Maximum diversity weighting for biomarkers with application in HIV-1 vaccine studies.

While studying the association between risk of HIV-1 infection and vaccine-elicited immune responses in preventative HIV-1 vaccine recipients, we encountered a need to combine a collection of biomarkers in an unsupervised fashion with the goal of preserving signal diversity within that collection. Inspired by methods for weighting protein sequences from the biological sequence analysis literature, we propose novel methods for weighting biomarkers, which we call maximum diversity weights. These weights are defined as the weights that maximize measures of signal diversity within a collection of biomarkers. While the optimization problems do not admit analytical solutions, they are convex and hence can be solved efficiently using iterative search algorithms. Through Monte Carlo studies and a real data example from HIV-1 vaccine research, we show that using maximum diversity weights in association studies can lead to an increase in power over other commonly used weights such as uniform weights or principal component-based weights.