Many multivalent vaccines target only a subset of all pathogenic types. If vaccine and nonvaccine types compete, vaccination may lead to type replacement. The plausibility of type replacement has been assessed using the odds ratio (OR) of co-infections in cross-sectional prevalence data, with OR > 1 being interpreted as low risk of type replacement. The usefulness of the OR as a predictor for type replacement is debated, as it lacks a theoretical justification, and there is no framework explaining under which assumptions the OR predicts type replacement.Methods:
We investigate the values that the OR can take based on deterministic S usceptible- I infected- S usceptible and S usceptible- Infected- Recovered- S usceptible multitype transmission models. We consider different mechanisms of type interactions and explore parameter values ranging from synergistic to competitive interactions.Results:
We find that OR > 1 might mask competition because of confounding due to unobserved common risk factors and cross-immunity, as indicated by earlier studies. We prove mathematically that unobserved common risk factors lead to an elevation of the OR, and present an intuitive explanation why cross-immunity increases the OR. We find that OR < 1 is predictive for type replacement in the absence of immunity. With immunity, OR < 1 remains predictive under biologically reasonable assumptions of unidirectional interactions during infection, and an absence of immunity-induced synergism.Conclusions:
Using the OR in cross-sectional data to predict type replacement is justified, but is only unambiguous under strict assumptions. An accurate prediction of type replacement requires pathogen-specific knowledge on common risk factors and cross-immunity.