方法で推定した分布であるが，赤い曲線を精度よく推定している． 








文献 


Tsuyoshi Kato, Takayuki Miura, Satoshi Okabe and Daisuke Sano, "Bayesian modeling of enteric virus density in wastewater using leftcensored data"Food and Environmental Virology, vol.5, no 4, 185193, 2013, DOI 10.1007/s1256001391251. 


Tsuyoshi Kato, Ayano Kobayashi, Toshihiro Ito, Takayuki Miura, Satoshi Ishii, Satoshi Okabe, Daisuke Sano, Estimation of concentration ratio of indicator to pathogenrelated gene in environmental water based on leftcensored data, Journal of Water and Health, accepted. 


Toshihiro Ito, Tsuyoshi Kato, Kenta Takagishi, Satoshi Okabe, and Daisuke Sano, Bayesian modeling of virus removal efficiency in wastewater treatment processes, Water Science and Technology, 2015;72(10):178995. doi: 10.2166/wst.2015.402. 


Toshihiro Ito, Tsuyoshi Kato, Makoto Hasegawa, Hiroyuki Katayama,
Satoshi Ishii, Satoshi Okabe, Daisuke Sano:
Evaluation of virus reduction efficiency in wastewater treatment unit
processes as a credit value in the multiplebarrier system for
wastewater reclamation and reuse,
Journal of Water and Health, , vol 14, no. 5, pp.879889, doi: 10.2166/wh.2016.096. 


小林彩乃・佐野大輔・加藤毅・伊藤寿宏・宮村明帆・三浦尚之・石井聡・岡部聡，水中病原体の許容感染リスクに基づいた水質衛生基準候補値の算出方法に関する提案，
土木学会論文集，Vol 72, No 3, 4049, 2016． 


伊藤寿宏，押木守，小林直央，加藤毅，瀬川高弘，幡本将史，山口隆司， 原田秀樹，北島正章，岡部聡，佐野大輔，下水再生処理におけるヒト腸管系ウイルスの目標除去効率の算定法，
土木学会論文集，採択済み． 


Naohiro Kobayashi, Mamoru Oshiki, Toshihiro Ito, Takahiro Segawa, Masashi Hatamoto, Tsuyoshi Kato, Takashi Yamaguchi, Kengo Kubota, Masanobu Takahashi, Akinori Iguchi, Tadashi Tagawa, Tsutomu Okubo, Shigeki Uemura, Hideki Harada, Toshiki Motoyama, Nobuo Araki, Daisuke Sano, Removal of human pathogenic viruses in a downflow hanging sponge (DHS) reactor treating municipal wastewater and health risks associated with utilization of the effluent for agricultural irrigation, Water Research, , IF=5.991 currently, accepted． 


Toshihiro Ito, Masaaki Kitajima, Tsuyoshi Kato,Satoshi Ishii, Takahiro Segawa, Satoshi Okabe, Daisuke Sano, Dr. Daisuke Sano.
Target virus log10 reduction values determined for two reclaimed wastewater irrigation scenarios in Japan based on tolerable annual disease burden.
Water Research. accepted. IF=5.991 currently． 


Miguel Varela, Imen Ouardani, Tsuyoshi Kato, Syunsuke Kadoya, Mahjoub Aouni, Daisuke Sano, and Jesús Romalde, Sapovirus in wastewater treatment plants in Tunisia: Prevalence, removal, and genetic characterization, Applied and Environmental Microbiology, accepted. IF=3.807 currently. 










