Estimation of viral infection and replication in cells by using convolution models

In some assays, a diluted suspension of infected cells is plated onto multiple wells. In each well the number of genome copies of virus, "Y", is recorded, but interest focuses on the number of infected cells, "X", and the number of genome copies in the infected cells, "W"₁,…,"W"_"X". The statistical problem is to recover the distribution or at least moments of "X" and "W" on the basis of the convolution "Y". We evaluate various parametric statistical models for this 'mixture'- type problem and settle on a flexible robust approach where "X" follows a two-component Poisson mixture model and "W" is a shifted negative binomial distribution. Data analysis and simulations reveal that the means and occasionally variances of "X" and "W" can be reliably captured by the model proposed. We also identify the importance of selecting an appropriate dilution for a reliable assay. Copyright Journal compilation (c) 2010 Royal Statistical Society. No claim to original US Government works.