Mathematical Model for the Natural History of Human PapillomavirusInfection and Cervical Carcinogenesis
Evan R. Myers,1^ Douglas C. McCrory,2^ Kavita Nanda,112 Lori Bastian,2-* and David B. Matchar2-4
The authors constructed a Markov model as part of a systematic review of cervical cytology conducted at theDuke University Evidence-based Practice Center (Durham, North Carolina) between October 1997 andSeptember 1998. The model incorporated states for human papillomavirus infection (HPV), low- and high-gradesquamous intraepithelial lesions, and cervical cancer stages t—IV to simulate the natural history of HPV infectionin a cohort of women from ages 15 to 85 years. The age-specific incidence rate of HPV, and regression andprogression rates of HPV and squamous intraepithelial lesions, were obtained from the literature. The effects ofvarying natural history parameters on cervical cancer incidence were evaluated by using sensitivity analysis. Thebase-case model resulted in a lifetime cervical cancer risk of 3.67% and a lifetime cervical cancer mortality riskof 1.26%, with a peak incidence of 81/100,000 at age 50 years. Age-specific distributions of precursors weresimilar to reported data. Lifetime risk of cancer was most sensitive to the incidence of HPV and the probabilityof rapid HPV progression to high-grade lesions (two- to threefold variations in risk). The model approximates theage-specific incidence of cervical cancer and provides a tool for evaluating the natural history of HPV infectionand cervical cancer carcinogenesis as well as the effectiveness and cost-effectiveness of primary andsecondary prevention strategies. Am J Epidemiol 2000; 151:1158-71.
cervical intraepithelial neoplasia; cervix neoplasms; models, theoretical; papillomavirus, human
Carcinoma of the cervix is one of the most commonmalignancies of women in many parts of the world.Secondary prevention by using cervical smears todetect preinvasive and early invasive disease has led tosignificant reductions in both incidence and mortalityin many countries (1). In the United States, both inci-dence and mortality have declined steadily;Surveillance, Epidemiology, and End Results (SEER)registry data show a 43 percent decrease in incidenceand a 45.9 percent decrease in mortality from 1973 to1995 (2). Such reductions have not been observed incountries in which cytologic screening is not widelyavailable (3).
Received for publication April 27,1999, and accepted for publica-tion August 20, 1999.
Abbreviations: CIN, cervical intraepithelial neoplasia; HPV, humanpapillomavirus; SEER, Surveillance, Epidemiology, and End Results(Program); SIL, squamous intraepithelial lesion.
1 Department of Obstetrics and Gynecology, Duke UniversityMedical Center, Durham, NC.
2 Evidence-based Practice Center, Center for Clinical HealthPolicy Research, Duke University Medical Center, Durham, NC.
3 Division of General Internal Medicine, Department of Medicine,Duke University Medical Center, Durham, NC.
4 Durtiam Veteran's Affairs Medical Center, Durham, NC.Reprint requests to Dr. Evan R. Myers, DUMC 3279, Department
of Obstetrics and Gynecology, Duke University Medical Center,Durtiam, NC 27710 (e-mail: myersO08®mc.duke.edu).
Although there have been no randomized trials ofthe effectiveness of cervical cytologic screening inpreventing mortality from cervical cancer, there iswide consensus based on results of historical seriesand case-control studies that screening does result insignificant decreases in incidence and mortality (4).However, considerable controversy remains about theoptimal frequency for such testing, the potential role ofadjunctive technologies for improving the sensitivityof screening, and the appropriate management of low-grade lesions that may be preinvasive. In addition,although there is general agreement on the broad out-lines of the natural history of cervical cancer (5, 6),uncertainty exists about the specifics of many of theelements that contribute to natural history. Theseissues have been approached primarily with modeling(7-14).
