We used Stella software (v7.0.3, High Performance Systems, Hanover, NH) to develop deterministic transmission models for heterosexual transmission of HPV types 16 and 18. Because level of sexual activity and HPV prevalence are highly age-dependent, we divided the population into nine age categories, from age 12 to age 50. We further divided each age category into four subcategories based on level of sexual activity (Table 1). HPV prevalence among their pool of sex partners, infectivity per infected partner, HPV shedding duration, and HPV infection rates were estimated for each age and activity group to develop a natural history transmission model. Vaccine penetration and efficacy were added to evaluate the effect of potential vaccine programs.

In our analysis, persons of both sexes were either HPV infected or uninfected at the beginning of each time period. In each period, uninfected persons could remain uninfected or become infected, on the basis of infection rates by age category (Figure 1). Infection rates were determined by number of sex partners, HPV prevalence among pool of sex partners, and infectivity per infected partner. HPV prevalence among the pool of sex partners was a function of HPV prevalence by age and risk group, and by sexual mixing patterns (preference of partners in different age groups for partners in different sexual classes) between age groups and between high- and low-risk sexual activity groups (Table 1). Details regarding the transmission model can be found in the Appendix.

In a previous analysis (25), we modeled the overall progression of high-risk oncogenic HPV types to different stages of cervical dysplasia and cancer. In our current analysis, we adapted this model to evaluate the natural history and vaccination scenarios regarding HPV-16 and HPV-18. Estimates regarding Pap screening, lesion treatment, cancer progression and survival, costs, and utilities are based upon our previous analysis (25). Specific progression rate of HPV-16 and HPV-18 to different stages of cervical dysplasia and cancer were estimated from the literature (15,19,20,26,27).

To validate the model, we compared the incidence of cervical cancer cases and deaths predicted by the prevaccination natural history arm of our model with those reported in the Surveillance, Epidemiology, and End Results (SEER) registry (28). Our model’s annual rates of cervical cancer cases and deaths matched 2001 SEER estimates within 10%. The predicted age-specific prevalence of HPV infection in our natural history arm also has a shape and peak of similar magnitude to that reported in the literature (15–18).

Under our base-case scenario, vaccinated girls would experience a 61.8% overall reduction in acquiring cervical cancers over a lifetime. The analysis predicted, given the current U.S. population of 12-year-old girls (approximately 2.0 million), that the number of expected lifetime cases of cervical cancer related to HPV-16 or HPV-18 would drop from 9,147 to 422, a 95.4% reduction. This strategy would add an average of 6.1 quality-adjusted days of life per woman and have a cost-effectiveness ratio of $14,583 per quality-adjusted life-year (QALY) gained compared to the current environment (Table 2).

If both sexes were vaccinated with an HPV-16/18 vaccine, total cervical cancer cases in that cohort would drop by 63.9%, compared to the number of cases in the scenario before vaccination. The number of cancer cases related to HPV-16 or HPV-18 would decrease from a prevaccination 9,147 to 113, a 98.8% drop from the number in the prevaccination scenario. Expanding the vaccination program to men and boys would add an incremental 0.21 quality-adjusted days of life per woman at a cost-effectiveness ratio of $442,039/QALY compared to the female-only strategy (Table 2).

Figure 2A shows how varying the vaccine coverage of a female-only HPV-16/18 vaccination program affects the number of lifetime cervical cancer cases. As expected, as vaccine coverage increases, the number of cervical cancer cases decreases. However, based on scenarios that used our transmission model, the relationship is not linear. Because of the benefits of herd immunity, vaccinating even a relatively small portion of the target population leads to substantial decreases in disease prevalence and resulting negative sequelae relative to prevaccination rates. Figure 2A also illustrates the effect of vaccinating both sexes. A combined male-female program always results in lower levels of cohort cervical cancer cases than a female-only program. However, this difference is only large when levels of female vaccine penetration are low.

Figure 2B shows the cost-effectiveness of HPV-16/18 vaccination programs compared to the current environment as coverage varies. The cost-effectiveness of female-only vaccination is attractive at all ranges of vaccine penetration. At lower vaccine penetration levels, including male participants in the vaccination program also becomes cost-effective. For example, at 30% female vaccine penetration, including male participants is reasonably cost-effective at $40,865/QALY compared to vaccinating female participants only. Figure 2C and D show similar data for changes in vaccine efficacy.

