Comparing the bivariate effects of toxicity and efficacy of treatments

Medical studies often involve comparing the toxicity and efficacy of drugs. Separately evaluating toxicity and efficacy, the usual practice, does not correspond to how doctors manage patients and does not use the information provided in their bivariate relationship. This paper presents methods for analysing the bivariate data. One method is based on assessing the benefit for patient values to lie in different regions of the toxicity-efficacy plane. A second method includes patient thresholds for tolerating drugs. We propose dividing the toxicity-efficacy plane into regions where patients are likely to tolerate the drug. Several statistics are defined on these regions for measuring the toxic-therapeutic relationship, and the bootstrap is proposed for estimating their variances. We illustrate with treatment information available on rheumatoid arthritis patients.