Comprehensive simulation models enable integra-tion of evidence from a wide variety of sources to eval-uate natural history as well as prevention and treatmentstrategies, and they have been used to evaluate strate-gies for preventing stroke (15). As part of a compre-hensive review of the effectiveness of both conven-tional cervical cytologic screening and new adjunctivetechnologies (16) performed at the Duke UniversityCenter for Clinical Health Policy Research (Durham,North Carolina), we took a similar approach, using
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HPV and Cervical Cancer Model 1159
simulation modeling to integrate available evidence onstrategies for preventing cervical cancer. This review,funded by the US Agency for Health Care Policy andResearch as part of its Evidence-based PracticeCenters program (a group of 12 sites in the UnitedStates and Canada that conduct systematic reviews anddata synthesis on topics designated by the agency),included a meta-analysis of studies on the sensitivityand specificity of the conventional cervical smear, ananalysis of costs associated with screening and treat-ment for cervical cancer and preinvasive lesions in theUnited States, and a cost-effectiveness analysis ofscreening strategies to prevent cervical cancer. In thispaper, we present a model of the natural history of cer-vical cancer that builds on both the work of previousauthors and recent epidemiologic evidence to predictthe age-specific incidence of cervical cancer inunscreened populations and can be used to assess thepotential impact of preventive strategies.
MATERIALS AND METHODS
We constructed a 19-state Markov model (17) byusing DATA 3.0 software (TreeAge Software,Williamstown, Massachusetts). In a Markov model, theconditional distribution of the outcomes given an expo-sure status depends on prior outcome observationsonly. Our model follows a simulated cohort of womenfrom ages 15 through 85 years. The probability of mov-ing from one state to another (e.g., from normal tohuman papillomavirus (HPV) infected) during a givenMarkov cycle (e.g., a 1-year time period) is determinedby the modeler; typically, these probabilities are stateand often cycle specific. States and allowed transitionsare shown in table 1 and figure 1. The model isdescribed in detail in the final evidence report preparedby Duke University (16), and copies of the softwareprogram are available from the authors on request.Because the model generates probabilities, the cohortcan be any size; for a person, the model generates life-time probabilities of being in a given health state.Acquisition of HPV is based on age-specific incidencerates. Regression and progression between the variousstates is based on published data. Because the topic ofour review was suggested to the Agency for HealthCare Policy and Research by the American College ofObstetricians and Gynecologists (Washington, DC), weused US data as much as possible for our probabilityand prevalence estimates.
Assumptions of the model
To produce a model with a manageable number ofpossible outcomes, some simplifying assumptionswere necessary. The following list outlines the main
underlying assumptions of the model and our rationalefor making them.
1. The model assumes that all cases of cervical can-cer begin with HPV infection. We incorporatedHPV status into the model for two reasons. First,although a small percentage of cervical cancersdo not contain detectable HPV DNA, even withsensitive assays there is consensus that HPVinfection is die causative agent for the vast major-ity of cervical cancers (5, 6, 18, 19). Second, cer-tain HPV types clearly are more likely to progressto cancer than others, and identification of thesetypes in cervical cells may help determine optimaldiagnostic and treatment strategies for patientswim abnormal cervical smears (20). Estimates ofthe age-specific incidence of HPV infection werederived from published cohort studies. For ourmodel, the HPV infected state is defined as thepresence of detectable HPV DNA with normalcervical cytology. Under the Bethesda System(21), cytologic changes consistent with HPVinfection that do not meet the criteria for a diag-nosis of cervical intraepithelial neoplasia (CTN)are classified as low-grade squamous intraepithe-lial lesions (SIL).
2. Studies that used older classification systems,primarily the one for CTN, were converted to theBethesda System (21) as follows: cytologic evi-dence of HPV infection and CIN I = low-gradeSIL; CIN II, CIN HI, and carcinoma in situ =high-grade SIL.
