Frequentist rules for regulatory approval of subgroups in phase III trials: A fresh look at an old problem

The number of Phase III trials that include a biomarker in design and analysis has increased due to interest in personalised medicine. For genetic mutations and other predictive biomarkers, the trial sample comprises two subgroups, one of which, say $$ is known or suspected to achieve a larger treatment effect than the other $$. Despite treatment effect heterogeneity, trials often draw patients from both subgroups, since the lower responding $$ subgroup may also gain benefit from the intervention. In this case, regulators/commissioners must decide what constitutes sufficient evidence to approve the drug in the $$ population.

Assuming trial analysis can be completed using generalised linear models, we define and evaluate three frequentist decision rules for approval. For rule one, the significance of the average treatment effect in $$ should exceed a pre-defined minimum value, say $$. For rule two, the data from the low-responding group $$ should increase statistical significance. For rule three, the subgroup-treatment interaction should be non-significant, using type I error chosen to ensure that estimated difference between the two subgroup effects is acceptable. Rules are evaluated based on conditional power, given that there is an overall significant treatment effect. We show how different rules perform according to the distribution of patients across the two subgroups and when analyses include additional (stratification) covariates in the analysis, thereby conferring correlation between subgroup effects.

When additional conditions are required for approval of a new treatment in a lower response subgroup, easily applied rules based on minimum effect sizes and relaxed interaction tests are available. Choice of rule is influenced by the proportion of patients sampled from the two subgroups but less so by the correlation between subgroup effects.