TY - JOUR

T1 - Prediction intervals for overdispersed binomial data with application to historical controls

AU - Menssen, Max

AU - Schaarschmidt, Frank

N1 - Funding information: We want to thank Prof Dr Ludwig Hothorn for giving helpful suggestions and Clemens Buczilowski for his technicalsupport. Furthermore, we want to thank the reviewers for reading the manuscript and for their helpful comments.

PY - 2019/6/30

Y1 - 2019/6/30

N2 - Bioassays are highly standardized trials for assessing the impact of a chemical compound on a model organism. In that context, it is standard to compare several treatment groups with an untreated control. If the same type of bioassay is carried out several times, the amount of information about the historical controls rises with every new study. This information can be applied to predict the outcome of one future control using a prediction interval. Since the observations are counts of success out of a given sample size, like mortality or histopathological findings, the data can be assumed to be binomial but may exhibit overdispersion caused by the variability between historical studies. We describe two approaches that account for overdispersion: asymptotic prediction intervals using the quasi-binomial assumption and prediction intervals based on the quantiles of the beta-binomial distribution. Both interval types were α-calibrated using bootstrap methods. For an assessment of the intervals coverage probabilities, a simulation study based on various numbers of historical studies and sample sizes as well as different binomial proportions and varying levels of overdispersion was run. It could be shown that α-calibration can improve the coverage probabilities of both interval types. The coverage probability of the calibrated intervals, calculated based on at least 10 historical studies, was satisfactory close to the nominal 95%. In a last step, the intervals were computed based on a real data set from the NTP homepage, using historical controls from bioassays with the mice strain B6C3F1.

AB - Bioassays are highly standardized trials for assessing the impact of a chemical compound on a model organism. In that context, it is standard to compare several treatment groups with an untreated control. If the same type of bioassay is carried out several times, the amount of information about the historical controls rises with every new study. This information can be applied to predict the outcome of one future control using a prediction interval. Since the observations are counts of success out of a given sample size, like mortality or histopathological findings, the data can be assumed to be binomial but may exhibit overdispersion caused by the variability between historical studies. We describe two approaches that account for overdispersion: asymptotic prediction intervals using the quasi-binomial assumption and prediction intervals based on the quantiles of the beta-binomial distribution. Both interval types were α-calibrated using bootstrap methods. For an assessment of the intervals coverage probabilities, a simulation study based on various numbers of historical studies and sample sizes as well as different binomial proportions and varying levels of overdispersion was run. It could be shown that α-calibration can improve the coverage probabilities of both interval types. The coverage probability of the calibrated intervals, calculated based on at least 10 historical studies, was satisfactory close to the nominal 95%. In a last step, the intervals were computed based on a real data set from the NTP homepage, using historical controls from bioassays with the mice strain B6C3F1.

KW - alpha-calibration bootstrap

KW - beta-binomial

KW - bioassay

KW - extra binomial variation

KW - quasi-binomial

UR - http://www.scopus.com/inward/record.url?scp=85062514015&partnerID=8YFLogxK

U2 - 10.1002/sim.8124

DO - 10.1002/sim.8124

M3 - Article

C2 - 30835886

AN - SCOPUS:85062514015

VL - 38

SP - 2652

EP - 2663

JO - Statistics in medicine

JF - Statistics in medicine

SN - 0277-6715

IS - 14

ER -