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. 2016 Dec 15;184(12):873-883.
doi: 10.1093/aje/kww152. Epub 2016 Dec 7.

Bias Due to Correlation Between Times-at-Risk for Infection in Epidemiologic Studies Measuring Biological Interactions Between Sexually Transmitted Infections: A Case Study Using Human Papillomavirus Type Interactions

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Bias Due to Correlation Between Times-at-Risk for Infection in Epidemiologic Studies Measuring Biological Interactions Between Sexually Transmitted Infections: A Case Study Using Human Papillomavirus Type Interactions

Talía Malagón et al. Am J Epidemiol. .
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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. We demonstrated that this residual association is due to correlation between the times-at-risk for different HPV types, where individuals become concurrently at risk for all of their partners' HPV types when they enter a partnership and are not at risk when they are single. 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.

Keywords: bias (epidemiology); coinfection; cross-protection; microbial interactions; papillomavirus infections; sexually transmitted diseases; time factors; viral interference.

Figures

Figure 1.
Figure 1.
Different combinations of susceptible (S), infected (I), and recovered/immune (R) statuses for 2 types of human papillomavirus (HPV), designated type 1 and type 2 (indicated by a subscript), with the first letter corresponding to HPV type 1 health status and the second corresponding to HPV type 2 health status. The boxes show mutually exclusive health states, with possible transitions indicated by arrows. Boxes in the left-hand column represent HPV type 1-susceptible individuals; boxes in the middle column represent HPV type 1-infected individuals; and boxes in the right-hand column represent HPV type 1-immune individuals. Boxes in the first row represent HPV type 2-susceptible individuals; boxes in the second row represent HPV type 2-infected individuals; and boxes in the third row represent HPV type 2-immune individuals. Dashed-dotted arrows correspond to population entry and exit points, solid black arrows to HPV type 1 natural history transitions, dashed arrows to HPV type 2 natural history transitions, and the white outlined arrow to natural history transitions affecting both types of HPV. See the Web Appendix for differential equations and parameters for transition rates between health states.
Figure 2.
Figure 2.
Measures of association between 2 types of human papillomavirus (HPV), designated type 1 and type 2, in the absence of interactions. The prevalence odds ratio (POR) (black columns) compares odds of a prevalent HPV type 2 infection in HPV type 1-infected versus -uninfected individuals. The incidence rate ratio (IRR) by infection status (striped columns) compares the HPV type 2 incidence rate in HPV type 1-infected versus -uninfected individuals. The IRR by immunity status (white columns) compares the HPV type 2 incidence rate in HPV type 1-immune versus -nonimmune individuals. The POR and IRRs are calculated in the full population including both single and partnered individuals (“Overall Crude”), in the full population with adjustment for sexual activity level (“Overall Adjusted”), in persons of each sexual activity level (“Low Sexual Activity” and “High Sexual Activity”), only among persons in current sexual partnerships (“Partnered”), and only among persons in current sexual partnerships with HPV type 2-infected partners (“At-Risk Partnered”). All associations (except for the overall crude association) were adjusted for sexual activity level. The y-axis is on a base-2 log scale.
Figure 3.
Figure 3.
Adjusted measures of association between 2 types of human papillomavirus (HPV), designated type 1 and type 2, under different combinations of infection duration (in years) and transmission probabilities (per sex act with an infected individual). No interactions between HPV types are assumed. A) Prevalence odds ratio (POR); compares HPV type 2 infection prevalence odds in HPV type 1-infected versus -uninfected individuals. B) Incidence rate ratio (IRR) by infection status; compares the HPV type 2 incidence rate in HPV type 1-infected versus -uninfected individuals. C) IRR by immunity status; compares the HPV type 2 incidence rate in HPV type 1-immune versus -nonimmune individuals. All PORs and IRRs are measured in the overall population and adjusted for sexual activity level using Mantel-Haenszel estimators. White areas represent combinations of transmission probabilities and infection durations for which sustained transmission becomes impossible and the infections are eliminated from the model population. The black circle represents the base-case scenario.
Figure 4.
Figure 4.
Sexual-activity-level–stratified measures of association between human papillomavirus (HPV) types 1 and 2 under different combinations of the partner change rate (per year) in the low sexual activity level and the degree of assortativity between sexual activity levels. A) Prevalence odds ratio (POR) in the high sexual activity level. B) Incidence rate ratio (IRR) by infection status in the high sexual activity level. C) IRR by immunity status in the high sexual activity level. D) POR in the low sexual activity level. E) IRR by infection status in the low sexual activity level. F) IRR by immunity status in the low sexual activity level. No interactions between HPV types are assumed. Black areas indicate values greater than or equal to 16 for the measured associations. The degree of assortativity corresponds to the proportion of sexual contacts made exclusively with members of the same sexual activity level (0 = proportionate, 1 = completely assortative). The black circle represents the base-case scenario.
Figure 5.
Figure 5.
Estimated adjusted measures of association between 2 types of human papillomavirus (HPV), type 1 and type 2, when interactions are modeled. The y-axis corresponds to associations measured in simulated epidemiologic studies. The x-axis represents the actual modeled underlying interactions. A) Prevalence odds ratio (POR) for HPV type 2 infection in HPV type 1-infected versus -uninfected individuals according to interaction effects caused by current infection (χ2). B) POR for HPV type 2 infection in HPV type 1-infected versus -uninfected individuals according to interaction effects caused by immunity (φ2). C) Incidence rate ratio (IRR) for HPV type 2 infection in HPV type 1-infected versus -uninfected individuals according to interaction effects caused by current infection (χ2). D) IRR for HPV type 2 infection in HPV type 1-infected versus -uninfected individuals according to interaction effects caused by immunity (φ2). E) IRR for HPV type 2 infection in HPV type 1-immune versus -nonimmune individuals according to interaction effects caused by current infection (χ2). F) IRR for HPV type 2 infection in HPV type 1-immune versus -nonimmune individuals according to interaction effects caused by immunity (φ2). Gray points correspond to associations measured in the overall population, adjusted for sexual activity level. Black points correspond to associations measured in analyses restricted to at-risk partnered individuals (persons in partnerships with HPV type 2-infected partners). Left-hand panels (A, C, and E) show the influence of interaction effect χ2—the relative probability of HPV type 2 infection per sex act with an infected partner among persons who are HPV type 1-infected compared with persons who are HPV type 1-susceptible. Right-hand panels (B, D, and F) show the influence of interaction effect φ2—the relative probability of HPV type 2 infection per sex act with an infected partner among persons who are HPV type 1-immune compared with persons who are HPV type 1-susceptible. Values to the left of 1.0000 on the x-axis correspond to modeled competitive interactions, while values to the right of 1.0000 correspond to modeled facilitative interactions. The dotted gray line represents the theoretical line of equality, where epidemiologic measures of association would validly estimate the actual modeled interactions. Both axes use a base-2 log scale.

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