3. Regression of HPV is defined as the inability todetect a previously detected HPV viral type in thesame patient by using the same diagnostic tech-niques. Published regression rates, usuallyexpressed as percentage of infections per timeperiod, and progression rates to low-grade SILand high-grade SIL were converted to transitionprobabilities (22).
4. Similarly, regression and progression probabili-ties for low-grade SIL and high-grade SIL werederived from the literature. Low-grade SILlesions were allowed to regress to both latentHPV infection and the Well state, and high-gradeSIL lesions were allowed to regress to low-gradeSIL, HPV, and WeU.
5. Base-case estimates for incidence, regression,and progression rates were chosen on the basis oftwo criteria. First, parameters were adjusted toresult in predicted age-specific prevalence ratesfor HPV, low-grade SIL, and high-grade SIL andage-specific incidence of cervical cancer thatwere within the range reported in cross-sectionaldata. Second, because we planned to use the
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TABLE 1. States and possible transitions between states: Markov model of human paplllomavlrus(HPV) Infection and cervical carclnogenesls
State Description Possible transitions
Well
HPV
Low-grade SIL
High-grade SIL
Unknown stage I cervicalcancer
Unknown stage Icancer
Unknown stage Icancer
cervical
I cervical
Unknown stage IV cervicalcancer
Detected stage WVcervical cancer (one stateper stage of cancer)
Cancer survivor (one stateper stage of cancer)
Hysterectomy
Dead from cervical cancer
Dead from other cause
Normal; no HPV infection orcervical dysplasia
HPV infection, no cytologicabnormality
Low-grade SIL (cervical intra-eptthelial lesion 1)
High-grade SIL (cervical intra-epithellal lesion 2-3, includingcarcinoma in situ)
Cancer confined to cervix
Cancer involving upper two-thirds of vagina or parametrialtissues but not to pelvicsidewall
Cancer involving lower one-thirdof vagina or parametrialtissues to pelvic sidewall
Cancer spread outside of thepelvis
Diagnosed cancer, years 1-5after diagnosis and treatment
Alive 5 years after detectionof cancer
Hysterectomy with removal ofthe cervix for indicationsother than SIL or cervicalcancer
Death due to cervical cancer orcomplications of therapy
Death from cause other thancervical cancer
Well, HPV, dead from other cause
Well, HPV, low-grade SIL,* high-gradeSIL, dead from other cause
Well, HPV, low-grade SIL, high-gradeSIL, dead from other cause
Well, HPV, low-grade SIL, high-gradeSIL, unknown stage I cervical cancer,dead from other cause
Unknown stage I cervical cancer,detected stage I cervical cancer,unknown stage II cervical cancer,dead from other cause
Unknown stage II cervical cancer,detected stage II cervical cancer,unknown stage III cervical cancer,dead from other cause
Unknown stage III cervical cancer,detected stage III cervical cancer,unknown stage IV cervical cancer,dead from other cause
Unknown stage IV cervical cancer,detected stage IV cervical cancer,dead from other cause
Detected Stage H V cervical cancer,dead from cervical cancer, cancersurvivor, dead from other cause
Cancer survivor, dead from other cause
Dead from other cause
Absorbing statet
Absorbing state
* SIL, squamous intraepithelial lesion.t Subjects remain in this state for the remainder of the simulation.
model as the basis of a cost-effectiveness analy-sis of screening strategies (16), we chose esti-mates that resulted in cervical cancer incidencesthat would bias the cost-effectiveness model infavor of improving screening sensitivity. Thus,our base-case estimates result in peak cervicalcancer incidence biased toward higher values atearlier ages.
6. We include a hysterectomy state, since removalof the organ at risk clearly affects calculation ofcervical cancer incidence (23, 24). However, we
did not correct for hysterectomy in our naturalhistory model, since population-based registriesdo not make a similar correction. We did test theimpact of hysterectomy on our estimates.
