Sieve analysis using the number of infecting pathogens

Assessment of vaccine efficacy as a function of the similarity of the infecting pathogen to the vaccine is an important scientific goal. Characterization of pathogen strains for which vaccine efficacy is low can increase understanding of the vaccine's mechanism of action and offer targets for vaccine improvement. Traditional sieve analysis estimates differential vaccine efficacy using a single identifiable pathogen for each subject. The similarity between this single entity and the vaccine immunogen is quantified, for example, by exact match or number of mismatched amino acids. With new technology, we can now obtain the actual count of genetically distinct pathogens that infect an individual. Let F be the number of distinct features of a species of pathogen. We assume a log-linear model for the expected number of infecting pathogens with feature “f,” f = 1, … , F. The model can be used directly in studies with passive surveillance of infections where the count of each type of pathogen is recorded at the end of some interval, or active surveillance where the time of infection is known. For active surveillance, we additionally assume that a proportional intensity model applies to the time of potentially infectious exposures and derive product and weighted estimating equation (WEE) estimators for the regression parameters in the log-linear model. The WEE estimator explicitly allows for waning vaccine efficacy and time-varying distributions of pathogens. We give conditions where sieve parameters have a per-exposure interpretation under passive surveillance. We evaluate the methods by simulation and analyze a phase III trial of a malaria vaccine.