Estimating the Natural History of Cervical Carcinogenesis Using Simulation Models: A CISNET Comparative Analysis

Background: The natural history of human papillomavirus (HPV)-induced cervical cancer (CC) is not directly observable, yet the age of HPV acquisition and duration of preclinical disease (dwell time) inﬂuences the effectiveness of alternative preventive policies. We performed a Cancer Intervention and Surveillance Modeling Network (CISNET) comparative modeling analysis to characterize the age of acquisition of cancer-causing HPV infections and implied dwell times for distinct phases of cervical carcinogenesis. Methods: Using four CISNET-cervical models with varying underlying structures but ﬁt to common US epidemiological data, we estimated the age of acquisition of causal HPV infections and dwell times associated with three phases of cancer development: HPV, high-grade precancer, and cancer sojourn time. We stratiﬁed these estimates by HPV genotype under both natural history and CC screening scenarios, because screening prevents cancer development that affects the mix of detected cancers. Results: The median time from HPV acquisition to cancer detection ranged from 17.5 to 26.0years across the four models. Three models projected that 50% of unscreened women acquired their causal HPV infection between ages 19 and 23years, whereas one model projected these infections occurred later (age 34years). In the context of imperfect compliance with US screening guidelines, the median age of causal infection was 4.4–15.9years

the health benefits and economic consequences of alternative CC prevention approaches. Although numerous CC models have been developed worldwide (5), direct comparisons between model structures and projections are limited, particularly comparisons that have standardized the epidemiological setting and common inputs. Because model-based analyses are increasingly being used for US policy guidance (6) and model complexity increases, a more comprehensive understanding of model structures and assumptions is imperative to improve model transparency and provide decision makers with confidence in model-based results (7). Model comparisons can also generate insights on unobservable epidemiological phases of the carcinogenic process.
The CC working group of the Cancer Intervention and Surveillance Modeling Network (CISNET-cervical) comprises four independently developed microsimulation models of HPV infection and cervical carcinogenesis and one model of HPV-HIV coinfection. These models can be used to conduct standardized, comparative analyses to enhance model transparency and help guide public health research and priorities (https://cisnet. cancer.gov/). We leveraged multiple models to gain insights on the natural history of CC and the impact of screening interventions using four independent CC models. In this analysis, we compared the underlying natural history of CC by estimating the dwell times for preclinical phases of cervical disease and characterizing the age of acquisition of causal HPV infections among women who develop clinical CC. Second, we describe how CC screening may, by selection, influence the timing of these key events. ) were used to project outcomes for a hypothetical cohort of individual women. All models applied common inputs from the US population and were fit to match common, standardized observed data in the United States but varied in their underlying structure and assumptions of the carcinogenic process (Table 1;  Supplementary Table 1, available online). For women diagnosed with CC in the absence of screening or vaccination, the models estimated the age of acquisition of the causal HPV infection and dwell times associated with phases of cancer development, including "HPV/CIN1 dwell time," defined as the time from acquisition of an HPV infection to development of a high-grade precancer (cervical intraepithelial neoplasia grade 2 [CIN2] and/or grade 3 [CIN3]); "high-grade precancer dwell time," defined as the time from development of a high-grade precancer (CIN2 and/or CIN3) to asymptomatic cancer development; cancer "sojourn time," defined as the time from asymptomatic cancer development to clinical detection; and "total dwell time," defined as the time from HPV acquisition to cancer detection ( Figure 1). Conditioned on developing cancer, we stratified these estimates by high-risk HPV, HPV16, and non-HPV16 genotypes. For each model, we calculated the median age of causal HPV infection and dwell times but also reported the interquartile ranges (IQR) and means. Because dwell times and the age of causal infections are likely altered in the presence and intensity of screening (eg, because of screening's preferential detection of precancers with longer dwell time during screening ages [ie, ages 21-65 years]) and to facilitate comparability with existing studies, we also projected these estimates in the context of imperfect compliance to US screening guidelines and full compliance to US screening guidelines. Screening scenarios involved triennial cytology-based screening with reflex HPV testing for women with atypical cells of undetermined significance and direct referral to diagnostic colposcopy for women with low-grade cytology results or worse.

