Marginal and mixed-effects models in the analysis of human papillomavirus natural history data

Human papillomavirus (HPV) natural history has several characteristics that, at least from a statistical perspective, are not often encountered elsewhere in infectious disease and cancer research. There are, for example, multiple HPV types, and infection by each HPV type may be considered separate events. Although concurrent infections are common, the prevalence, incidence, and duration/persistence of each individual HPV can be separately measured. However, repeated measures involving the same subject tend to be correlated. The probability of detecting any given HPV type, for example, is greater among individuals who are currently positive for at least one other HPV type. Serial testing for HPV over time represents a second form of repeated measures. Statistical inferences that fail to take these correlations into account would be invalid. However, methods that do not use all the data would be inefficient. Marginal and mixed-effects models can address these issues but are not frequently used in HPV research. The current study provides an overview of these methods and then uses HPV data from a cohort of HIV-positive women to illustrate how they may be applied, and compare their results. The findings show the greater efficiency of these models compared with standard logistic regression and Cox models. Because mixed-effects models estimate subject-specific associations, they sometimes gave much higher effect estimates than marginal models, which estimate population-averaged associations. Overall, the results show that marginal and mixed-effects models are efficient for studying HPV natural history, but also highlight the importance of understanding how these models differ.