The Probability of Observing Negative Subgroup Results When the Treatment Effect is Positive and Homogeneous across All Subgroups

Subgroup analysis is an important part in the design and analysis of clinical trials. The importance arises from the scientific and commercial implications of such analysis. The predominant concerns about subgroup analysis relate to the increased false-positive and false-negative rates. Much of the existing literature on subgroup analysis focuses on the former. In this article, we will concentrate on the false-negative aspect. Using theoretical derivation and simulations, we investigate factors that affect the probability of observing at least one negative subgroup result (ie, numerically negative treatment effect estimate) even though the true treatment effect is positive (ie, the new treatment is more efficacious than the comparator) and homogeneous across all subgroups. This probability, conditioning or unconditioning on a statistically significant overall treatment effect, is assessed for design scenarios that are commonly encountered in practice. In addition, we assess the probability of observing at least one statistically significant negative subgroup result, again conditioning or unconditioning on a statistically significant overall treatment effect. We submit that knowledge of such probabilities could provide clinical researchers with insight into the reliability of subgroup results and help set proper expectations vis-à-vis such analysis. The latter facilitates a balanced interpretation of subgroup results.