Our analysis assumes that vaccination would focus on children 12 years of age. We considered alternative vaccination strategies that would focus on either infants or persons 18 years of age. Because most women are not sexually active until after age 12, focusing on infants or 12-year-old children leads to approximately the same decrease in lifetime cases of cervical cancer. However, delaying initial vaccination until age 18 leads to only a 54.7% decrease in the number of cancer cases in this cohort. If focusing on the older age group also leads to a decrease in vaccine penetration (60%), then program effectiveness drops further to a 50.9% decrease in lifetime cervical cancer cases in this cohort.

We also considered how the optimal vaccination age was affected if the efficacy of the vaccine waned. If the vaccine efficacy waned over 10 years and no booster was provided, a vaccination program that targeted 18-year-old women would dominate one which targeted 12-year-old girls. In this scenario the cost-effectiveness of also vaccinating 18-year-old men would be economically favorable, with a cost-effectiveness of $57,795/QALY compared to the cost-effectiveness of vaccinating women only. If, however, two booster shots were given at 5-year intervals to maintain the vaccine's efficacy, 12-year-old girls would return to being the optimal vaccination group, but the cost-effectiveness of vaccinating boys would increase to $388,368/QALY.

Under our base-case scenario with an HPV-16/18 vaccine, the first cohort of vaccinated 12-year-old girls would experience a 29.7% decrease in overall cervical cancer cases at a cost-effectiveness of $27,566/QALY, compared to their experience without vaccination. Vaccinating boys would cost $285,776/QALY compared with a female-only program to reduce cervical cancer cases an additional 4.7%. In time, however, lifetime cervical cancer cases would reach a steady-state of 62% of prevaccination level. Thus, even the first cohort would experience almost half of the achievable benefit of a long-term vaccination program. Table 3 displays the average reduction in lifetime cervical cancer risk for girls vaccinated at age 12 through a large-scale vaccination program, compared to the reduction in risk to women ages 24 and 30 who opt for catch-up vaccination once a vaccine becomes available.

Although an HPV-16/18 vaccine would not protect against all oncogenic HPV strains, we wanted to explore whether the vaccine could sufficiently reduce the prevalence of cervical cancer and precancerous lesions to allow for less frequent cervical cancer screening. Our base-case analysis assumes that 71% of women get Pap smears every 2 years (29). Figure 3 presents the cost-effectiveness of moving to more or less frequent screening intervals, in the presence of an established vaccine program.

We performed sensitivity analyses on a range of model variables. The female-only vaccination program remained economically attractive under a wide range of variable assumptions. However, the incremental benefit of vaccinating men and boys was sensitive to changes in key variables. Figure 4 shows one-way sensitivity analyses of the cost-effectiveness of incrementally vaccinating male participants compared to the cost-effectiveness of female-only vaccination.

In our analysis, both sexes are either HPV infected or uninfected at the beginning of each period. In each period, uninfected persons can remain uninfected or become infected, based on infection rates by age category. G_a,r,t,v=0 represents unvaccinated women (v = 0) of a given age (a), of a given sexual activity subgroup (r), in time period (t) who are not HPV infected. In the next time period, as these women move into the next age category (a+1), they can remain uninfected, assuming the status of G_{a+1,r,t+1,v=0}, or they can become infected, assuming the status of infected women of age (a+1) and sexual activity subgroup (r), F_{a+1,r,t+1,v=0}. The rate of HPV infection is a function of p_a,r, the number of partners per year for age group (a) and sexual activity group (r); i_a, the infectivity per infected partner for persons of age (a); and Q_a,r, the prevalence of HPV infection in the pool of male partners for women of this age and sexual activity subgroup. Overall prevalence of HPV infection in their specific pool of male partners (Q_a,r,), in turn, depends on the preference of women in this age group for male partners in younger (l_f,a), older (h_f,a), and the same (1–l_f,a–h_f,a) age group and the prevalence of HPV infection in these respective male groups. The resulting rate of HPV infection differs by age group and differs for women in different sexual activity subgroup within the different age groups. Rate of HPV regression, d_a, when active infection clears and at which time a woman is no longer infective, is also age dependent.

Women can enter the transmission model already having been vaccinated or can receive the vaccine at older ages, depending on vaccination scenario being evaluated. The rate of HPV infection for vaccinated women, G_a,r,t,v=1, is a function of p_a,r, the number of partners per year; i_a, the infectivity per infected partner for persons of age (a); Q_a,r, the prevalence of HPV infection in the pool of male partners for women of this age and sexual activity subgroup; and vaccine efficacy (e).

