Clustered Hierarchical Modeling for Identifying Promising Subgroups
Liz Krachey, Berry Consultants  *Kert Viele, Berry Consultants 

Keywords: subgroup analysis, borrowing information, Dirichlet Process mixture

Many medical conditions are heterogeneous. As we evaluate new treatments, we must identify specific subgroups where patients would benefit from the treatment. As the number of groups increase in these studies, we find what has been called “the approaching wall”, where pooling across different effects is inappropriate, but analyzing the groups separately is not possible due to limited resources. In these situations, we need clever methods to effectively leverage all available information both across and within subgroups.

Hierarchical models hold promise, as they allow borrowing of information across subgroups (allowing larger effective sample sizes) while recognizing there is variation across subgroups. These models make use of the intuition that the data in a single group may not be conclusive by itself, but repeatedly seeing a common trend across many subgroups may be conclusive when viewed as a whole.

The assumed across group distribution heavily influences the performance of hierarchical models. The commonly used single unimodal distribution often works well, but has difficulties when there are “nugget” groups (a single outlying subgroup) or a small number of distinct clusters of subgroups (for example, where the treatment either works well or does not work at all).

We propose a Dirichlet Process based clustering approach to the across subgroup distribution, effectively replacing the single normal distribution with a mixture of normals. This approach more flexibly handles many situations, such as allowing single outlying subgroups to be treated differently from the other groups, or allowing a “half and half” mixture. Many of the advantages of a single normal hierarchical model are retained while providing increased flexibility.