This article develops methods for estimating treatment effects in mixed-effects models using outcome data gathered from serial dilution assays. Our application allows us to estimate the viral burden of HIV infection before and after antiviral treatment from cell dilution assays. This assay is designed to determine the infectious units per patient peripheral blood mononuclear cell (PBMC). The infectious unit is the amount of virus required to produce detectable HIV infection in PBMC's from healthy, uninfected donors. At each dilution level of the patient cells, one observes whether or not it was possible for the virus from these cells to infect donor cells. Thus the assay result for each subject consists of a series of repeated binary outcomes. We propose an analytic approach in which patient-specific titers (measures of viral burden) are modeled as random effects from an unknown distribution, and treatment effects are modeled as fixed. This approach makes use of all assay results, even if many assays fail to reach endpoint (i.e., they turn negative at the highest dilution level) and the assay design (dilution scheme) changes over time.