Model parameters
Incidence of HPV infection. The natural history ofHPV infection is complex, and clearance and persis-tence of viral DNA, along with progression to SIL,vary depending on the viral type, patient characteris-
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HPV and Cervical Cancer Model 1161
Death fromOther Cause
Wen
UndetectedHPV
BtnJgnHysterectomy
Low grade SIL
High grade 8IL
Death from OtherCause
UnknownCervical Cancer
Stage* WV
Cervical CancerStages HV
Cervical CancerDeath
CtrvtciJ ctnctr•urvtvor
^DRGURE 1. Depiction of the Markov model for the natural history of human papillomavirus (HPV) infection and cervical cardnogenesis. Boxesrepresent health states; arrows allowed transitions between states. SIL, squamous intraeplthelial lesion.
tics such as age and immune status, and study designand assay methods (5, 6, 18, 19, 25). We do not distin-guish between different types of HPV; our incidence,progression, and regression estimates are averages forall viral types. The risk of developing cervical cancerafter infection is clearly related to HPV type. Our base-line estimates for HPV and low-grade SIL prevalencealso are lower than reported in studies of cervicalsmears in adolescents (26, 27). However, since wemodeled an entire population and not just those whoare sexually active, prevalence should be lower thanfor only those who are sexually active.
Table 2 shows the baseline age-specific estimatesand ranges for the sensitivity analysis of HPV inci-dence in the model. We varied the incidence rates byfactors of 0.5-2 to examine the effects of changingHPV incidence on cervical cancer incidence inunscreened populations. We also varied the age of peakincidence from 20 to 30 years to examine the effects ofa later onset of sexual activity on age-specific cervicalcancer incidence.
Regression, persistence, and progression of HPVinfection. Estimates of regression and progression
rates of HPV infection are subject to variability instudy design, patient population, and viral assay tech-niques. Reported regression rates for prevalent casesinclude 70 percent after 2 years for a cohort of adoles-cents and college-age women (26), 68 percent over 14months for women less than age 25 years, and 35 per-cent for women more than age 30 years (28). Ho et al.(27) reported a 1-year regression rate of 70 percent fortheir incident cases. All of these results were forwomen whose cytology was normal. The overallregression rate in a large Finnish cohort was 42.8 per-cent over 50 months (29, 30). However, the diseasestatus in this group was determined on the basis ofcytologic evidence of HPV infection. Under theBethesda System (21), these abnormalities would beclassified as low-grade SIL.
Progression probabilities are also difficult to deter-mine. Moscicki et al. (26) reported progression to SILin 15.7 percent of their cases over 40 months, 7.6 per-cent of which progressed directly to high-grade SIL.Ho et al. (27) reported a cumulative 36-month inci-dence of SIL of approximately 25 percent; 6.5 percentwere high-grade lesions. Koutsky et al. (31) found a
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1162 Myers et al.
TABLE 2. Transition probabilities and Incidence rates* at prelnvasive human paplllomavlrus (HPV)disease: Markov model
Parameter (reference no.)
Prevalence of HPV infection, age 15 years
Prevalence of low-grade SlUt age 15 years
Age (years)-speclfic incidence of HPV infection(5, 6, 27, 28)
15161718192021222324-2930-49250
Age (years)-specific regression rate, HPV infection(HPV to Well) (26, 28, 31)
15-2425-29£30
Progression rate (HPV to low-grade SIL) (26, 28, 31)
Proportion of infections progressing directly to high-gradeSIL (26, 28, 31)
Regression rate (age (years)) (low-grade SIL to HPV orWell) (27, 32-34)
15-34£35
Proportion of low-grade SIL reverting to Well (27, 32-34)
Progression rate (age (years)) (low-grade SIL to high-grade SIL (27,32-34)
15-34£35
Regression rate (high-grade SIL to low-grade SIL orWell) (27, 32-34)
Proportion of high-grade SIL reverting to Well (27, 32-34)
Progression rate (high-grade SIL to stage I cancer(8, 9, 35-38)
* Rates are converted to probabilities in the model,t SIL, squamous intraepithelial lesion.
