Details
| Original language | English |
|---|---|
| Journal | Pharmaceutical statistics |
| Early online date | 30 Oct 2024 |
| Publication status | E-pub ahead of print - 30 Oct 2024 |
Abstract
In pre-clinical and medical quality control, it is of interest to assess the stability of the process under monitoring or to validate a current observation using historical control data. Classically, this is done by the application of historical control limits (HCL) graphically displayed in control charts. In many applications, HCL are applied to count data, for example, the number of revertant colonies (Ames assay) or the number of relapses per multiple sclerosis patient. Count data may be overdispersed, can be heavily right-skewed and clusters may differ in cluster size or other baseline quantities (e.g., number of petri dishes per control group or different length of monitoring times per patient). Based on the quasi-Poisson assumption or the negative-binomial distribution, we propose prediction intervals for overdispersed count data to be used as HCL. Variable baseline quantities are accounted for by offsets. Furthermore, we provide a bootstrap calibration algorithm that accounts for the skewed distribution and achieves equal tail probabilities. Comprehensive Monte-Carlo simulations assessing the coverage probabilities of eight different methods for HCL calculation reveal, that the bootstrap calibrated prediction intervals control the type-1-error best. Heuristics traditionally used in control charts (e.g., the limits in Shewhart c- or u-charts or the mean ± 2 SD) fail to control a pre-specified coverage probability. The application of HCL is demonstrated based on data from the Ames assay and for numbers of relapses of multiple sclerosis patients. The proposed prediction intervals and the algorithm for bootstrap calibration are publicly available via the R package predint.
Keywords
- Ames-test, bootstrap-calibration, historical control data, negative-binomial distribution, quasi-likelihood, Shewhart control chart
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Pharmacology, Toxicology and Pharmaceutics(all)
- Pharmacology
- Medicine(all)
- Pharmacology (medical)
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In: Pharmaceutical statistics, 30.10.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Prediction Intervals for Overdispersed Poisson Data and Their Application in Medical and Pre-Clinical Quality Control
AU - Menssen, Max
AU - Dammann, Martina
AU - Fneish, Firas
AU - Ellenberger, David
AU - Schaarschmidt, Frank
N1 - Publisher Copyright: © 2024 The Author(s). Pharmaceutical Statistics published by John Wiley & Sons Ltd.
PY - 2024/10/30
Y1 - 2024/10/30
N2 - In pre-clinical and medical quality control, it is of interest to assess the stability of the process under monitoring or to validate a current observation using historical control data. Classically, this is done by the application of historical control limits (HCL) graphically displayed in control charts. In many applications, HCL are applied to count data, for example, the number of revertant colonies (Ames assay) or the number of relapses per multiple sclerosis patient. Count data may be overdispersed, can be heavily right-skewed and clusters may differ in cluster size or other baseline quantities (e.g., number of petri dishes per control group or different length of monitoring times per patient). Based on the quasi-Poisson assumption or the negative-binomial distribution, we propose prediction intervals for overdispersed count data to be used as HCL. Variable baseline quantities are accounted for by offsets. Furthermore, we provide a bootstrap calibration algorithm that accounts for the skewed distribution and achieves equal tail probabilities. Comprehensive Monte-Carlo simulations assessing the coverage probabilities of eight different methods for HCL calculation reveal, that the bootstrap calibrated prediction intervals control the type-1-error best. Heuristics traditionally used in control charts (e.g., the limits in Shewhart c- or u-charts or the mean ± 2 SD) fail to control a pre-specified coverage probability. The application of HCL is demonstrated based on data from the Ames assay and for numbers of relapses of multiple sclerosis patients. The proposed prediction intervals and the algorithm for bootstrap calibration are publicly available via the R package predint.
AB - In pre-clinical and medical quality control, it is of interest to assess the stability of the process under monitoring or to validate a current observation using historical control data. Classically, this is done by the application of historical control limits (HCL) graphically displayed in control charts. In many applications, HCL are applied to count data, for example, the number of revertant colonies (Ames assay) or the number of relapses per multiple sclerosis patient. Count data may be overdispersed, can be heavily right-skewed and clusters may differ in cluster size or other baseline quantities (e.g., number of petri dishes per control group or different length of monitoring times per patient). Based on the quasi-Poisson assumption or the negative-binomial distribution, we propose prediction intervals for overdispersed count data to be used as HCL. Variable baseline quantities are accounted for by offsets. Furthermore, we provide a bootstrap calibration algorithm that accounts for the skewed distribution and achieves equal tail probabilities. Comprehensive Monte-Carlo simulations assessing the coverage probabilities of eight different methods for HCL calculation reveal, that the bootstrap calibrated prediction intervals control the type-1-error best. Heuristics traditionally used in control charts (e.g., the limits in Shewhart c- or u-charts or the mean ± 2 SD) fail to control a pre-specified coverage probability. The application of HCL is demonstrated based on data from the Ames assay and for numbers of relapses of multiple sclerosis patients. The proposed prediction intervals and the algorithm for bootstrap calibration are publicly available via the R package predint.
KW - Ames-test
KW - bootstrap-calibration
KW - historical control data
KW - negative-binomial distribution
KW - quasi-likelihood
KW - Shewhart control chart
UR - http://www.scopus.com/inward/record.url?scp=85208031524&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2404.05282
DO - 10.48550/arXiv.2404.05282
M3 - Article
AN - SCOPUS:85208031524
JO - Pharmaceutical statistics
JF - Pharmaceutical statistics
SN - 1539-1604
ER -