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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 asingle assay is not a major restriction in evaluating biomarkers, pooling canbe a powerful design that increases the efficiency of estimation based on datathat is censored due to an instrument's lower limit of detection (LLOD).However, there are situations when the pooling design strongly aggravates thedetection limit problem. To combine the benefits of pooled assays andindividual assays, hybrid designs that involve taking a sample of both pooledand individual specimens have been proposed. We examine the efficiency of thesehybrid designs in estimating parameters of two systems subject to a LLOD: (1)normally distributed biomarker with normally distributed measurement error andpooling error; (2) Gamma distributed biomarker with double exponentiallydistributed measurement error and pooling error. Three-assay design andtwo-assay design with replicates are applied to estimate the measurement andpooling error. The Maximum likelihood method is used to estimate theparameters. We found that the simple one-pool design, where all assays but oneare random individuals and a single pooled assay includes the remainingspecimens, under plausible conditions, is very efficient and can be recommendedfor practical use.

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