A revision of sexual mixing matrices in models of sexually transmitted infection

Two sexual mixing matrices previously used in models of sexually transmitted infections (STIs) are intended to calculate the probability of sexual interaction between age groups and sexual behaviour subgroups. When these matrices are used to specify multiple criteria for how people select sexual partners (such as age group and sexual behaviour class), their conditional probability structure means that they have in practice been prone to misuse. We constructed revised mixing matrices that incorporate a corrected conditional probability structure and then used one of them to examine the effect of this revision on population modelling of STIs. Using a dynamic model of human papillomavirus (HPV) transmission as an example, we examined changes to estimates of HPV prevalence and the relative reduction in age-standardised HPV incidence after the commencement of publicly funded HPV vaccination in Australia. When all other model specifications were left unchanged, the revised mixing matrix initially led to estimates of age-specific oncogenic HPV prevalence that were up to 11% higher than our previous models at certain ages. After re-calibrating the model by modifying unobservable parameters characterising HPV natural history, the revised mixing matrix yielded similar estimates to our previous models, predicting that vaccination would lead to relative HPV incidence reductions of 43% and 85% by 2010 and 2050, respectively, compared with 43% and 86% using the unrevised mixing matrix formulation. Our revised mixing matrix offers a rigorous alternative to commonly used mixing matrices, which can be used to reliably and explicitly accommodate conditional probabilities, with appropriate re-calibration of unobservable model parameters.