A combined efficient design for biomarker data subject to a limit of detection due to measuring instrument sensitivity

Pooling specimens, a well-accepted sampling strategy in biomedical research, can be applied to reduce the cost of studying biomarkers. Even if the cost of a single assay is not a major restriction in evaluating biomarkers, pooling can be a powerful design that increases the efficiency of estimation based on data that is censored due to an instrument's lower limit of detection (LLOD). However, there are situations when the pooling design strongly aggravates the detection limit problem. To combine the benefits of pooled assays and individual assays, hybrid designs that involve taking a sample of both pooled and individual specimens have been proposed. We examine the efficiency of these hybrid designs in estimating parameters of two systems subject to a LLOD: (1) normally distributed biomarker with normally distributed measurement error and pooling error; (2) Gamma distributed biomarker with double exponentially distributed measurement error and pooling error. Three-assay design and two-assay design with replicates are applied to estimate the measurement and pooling error. The Maximum likelihood method is used to estimate the parameters. We found that the simple one-pool design, where all assays but one are random individuals and a single pooled assay includes the remaining specimens, under plausible conditions, is very efficient and can be recommended for practical use.