Microsimulation Models
Each of the four CISNET-cervical models simulates the underlying natural history of HPV-induced CC ( Figure 1) but differs structurally with respect to the type and number of health states, HPV genotype categorizations, cycle length, and data sources used to parameterize the baseline model before model fitting to the US setting (Table 1).
Brief model descriptions summary of key differences are available in the Supplementary Methods (available online), and standardized profiles of each model's structure and underlying model parameters and assumptions, with additional references, are available at http://cisnet.cancer.gov/profiles/.

Dwell Times
In the absence of primary (ie, HPV vaccination) or secondary (ie, screening) prevention, there were important similarities and differences among the natural history models with respect to the duration of preclinical disease and their variation by HPV genotype (Figure 2, left panels). The total median dwell time from acquisition of a high-risk HPV infection to cancer detection was shortest for MISCAN-Cervix (17.5 years, IQR ¼ 12.  Table 3, available online). When we stratified by HPV genotype, the Harvard model projected a shorter median total dwell time for HPV16-related cancers compared with non-HPV16-related cancers (ie, 22.0 vs 33.7 years), whereas Policy1-Cervix and UMN-HPV CA projected total median dwell times that were 2-6 years longer for HPV16-related cancers compared with non-HPV16-related cancers. MISCAN-Cervix did not project differences in median dwell times for HPV16-related vs non-HPV16-related cancers. For all models, the mean dwell times were generally longer than the median dwell times (19.8-28.8 years), but the overall trends across models and HPV genotypes remained consistent (Supplementary Table 3, available online). When we stratified dwell times by preclinical phases, we found that the median dwell time of HPV and CIN1 for any high-risk HPV infections ranged from 2.2 years (MISCAN-Cervix) to 8.0 years (Harvard) ( Figure 2C). For high-grade precancers, the median dwell times for any high-risk HPV infections were the shortest for MISCAN-Cervix (8.  Table 3 available online). When we stratified by HPV genotype, the Harvard model projected a median high-grade precancer dwell time that was 4.4 years shorter for HPV16-related precancers compared with cancers related to non-HPV16 infections (ie, HPV16-related lesions progressed more quickly). Conversely, both Policy1-Cervix and UMN-HPV CA projected median dwell times that were 4 years longer for HPV16-related high-grade precancers compared with non-HPV16-related precancers. All four models projected comparable median cancer sojourn times, ranging from 2.3 to 5.3 years ( Figure 2G).
In the context of cytology-based screening, total median dwell times were shorter in all models, and there was less variation across the four models (Figure 2 Table 5, available online). Mean dwell time for all models was longer than median dwell times, reflecting a right-skewed distribution across all models (Supplementary Tables 4 and 5, available online).

Cumulative Incidence of Causal HPV Infections
Three models projected that 50% of the women diagnosed with cancer acquired their causal high-risk HPV infection between  Figure 3A). The same three models projected that 75% of causal HPV infections occurred before age 35 years, whereas MISCAN-Cervix projected that 75% of causal HPV infections occurred 17 years later (ie, by age 52 years). When we stratified by HPV genotype, all four models projected that causal HPV16 infections occurred between 0.1 and 6.0 years earlier compared with non-HPV16 infections (Figure 3, B and C). In the context of triennial cytology-based screening assuming imperfect compliance with US guidelines, the median age of the causal infection occurred between 4.4 years (Harvard) and 15.9 years (MISCAN-Cervix) later compared with the model projections in the absence of a screening program (Figure 4). Screening reduced the absolute risk of cancer between 60% and 80% in all models and delayed the median age of acquiring the causal high-risk infection associated with the remaining cancers to ages 25

Discussion
Although all four of the CISNET-cervical natural history models are generally consistent with observed empirical data in the United States, this comparative analysis highlights important similarities and differences in the duration of preclinical disease that is targeted by screening, the inferred age of acquiring cancer-causing HPV infections targeted by vaccines, the role of HPV genotypes, and the potential impact of screening on these outcomes. To our knowledge, this is the first such comparative analysis. Due to ethical reasons and feasibility constraints of empirical studies (eg, observation period, treatment of highgrade lesions), we are unlikely to ever have direct observations of the acquisition age of the causal infection or dwell times among women who progress to CC. Consistent with the well-established understanding of cervical carcinogenesis (12), all four models projected that the natural history from acquisition