%0 Journal Article
%T A Bootstrap Prediction Confidence Band for QMRA Beta-Poisson Dose-Response Models
%A Gang Xie
%J Journal of Computational Biology | Symbiosis Online Publishing
%D -1
%X Let P I ( d ) MathType@MTEF@5@5@+= feaagGart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaBa aaleaacaWGjbaabeaakiaacIcacaWGKbGaaiykaaaa@3A10@ denote the probability of infection at a given mean dose d . In the quantitative microbial risk assessment (QMRA) framework, the beta-Poisson dose-response model P I ( d ) = 1 £¿ 1 F 1 ( ¦Á , ¦Á + ¦Â , £¿ d ) MathType@MTEF@5@5@+= feaagGart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaBa aaleaacaWGjbaabeaakiaacIcacaWGKbGaaiykaiabg2da9iaaigda cqGHsislcaqGGaWaaSbaaSqaaiaaigdaaeqaaOGaamOramaaBaaale aacaaIXaaabeaakiaacIcacqaHXoqycaGGSaGaeqySdeMaey4kaSIa eqOSdiMaaiilaiabgkHiTiaadsgacaGGPaaaaa@4A5E@ where 1 F 1 ( . , . , . ) MathType@MTEF@5@5@+= feaagGart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSbaaSqaai aaigdaaeqaaOGaamOramaaBaaaleaacaaIXaaabeaakiaacIcacaGG UaGaaiilaiaac6cacaGGSaGaaiOlaiaacMcaaaa@3D71@ denotes the Kummer confluent hypergeometric function and ¦Á,¦Â are the model parameters, remains the most popular plausible dose response model in practice. One commonly accepted way of constructing the confidence band about the dose-response curve in QMRA literature is to follow a bootstrap procedure based on the maximum likelihood estimates of the model parameters ¦Á and ¦Â. Here, it is shown that this bootstrap confidence bands reported in the literature represent the confidence intervals for the mean value of the probability of adverse effect, (i.e., P I ( d ) MathType@MTEF@5@5@+= feaagGart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaBa aaleaacaWGjbaabeaakiaacIcacaWGKbGaaiykaaaa@3A10@ which may represent the probability of infection at mean dose levels), not the confidence intervals for prediction. Therefore, the existing literature bootstrap (95%) confidence bands normally
%U https://symbiosisonlinepublishing.com/quantitative-computational-biology/structural-computational-biology03.php