# Layman’s abstract for Statistics in Medicine paper on the properties of the toxicity index and its statistical efficiency

Each week, we will be publishing layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.

The article featured today is from Statistics in Medicine, with the full article now published in Volume 40, Issue 6 and available to read here.

On the properties of the toxicity index and its statistical efficiencyStatistics in Medicine2021401535– 1552https://doi.org/10.1002/sim.8858

In cancer clinical trials, patients are assigned to different treatment groups, and for each patient, graded toxicities are documented. This is a crucial step in the assessment of treatments to ensure their safety and tolerability. The most used approach to summarize multiple toxicities per patient is the maximum-grade. However, this approach suffers from the lack of representation of the toxicity burden experienced by patients.

In an effort to address the shortcomings of the maximum-grade, the toxicity index (TI) was proposed. The TI is a summary measure that preserves the highest grade while incorporating lower grade toxicities and can avoid the loss of information and improve clinical interpretability.

While the TI was introduced more than a decade ago, its mathematical and statistical properties have never been studied. In this paper, the authors report on the novel characteristics of TI as a summary measure and its effectiveness in comparing treatments. They introduce an ordering on toxicity profiles, called T-rank, and argue that preserving T-rank is a desirable property that allows investigators to achieve clinically-meaningful ranking of the toxicity profiles. They show that TI is the only measure that preserves the T-rank among its competitors.

Moreover, they propose a Poisson-Limit model for sparse toxicity data. Under this model, a general family of tests is developed for detecting differences among two populations of toxicity data, based on any summary measure. The authors derive the large sample properties of this class and show that TI is more efficient (needs smaller sample size) than the maximum and the average summary measures. The methods are evaluated on clinical trial toxicity data and TI is shown to be more powerful in detecting the differences in toxicity profiles among treatments. The results of this paper can be applied beyond toxicity modeling, to any problem where one observes a sparse array of scores on subjects and a ranking based on extreme scores is desirable.