Published online Dec For permissions, please e-mail: Abstract The clustering of human papillomavirus HPV infections in some individuals is often interpreted as the result of common risk factors rather than biological interactions between different types of HPV. The intraindividual correlation between times-at-risk for all HPV infections is not generally considered in the analysis of epidemiologic studies. We used a deterministic transmission model to simulate cross-sectional and prospective epidemiologic studies measuring associations between 2 HPV types.
When we assumed no interactions, the model predicted that studies would estimate odds ratios and incidence rate ratios greater than 1 between HPV types even after complete adjustment for sexual behavior.
This correlation can be controlled in prospective studies by restricting analyses to susceptible individuals with an infected sexual partner. The bias in the measured associations was largest in low-sexual-activity populations, cross-sectional studies, and studies which evaluated infection with a first HPV type as the exposure. These results suggest that current epidemiologic evidence does not preclude the existence of competitive biological interactions between HPV types.
These observations have sparked inquiry into the causal effects a first STI might have on the probability that a second STI can establish an active infection upon contact with an infected sexual partner.
This causal effect on transmission would entail a biological interaction between the STIs. It is important to ascertain the existence of biological interactions from a public health perspective, because interventions against one STI could also affect the other STIs with which it interacts 13 — If previous infection with a first STI reduces the risk of becoming infected with other STIs competitive interaction , then interventions targeted against the first STI could increase the incidence of infections with other STIs due to the reduced competition.
For example, human papillomavirus HPV vaccination might increase the incidence of infection with nonvaccine HPV types through type replacement In practice, measures of association between STIs are biased estimates of their causal effects on each other's transmission.
It is largely recognized that because both the exposure the first STI and the outcome the second STI are sexually acquired, the effect estimate will be confounded by common risk factors 17 — Notably, sexual behaviors and networks which increase the risk of being infected with one STI also increase the risk of being infected with a second STI, so their incidence is expected to be associated.
To our knowledge, this issue has not been considered when analyzing STI associations. When individuals create and break off sexual partnerships, their at-risk status changes concurrently over time for all STIs. This issue is separate from sexual risk confounding, because adjustments for sexual behavior markers e. These markers do not control for the intraindividual correlation between the times an individual is at risk for different STIs due to partnership creation.
Eliminating the correlation requires restricting analyses to times when individuals are at risk of being infected with the outcome STI due to sexual contacts with infected partners. However, this restriction is not often feasible in studies of STIs.
Mathematical transmission-dynamic models can help us analyze results of epidemiologic studies by explicitly incorporating the dependence of outcomes inherent to STI dynamics.
They are thus valuable complements to traditional statistical analyses, which are often not adapted for dependent outcomes In this paper, we use HPV as an example with which to examine this bias. However, various cross-sectional and prospective studies have shown that HPV types cluster together 23 — 28 and that persons currently infected with one type have a higher risk of incident infection with another type, even after adjustment for sexual behaviors 9 — 12 , 26 — The remaining association is generally interpreted as residual confounding by sexual activity or immune responses, and the existence of competitive interactions and type replacement following HPV vaccination are generally deemed unlikely 26 — However, none of these analyses have considered the correlation between the times-at-risk for all HPV types.
Using a transmission-dynamic model of 2 HPV types, we aim to illustrate how the correlation between the times-at-risk for infection biases the estimation of causal effects between HPV types in cross-sectional and prospective studies even when we assume that they do not interact.
We identify which epidemiologic research designs minimize or eliminate this bias to estimate causal effects. We then generalize results to the situations of 1 STIs with different natural histories, 2 STIs in populations with different sexual behaviors, and 3 the assumption that competitive and facilitative interactions do exist. In this population, we simulated epidemiologic studies which measure the association between 2 HPV types.
If the measured association between HPV types in these studies did not match the underlying modeled effect of the first HPV type on the second, we considered the association to be a biased estimate of the biological interaction. Further details on model structure, parameters, and equations can be found in the Web Appendix available at http: Model structure The modeled population is heterosexual, open, and stable.
Age is not modeled. Individuals spend on average 40 years in the modeled population, representing their most sexually active years approximately ages 15—54 years.
Individuals are stratified into high and low sexual activity levels, which differ according to their rate of sexual partner acquisition. We model the duration of sexual partnerships between individuals and the rate of sex acts within partnerships. HPV type 1 or 2 is marked by the subscript i. We assumed that 1 infections with each HPV type are cleared independently 9 , 12 ; 2 individuals only acquire immunity once they clear an infection; 3 immunity is type-specific and wanes over time; 4 susceptible individuals can only be infected when they are in a sexual partnership with an infected partner; and 5 transmission probabilities of both HPV types are independent per sex act.
These independence assumptions were made so that in the base case, HPV types do not affect each other's natural history no interactions. However, the time periods during which individuals are at risk of getting HPV types 1 and 2 are correlated in the model, because they are not at risk for either type unless they are in a partnership with an infected person.