of an HPV infection to clinical cancer generally required 18-26 years, although MISCAN-Cervix had a shorter median total dwell time compared with the other models. The differences in total dwell time were primarily driven by the length of time spent with HPV and CIN1, followed by length of time with a high-grade lesion. For the Harvard model, transition probabilities following acquisition of HPV are a function of duration of infection or lesion, not age, based on longitudinal data that suggests that viral persistence is a function of duration of the infection or lesion, irrespective of a woman's age (13)(14)(15). This assumption contributed to a longer HPV and CIN1 dwell time among women who developed cancer compared with the other models, an outcome for which data are not available. In contrast, in two models (Policy1-Cervix and UMN-HPV CA), progression (regression) probabilities increase (decrease) with age, consistent with the literature (16)(17)(18)(19)(20); finally, in MISCAN-Cervix, progression potential but not dwell time is modified by age. Age may act at least in part as a proxy for duration; therefore, age-based transitions could potentially overestimate the oncogenic potential for infections acquired later in life, resulting in a shorter dwell time and an overestimation of the age of causal infection (and overestimation of the impact of vaccination at older ages). The magnitude and impact of these structural differences may become more apparent as we begin to evaluate HPV vaccination policies or as we consider more nuanced screening strategies. For example, in all four models, there would generally be at least two full screening rounds (assuming a 3-year screening interval) to detect a CIN2 or CIN3 lesion before cancer development. In contrast, when evaluating extended primary HPV-based screening intervals (eg, 5 years), MISCAN-Cervix, which had the shortest median highgrade precancer dwell time (8.2 years), would be expected to favor strategies with shorter intervals compared with other models.
There is considerable variability in the several efforts to estimate high-grade precancer dwell times in different settings. Vink et al. (21) projected a median dwell time of 23.5 years, which is longer than the median high-grade precancer dwell times projected by the CISNET-cervical models, under either assumption of natural history or screening. Several additional studies demonstrate similar variability, reporting mean highgrade dwell times ranging between 11.8 and 24.3 years (22)(23)(24)(25). The mean natural history high-grade precancer dwell times reported across the CISNET-cervical models varied from 11 to 20 years; however, under assumptions of imperfect compliance to US cytology-based screening, the CISNET models projected mean high-grade precancer dwell times that were substantially shorter and more consistent, ranging between 7 and 12 years. However, there are complex interactions with the specifics of screening being conducted (eg, test, interval, age range, compliance) that make comparisons difficult between the aforementioned studies and our model projections.
We found that in the absence of screening, the projected median age of acquisition of the causal HPV infection was between ages 19 and 23 years for three models but was much later (age 34 years) for MISCAN-Cervix. The age of causal infection is a function of 1) the age at which women develop clinical cancer, and 2) the length of time required to develop clinical cancer (ie, total dwell time). Because the age distribution of the background cancer incidence in all models is similar, the differences and similarities in median age of causal infection stem from total dwell time. In particular, the later age of causal infection in MISCAN-Cervix is explained by shorter dwell time (described above), and the total median dwell time in the other models is similar. Under assumptions of imperfect compliance with screening, the relatively small number of remaining cancers compared with no screening occur among women: after age 65 years (screening end age), with shorter dwell times (cancer developed between screening intervals), with a false negative screen(s), or did not attend screening. Both the first and second reasons, by selection, are expected to result in a later age of infection. Indeed, all four models projected that the causal infection among the cancers occurring because of these underlying causes was delayed. These findings have important implications for prevention policies in the United States and internationally. For example, the proportion of vaccine-preventable cancers decreases with age, and therefore the added value of HPV vaccination policies that extend to mid-adult individuals diminishes [eg, HPV-FASTER (26) or US Advisory Committee on Immunization Practices (27)] in all of the models but is less pronounced in MISCAN-Cervix. Even though the median age of the causal infection is delayed with screening, vaccinating mid-adult women has been found to be either inefficient or associated with very high cost-effectiveness ratios in a recent comparative modeling analysis (27).
