A mixed model for repeated dilution assays

We propose a generalized linear mixed model to estimate and test marginal effects on titers repeatedly measured by serial dilution assays. The link is log-log and the titer is assumed to follow a gamma distribution. The parameters are estimated by generalized estimating equations. The marginal effects are tested by means of Wald and score tests, using the robust estimator of the variance. This approach avoids the problems arising from assays leading to nonestimable individual titers. Simulations were used to compare the Wald and score tests to Wilcoxon and Student t-tests. This method is applied to the comparison of the antiviral efficiency of three treatments against HIV.