Semiparametric regression models for a right-skewed outcome subject to pooling

Pooling specimens prior to performing laboratory assays has various benefits. Pooling can help to reduce cost, preserve irreplaceable specimens, meet minimal volume requirements for certain lab tests, and even reduce information loss when a limit of detection is present. Regardless of the motivation for pooling, appropriate analytical techniques must be applied in order to obtain valid inference from composite specimens. When biomarkers are treated as the outcome in a regression model, techniques applicable to individually measured specimens may not be valid when measurements are taken from pooled specimens, particularly when the biomarker is positive and right skewed. In this paper, we propose a novel semiparametric estimation method based on an adaptation of the quasi-likelihood approach that can be applied to a right-skewed outcome subject to pooling. We use simulation studies to compare this method with an existing estimation technique that provides valid estimates only when pools are formed from specimens with identical predictor values. Simulation results and analysis of a motivating example demonstrate that, when appropriate estimation techniques are applied to strategically formed pools, valid and efficient estimation of the regression coefficients can be achieved.