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Prediction Intervals for Overdispersed Poisson Data and Their Application in Medical and Pre-Clinical Quality

Max Menssen¹, Martina Dammann², Firas Fneish³

¹Department of Biostatistics, Leibniz University Hannover, Hanover, Germany.

Pharmaceutical Statistics

|October 30, 2024

Summary

This study introduces novel prediction intervals for overdispersed count data, offering improved historical control limits (HCL) for quality control. Bootstrap calibration ensures accurate error control, outperforming traditional methods in simulations.

Keywords:

Ames‐test Shewhart control chart bootstrap‐calibration historical control data negative‐binomial distribution quasi‐likelihood

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Area of Science:

Biostatistics
Statistical Process Control
Quality Control

Background:

Historical control limits (HCL) are crucial for process monitoring and validating observations in pre-clinical and medical quality control.
Traditional HCL methods applied to count data (e.g., Ames assay, multiple sclerosis relapses) often struggle with overdispersion, right-skewness, and varying cluster sizes.

Purpose of the Study:

To propose robust prediction intervals for overdispersed count data as effective HCL.
To develop a bootstrap calibration algorithm for accurate control of type-1 error rates, especially with skewed data and variable baseline quantities.

Main Methods:

Utilized quasi-Poisson and negative-binomial distributions to model overdispersed count data.
Incorporated offsets to handle variable baseline quantities (e.g., petri dish counts, monitoring times).
Developed and applied a bootstrap calibration algorithm to ensure equal tail probabilities and control type-1 error.

Main Results:

Bootstrap-calibrated prediction intervals demonstrated superior control of type-1 error compared to eight other HCL methods in Monte-Carlo simulations.
Traditional heuristics like Shewhart charts (c- or u-charts, mean ± 2 SD) were found to inadequately control pre-specified coverage probabilities.
The proposed methods were successfully applied to Ames assay data and multiple sclerosis relapse counts.

Conclusions:

The proposed bootstrap-calibrated prediction intervals provide a statistically sound and reliable method for establishing HCL with overdispersed count data.
This approach offers a significant improvement over traditional methods, ensuring better process stability assessment and observation validation.
The methodology and calibration algorithm are accessible through the R package 'predint'.