RANDOM-EFFECTS MODEL OF DEPENDENCE BETWEEN EFFICACY AND TOXICITY IN DOSE-RANGING TRIALS

A random-effects model of the relationship of drug dosage to potentially correlated binary variables for efficacy and toxicity is developed, in which values of logistic dose-response parameters are allowed to vary among individuals. Parameter estimation is difficult, but Monte Carlo simulations can be used to determine the consequences of incorrectly applying a fixed-effects model of independence of efficacy and toxicity to data actually generated by the random-effects mechanism. Of particular interest is the spread of individuals' 'therapeutic windows' of doses about the overall population window that would be deduced from application of the model of independence. The scatter and dimensions of the windows are strongly influenced by the variances of the median effective (mu1) and median toxic (mu2) doses and by their separation (mu2 - mu1). The correlation between mu1 and mu2 has surprisingly little effect on the pattern of individuals' windows, but it does result in an imbalance in the values of mu1 in subjects with and without intolerable side effects. That imbalance, however, translates into only small differences in parameter estimates obtained with and without censoring of efficacy measurements for subjects experiencing toxicity, at least for the parameter values used in these simulations.