  Pooled testing is widely used for screening for viral or bacterial infections
with low prevalence when individual testing is not cost-efficient. Pooled
testing with qualitative assays that give binary results has been well-studied.
However, characteristics of pooling with quantitative assays were mostly
demonstrated using simulations or empirical studies. We investigate properties
of three pooling strategies with quantitative assays: traditional two-stage
mini-pooling (MP) (Dorfman, 1943), mini-pooling with deconvolution algorithm
(MPA) (May et al., 2010), and marker-assisted MPA (mMPA) (Liu et al., 2017).
MPA and mMPA test individuals in a sequence after a positive pool and implement
a deconvolution algorithm to determine when testing can cease to ascertain all
individual statuses. mMPA uses information from other available markers to
determine an optimal order for individual testings. We derive and compare the
general statistical properties of the three pooling methods. We show that with
a proper pool size, MP, MPA, and mMPA can be more cost-efficient than
individual testing, and mMPA is superior to MPA and MP. For diagnostic
accuracy, mMPA and MPA have higher specificity and positive predictive value
but lower sensitivity and negative predictive value than MP and individual
testing. Included in this paper are applications to various simulations and an
application for HIV treatment monitoring.