2-year cumulative incidence of high-grade SIL of 28percent in women with HPV DNA; only 36 percent ofthese women had had a prior low-grade SIL smear.Consistent with our other estimates, our base-caseestimates (table 2) were derived from the higher endof the reported ranges. Cases that progress directly tohigh-grade SIL are similar to the "rapidly progres-sive" cases used in other models (9). Again, we variedage-specific regression rates to produce an age-specific cancer incidence curve similar to that seen inunscreened populations.
Low-grade and high-grade squamous intraepithelialneoplasia. Determining transition probabilities fromthe literature that accurately reflect natural history is asdifficult for SIL as it is for HPV infection. The diffi-culties in converting rates collected over varying,often-unspecified times and in heterogeneous popula-tions are further magnified by differences in terminol-ogy. For example, many studies report transitions fromHPV-associated cytologic changes to CIN I to CIN IIto CIN HI to carcinoma in situ, which may be difficultto translate into the Bethesda System (21) terminology
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HPV and Cervical Cancer Model 1163
of low-grade SIL and high-grade SIL. Our modelassumes an age dependence in regression and progres-sion rates (28, 32, 33). For our baseline case, we usethe estimates of Syrjanen et al. (34), the largest cohortthat reports results by using the Bethesda System. Thelength of time for high-grade SIL progression is moredifficult to estimate from these data than are the otherparameters; in this cohort, all patients who progressedto carcinoma in situ, according to an older classifica-tion system, were treated. Prior models have estimatedthe duration from severe dysplasia/carcinoma in situ toinvasive cancer as 10-15 years. We used 12 years forthe base case (table 2), since this interval resulted in anage-specific incidence of cervical cancer most consis-tent with observed data.
Natural history of invasive cancer. Almost no dataexist for estimating the rates of progression from stageI through stage IV cervical carcinoma. There is also noway to determine the likelihood of developing symp-toms. Since distribution of cases by stage in anunscreened population should be a function of both theprogression rate and the likelihood of presentation withsymptoms (since incident cases would be detected onlyupon presentation with symptoms), we adopted theapproach taken by others (8, 9). We adjusted these esti-mates by varying the progression rates and the proba-bility of presentation with symptoms across previouslyreported ranges so the proportion of cases representedby each stage was similar to that for cervical cancerpatients who have never been screened (35-38). Ourestimates are described in table 3.
Stage-specific survival. Survival probabilities at 1,2, 3, 4, and 5 years postdiagnosis for each stage wereobtained from the Patterns of Care Evaluation projectof the American College of Surgeons (39, 40) (and A.Fremgen, American College of Surgeons, "personalcommunication," 1997) (table 3). These values werechosen because they represent data from a wide rangeof facilities that treat women with cervical cancer andshould be relatively representative of the range of cur-rent US practice. Five-year survival rates based onthese data were as follows: stage I, 86.0 percent; stagen, 62.5 percent; stage HI, 37.9 percent; and stage IV,11.3 percent.
We assumed no cancer-related mortality after 5years. Although the Patterns of Care Evaluation datashow some deaths after 5 years for all stages, they arerelatively rare compared with the first 5 years. Othermodels also have used 5-year survival. These data aredisease specific; therefore, patients are also at risk forother causes of death during the 5-year postdiagnosisperiod.
Mortality from other causes. Mortality from causesother than cervical cancer was estimated by subtract-
TABLE 3. Transition probabilities and estimated rates ofprogression of Invasive cervical cancer: Markov model
Parameter (reference no.)