In the context of screening, HPV16 infections, which are responsible for only 20% of HPV infections but more than 50% of CCs, are considered the most carcinogenic HPV genotype because these infections are less likely to clear and more likely to progress to precancer and cancer (12). HPV16-related cancers contribute to a larger proportion of cancers that develop among younger women (before age 50 years) compared with cancers that occur after age 50 years (10,28). A study by Wheeler et al. (29) also supports an earlier age of occurrence for HPV16positive cancers compared with non-HPV16 cancers, although type attribution studies for cancer can be subject to biases (30). Conditioned on developing cancer, the Harvard model projected shorter median HPV and CIN1, high-grade precancer, and total dwell times for cancers related to HPV16 infections compared with non-HPV16 infections, whereas the Policy1-Cervix and UMN-HPV CA models projected longer total dwell times for HPV16 infections. A study by Wentzensen et al. (31) that evaluated patients with Loop electrosurgical excision procedure confirmed CIN2 or CIN3 cases to estimate the time from sexual activity onset to development of CIN2 or CIN3 found that HPV16-related CIN2 and CIN3s grew more rapidly than lesions related to other HPV genotypes, with a progression time that was on average 30% shorter for HPV16-related CIN3s. However, these estimates were not isolated to precancers that ultimately progressed to cancer. In contrast, the statistical model by Vink et al. (21) compared dwell times between HPV16-and non-HPV16-related lesions and did not find differences in the median high-grade lesion dwell times by HPV genotype, though that study did find a larger proportion of HPV16 CIN2 or CIN3s that progressed within the first 10 years. However, higher probability to progress does not rule out equal median dwell time. Observable information on the genotype specificity is fraught with complex interactions between age effects of HPV16, the differential accuracy of screening in detecting HPV16-related lesions, and the impact of screening on cancer prevention. The impact of different genotype-specific model assumptions will be relatively more important for screening strategies that involve genotyping for HPV16 and HPV18 infections or for screening among women vaccinated against HPV16 and HPV18 infections. Analyses from the Harvard model would be expected to differentially favor more intensive screening strategies for HPV16 infections compared with the Policy-Cervix and UMN-HPV CA models.
The differences by HPV genotype may in part stem from two of the models assuming age-specific transition probabilities, whereas the Harvard model assumes transitions that are duration based. The age-specific transition models that capture non-HPV16 infections occurring at older ages compared with HPV16 infections will necessarily have faster transitions (and shorter dwell times) associated with non-HPV16 infections because they occur at older ages and face increasing probabilities of progression. In contrast, the Harvard model transitions are a function of time and assume HPV16 infections are more likely to persist, and therefore progress, irrespective of age.
There are several notable limitations to this study. First, we report results from only four models, but there may be alternative plausible model structures that could fit the observed empirical data. Our imperfect screening compliance scenario was not intended to mimic current practice, and direct comparison with empirical data requires more refined model assumptions; however, simulating screening provides projections for the impact of screening on the age of causal infection. Generalizing these findings to other populations may be limited in that they are based on US patterns of HPV acquisition, benign hysterectomy utilization, and background mortality, all of which can affect age patterns in CC.
Ongoing analyses performed by the CISNET-cervical working group involve reevaluation of CC strategies outlined by the US Preventive Services Task Force (2). Despite structural differences in the natural history of the models reported in this study, preliminary analyses evaluating US Preventive Services Task Force strategies indicate similar policy findings across the models (32), strengthening the validity of policy conclusions. Using multiple models will serve as an important approach to understanding the drivers of potential model disagreements in identifying optimal cancer control policies. In addition, using multiple, independently developed models for policy analyses is the most robust approach to undertake sensitivity analysis on underlying model structure and on the "deep" unobservable model parameters, in line with good modeling practice (7).
This comparative analysis highlights important similarities and differences, in part because of evidence gaps, among four validated CISNET CC natural history models. Our findings elucidate important drivers of HPV prevention and CC screening policies and emphasize the value of comparative modeling when evaluating optimal public health policies.