Single-index regression for pooled biomarker data

Laboratory assays used to evaluate biomarkers (biological markers) are often prohibitively expensive. As an efficient data collection mechanism to save on testing costs, pooling has become more commonly used in epidemiological research. Useful statistical methods have been proposed to relate pooled biomarker measurements to individual covariate information. However, most of these regression techniques have proceeded under parametric linear assumptions. To relax such assumptions, we propose a semiparametric approach that originates from the context of the single-index model. Unlike with traditional single-index methodologies, we face a challenge in that the observed data are biomarker measurements on pools rather than individual specimens. In this article, we propose a method that addresses this challenge. The asymptotic properties of our estimators are derived. We illustrate the finite sample performance of our estimators through simulation and by applying it to a diabetes data set and a chemokine data set.