Progression rates and probability ofsymptoms in unscreened patientswith cancer (8, 9, 35-38)
Stage 1Progression rate (stage 1 to stage II)Annual probability of symptoms
Stage IIProgression rate (stage II to stage III)Annual probability of symptoms
Stage IIIProgression rate (stage III to stage IV)Annual probability of symptoms
Stage IVAnnual probability of symptoms
Annual probability of survival afterdiagnosis, by stage* (39, 40)
Additional reference: A. Fremgen, American College ofSurgeons, "personal communication,' 1997.
ing age-specific cervical cancer mortality rates fromage-specific all-cause mortality rates by using US lifetables from 1995 (41).
Hysterectomy for benign disease. We used age-specific hysterectomy rates obtained from the NationalHospital Discharge Survey (42) and Maryland dis-charge data (43) to estimate age-specific hysterectomy
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1164 Myers et al.
rates. For two reasons, we did not correct these ratesfor hysterectomies performed because of cervical can-cer. First, because the majority of surgically treatedcervical cancer cases are radical hysterectomies, whichhave a separate International Classification ofDiseases, Ninth Revision code, most hysterectomiesfor cervical cancer are not included in these data sets.Second, the proportion of nonradical hysterectomiesperformed for preinvasive diseases is relatively small:less than 2 percent of all cases performed over a 6-yearperiod in North Carolina (E. R. Myers, DukeUniversity Medical Center, unpublished data).
Sensitivity and specificity of cervical smears. Weperformed a meta-analysis of studies of conventionalcervical smears, using colposcopy and histology as thereference standard (16). When we used a cytologicthreshold of Atypical Squamous Cells of UncertainSignificance or higher and a histologic threshold oflow-grade SIL or higher, we found a sensitivity of 51percent and a specificity of 97 percent. These valueswere similar to those found in a previously publishedmeta-analysis (44). We used these values to test theimpact of screening at 1-, 2-, 3-, and 5-year intervalson the age-specific incidence of cervical cancer.
RESULTS
Age-specific prevalence of HPV and SIL
The age-specific prevalence of HPV infection inwomen whose cytology is normal, predicted by themodel in which base-case estimates are used, is shown
in figure 2, which also illustrates the predicted age-specific prevalence of low-grade and high-grade SILlesions. The model predicts peak prevalences of HPVof 24.7 percent at age 21 years, low-grade SIL of 8.3percent at age 28 years, and high-grade SIL of 2.6 per-cent at age 42 years.
Age-specific Incidence of cervical cancer
Figure 3 shows the age-specific incidence of cervi-cal cancer predicted by the base-case model parame-ters. The peak incidence is 81/100,000 at age 48 years.The predicted distribution of cases by stage was as fol-lows: stage 1,46.4 percent; stage n, 27.0 percent, stageEl, 18.1 percent; and stage IV, 8.5 percent.
Sensitivity analyses
We tested the impact of varying the age-specificincidence of HPV from one-half to twice the base-caseestimates. As shown in figure 4, peak incidence andoverall risk of cervical cancer varies with HPV inci-dence. Cancer incidence in younger women increasesas HPV incidence increases, although the age of peakincidence does not change.
We also tested the impact of varying the prevalenceof HPV and low-grade SIL at age 15 years on the sub-sequent incidence of cervical cancer (figure 5). Wefound that increasing the prevalence at younger ageswithout changing other parameters increases overallincidence and lowers the youngest ages at which can-cer appears.
0.3 -,
15 25 35 45 55 65 75
Age
FIGURE 2. Age (years)-specific prevalence of human papillomavirus (HPV) (defined as the presence of detectable DMA with normal cytolog-ic findings), low-grade squamous intraeplthellal lesions (LSIL), and high-grade squamous intraepithelial lesions (HSIL) (defined by histology)predicted by the Markov model in which baseline parameters and assumptions are used.
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HPV and Cervical Cancer Model 1165
0.0009
0.0008
0.0007
0.0006
8 0.0005a
TO
g 0.0004
0.0003
0.0002
0.0001
0 15
z\
z25 35 45 55
Age65 75
FIGURE 3. Age (years)-specific incidence of invasive cervical cancer (all stages) in the absence of screening predicted by the Markov modelin which baseline parameters and assumptions are used.
