  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.