J_a,r,t,v represents men of a given age (a), of a given sexual activity subgroup (r), in time period (t), who are not HPV infected. K_a,r,t,v represents men of a given age (a), of a given sexual activity subgroup (r), in time period (t) who are HPV infected. Infection rates for men and the effect of a vaccine are determined in the same way as for women, though the values of variables differ between men and women of similar age groups (e.g., in most age categories, more men than women prefer partners in lower age groups).

During each period a new cohort of approximately 2 million male participants and 2 million female participants enters the model. This cohort is divided into vaccinated and unvaccinated persons. Vaccination rates for a given age cohort are 0%–100%, depending on which scenario is being evaluated. Vaccination rates can also vary by sex, and vaccination rates of persons the same age can differ according to sexual activity risk groups. This variation enables us to evaluate scenarios of differing vaccine penetration by risk category.

Vaccine efficacy (e) can vary from 0% to 100%. To capture the effect of alternative vaccines with different durations of effectiveness, we adjust the variable (e) for different age groups. For instance, to model a vaccination strategy for 12-year-old girls with a 90% effective vaccine that has a 10-year duration, the variable (e) would be set equal to 90% for ages 12–21. For ages 22 or older, efficacy can be set to equal 0%. To model a 10-year booster in the above scenario, the variable (e) can also be set equal to 90% for ages 22–31, to reflect the protection of the booster. In addition, gradually waning vaccine efficacy can be modeled by gradually decreasing variable (e) from 90% to 0% over a given number of age categories

Using the transmission model, we estimated the prevalence of HPV-16 and HPV-18 infection by age group, in the absence of a vaccine (Figure A1). For both HPV-16 and HPV-18, prevalence increases rapidly after sexual debut, peaking in women and men in their early 20s. Prevalence drops off for persons in their late 20s and early 30s, which corresponds to a drop in the number of new sex partners per year in these age groups. For both men and women overall (including all sexual activity categories), population prevalence of HPV-16 peaks at ≈5% and population prevalence of HPV-18 peaks at ≈2%, Prevalence decreases to <1% for both HPV types for persons >40 years old. The predicted age-specific prevalence of HPV infection in our natural history arm has a shape and peak of similar magnitude to that seen in the literature (40–43).

We evaluated various vaccination program scenarios to assess how different vaccination program options would affect HPV transmission and prevalence. We used the transmission model to estimate the incidence and prevalence of HPV-16 and HPV-18 by age group for both vaccinated and unvaccinated women under two main vaccination scenarios. First, we evaluated the effect of vaccinating only female participants. We then compared that to the effect of vaccinating both sexes. Results are presented in Figure A1 and A2.

In a previous analysis (44), we developed a probabilistic Markov decision model to estimate the progression of high-risk oncogenic HPV types to different stages of cervical dysplasia or cancer and to evaluate different female-only vaccine strategies. In our original modeling approach, we assumed that vaccinated women would have reduced HPV infection rates that equaled the estimated vaccine efficacy. Also, in the original model, unvaccinated women had no decrease in HPV infection rates, despite the presence of a widespread vaccination program. In truth, the effect of a vaccine on HPV infection rates for vaccinated women depends on both the vaccine efficacy and the overall impact of the vaccination program at reducing population prevalence of HPV in both men and women. Additionally, a vaccine program will reduce infection rates for unvaccinated women by a herd immunity benefit. Our modeling approach includes these factors.

In our approach, we use the transmission model described above to estimate the reduction in HPV infection rates for both vaccinated and unvaccinated women under a female-only vaccination strategy. For each age group, for vaccinated and unvaccinated women, these infection rates are incorporated into the Markov model, which then estimates disease progression, cervical cancer incidence, cervical cancer deaths and associated costs, and health utilities under a female-only vaccine program. In this way, we capture both the direct vaccine effect and the indirect benefit of herd immunity to both vaccinated and unvaccinated women for a female-only vaccine program.

Next, we used the transmission model to estimate the reduction in HPV infection rates for both vaccinated and unvaccinated women when both sexes are vaccinated. These scenario-specific infection rates for each age group and for both vaccinated and unvaccinated women are included in the Markov model, and the costs and health benefits are evaluated.