0.0014 -|
15 75
FIGURE 4. Predicted effect of a 50% reduction (bottom curve) and atwofoW increase (top curve) in human papillomavirus (HPV) incidenceon subsequent cervical cancer incidence according to age (years).
0.001
0.0009
0.0008
0.0007
0.0006
0.OOO5
0.0004
0.0003
0.0002
0.0001
15
• - HPVO.LSa.0HPV 0.1. LSI. 0.01
•HPVOJ.LSa.O.OS
7£-
\
\\
25 35 45 55
Age
65 75
FIGURE 5. Predicted effect of varying the prevalence of humanpapillomavirus (HPV) and low-grade squamous IntraepttheliaLlesions (LSIL) at age 15 years on subsequent cervical cancer inci-dence from 0% for both, 10% for HPV and 1% for LSIL, and 30% forHPV and 5% for LSIL
Changing the age of peak HPV prevalence from 20to 30 years changed the curve for cervical cancer inci-dence, but the peak age remained the same. However,delaying the age of peak HPV incidence and decreas-ing the annual probability that women would presentwith early-stage cancer did move the peak incidence tolater ages (figure 6).
Accounting for hysterectomy incidence lowered theoverall population risk of cervical cancer, especially atlater ages. However, the estimated risk for women witha cervix is higher than that based on population-basedestimates (23) (figure 7).
We tested the impact of our natural history estimateson lifetime risk of cervical cancer in the absence of
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1166 Myers et al.
0.001
0.0009
0.0008
0.0007
g 0.0006
•g 0.0005
I 0.0004
0.0003
0.0002
0.0001
0
Base Case
- - Delayed HPV andPresentation
/
/
/ '
/ :
1 '1 :
1 /
\̂V \ \\\
15 25 35 45 55
Age
65 75
FIGURE 6. Predicted effect of later age of infection with humanpapiilomavirus (HPV) and delay in obtaining medical care on the age(years)-specific incidence of cervical cancer.
screening. Table 4 presents the parameters, the inputrange for sensitivity analysis, and the resulting rangeof lifetime cervical cancer risk. On the basis of oursensitivity analysis of these parameters, the model sug-gests that cervical cancer risk is most related to HPVincidence, to the proportion of HPV infections thatprogress directly to high-grade SIL, and to low-gradeSIL progression rates. Changes in these parametersresult in two- to threefold differences in cervical can-cer risk. Changes in low-grade SIL regression rates
and in high-grade SIL progression and regression ratesresulted in 50-75 percent differences in cancer risk.The proportion of low-grade SIL lesions that regresseddirectly to the Well state instead of to the HPV state,and the proportion of high-grade SIL lesions thatregressed to Well instead of to low-grade SIL, hadminimal impact on cervical cancer risk.
Examples of model applications
We estimated the Lifetime risk of cervical cancer forwomen with no evidence of HPV DNA or SIL andwith HPV, low-grade SIL, and high-grade SIL at vari-ous ages in the absence of further treatment. For awoman older than age 50 years who has no evidenceof HPV infection, the risk of subsequent cervical can-cer, even in the absence of screening, is less than 0.5percent (figure 8).
We also tested the impact of screening at variousintervals on the age-specific incidence of cancer (figure9). With screening every 5 years, incidence increasedmarkedly in younger women. As screening frequencyincreased, the proportion of cases in younger womenalso increased: with no screening, 47.7 percent of casesoccurred in women younger than age 50 years, while68.1 percent occurred in women younger than age 50years who were screened every year.
DISCUSSION
We developed a Markov model that, when estimatesfor HPV incidence, regression, and progression as well
0.0009 -,
0.0008
0.0007
0.0006
y 0.0005UJ
a
O 0.0004
0.0003
0.0002
0.0001
0
- - -Hysterectomy
/ - - - - -
v\
J15 25 35 45 55
AGE65 75
FIGURE 7. Effect of correcting for age-specific US hysterectomy rates on the age (years)-specific incidence of cervical cancer in the entirepopulation.
