Maximum likelihood estimation from replicate limiting dilution assays from a binomial markov chain model

Abstract

The limiting dilution assay is often used to estimate the concentration of a certain kind of cell or the titer of a virus in a sample. Balch et al. (1994) exploited a Markov Chain model of the limiting dilution assay to develop a maximum likelihood estimate based on the extinction time. We extend these results to address: 1) a finite number of assay wells, 2) optional discard of material from the last assay well, and 3) maximum likelihood for multiple assays. The results on multiple assays suggest that substantial replication is needed (n ≥5) before assay results become useful.

Keywords:

• extinction time
• marginal maximum likelihood