Statistical evaluation of toxicological assays with zero or near-to-zero proportions or counts in the concurrent negative control group:a tutorial

Jaki, Thomas and Kitsche, Andreas and Hothorn, Ludwig A (2014) Statistical evaluation of toxicological assays with zero or near-to-zero proportions or counts in the concurrent negative control group:a tutorial. JP Journal of Biostatistics, 11 (1). pp. 1-32. ISSN 0973-5143

Abstract

In toxicological studies interest often lies in proportions or counts for which an increase in the dose group over control indicates a safety risk. Additionally, the control group observes values that are zero or near-to-zero for endpoints characterizing pathological processes. In such instances, the comparison of dose groups versus control requires special attention as inference for ratio-to-control is infeasible or unstable and inference for difference-to-control is highly sensitive to the number of zeros or near-to-zero values. In practice, assays are commonly performed multiple times in a laboratory so that data of some historical controls are available. When the concurrent control values fall within a corresponding normal range, the evaluation is performed by comparing doses versus the concurrent control. If the data of the concurrent control are outside the normal range, a test versus the concurrent control has either an increased risk of a false-positive result or an increased risk of a false-negative result, depending on the direction of the deviation. In this work, we discuss a simple to use Williams-type approach for comparing against a mean historical value. The idea is illustrated on three examples and we show how the method can be implemented the statistical software package R.