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HPV and Cervical Cancer Model 1167
TABLE 4. Parameters, Input range for sensitivity analysis, and range of lifetime cervical cancer risk*:Markov model
Parameter Basecase Range
Relative risk of HPVt infection (age specific)
Proportion of HPV progressing directly tohigh-grade SILt
Proportion of low-grade SIL regressing toWell instead of HPV
Proportion of high-grade SIL regressing toWell instead of low-grade SIL
HPV prevalence at age 15 years
HPV progression rate
Low-grade SIL progression ratej
Low-grade SIL regression rate}:
High-grade SIL progression rate
High-grade SIL regression rate
1.0 0.5-2.0
0.1
0.05
0.01
0.1
0.2/36 months
0.1-0.3/72 months
0.4-0.65/120 months
0.35/72 months
0.4/120 months
0-0.3
0-1
0.1
0-0.15
0.15-0.3
0.1-0.5
0.3-0.8
0.3-0.5
0.3-0.5
* Uncorrected for hysterectomy.t HPV, human papillomavirus; SIL, squamous intraepithelial lesion.t Age dependent.
Lifetime risk (%)(base case,
3.67)
2.15-6.00
2.84-5.35
3.61^.27
3.47-3.67
3.57-3.72
2.5M.7
2.42-5.88
2.92-4.83
2.91-4.1
2.98-3.8
1 0.15
— • — - _
20
'—
25 30 35 40
Afle
———
45I
50
• • •
55
" • .
60 616
FIGURE 8. Predicted lifetime risk of cervical cancer in the absenceof treatment, by age (years), for women with (from top to bottom) nopathologic diagnosis (bottom curve), detectable human papillo-mavirus (HPV) (third curve), and biopsy-proven low-grade (secondcurve) and high-grade (top curve) squamous intraepithelial lesions(LSIL and HSIL, respectively); risks are corrected for hysterectomy.
as for SIL regression and progression were used,resulted in a predicted age-specific incidence of cervi-cal cancer similar to that seen in a number ofunscreened populations (3, 45). The age-specific
prevalence of HPV and SIL also was similar to thatreported in cross-sectional data. These prevalence fig-ures are not inconsistent with cross-sectional data froma low-risk population in Portland, Oregon (46). In thisstudy, age-specific prevalences were 32.1 percent forages 16-24 years, 27.4 percent for ages 25-29 years,11.3 percent for ages 30-34 years, 10.8 percent forages 35-39 years, 19.7 percent for ages 40-44 years,and 4.4 percent for age 45 years or older (46). Theshapes of the prevalence curves for SIL (figure 2) areconsistent with the series of Carson and DeMay (47),who found asymmetric distributions skewed toyounger ages for CIN I and CIN II and more normaldistributions for higher grade lesions. The prevalenceswe found were also in the range reported by theNational Breast and Cervical Cancer Early DetectionProgram, which targets underscreened, relatively high-risk women (48). Because the model was initiallydeveloped to assess screening policies in the UnitedStates, we predominantly used US data for our modelinputs. Future research should include validation of themodel by using data from other populations.
Our predicted age-specific incidence of cervicalcancer in unscreened populations (figure 2) is similarto that reported in epidemiologic data. Data from mul-tiple unscreened populations show a striking similarityin the pattern of age-specific incidence (1, 3, 45).Gustafsson et al. (45) described two separate curves,one with a peak incidence between ages 40 and 50years with a more rapid decline and one with a peak
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FIGURE 9. Age (years)-specific incidence of cervical cancer without screening (No Pap, top curve) and screening with conventional cervicalsmears (sensitivity of 5 1 % and specificity of 97% using Atypical Squamous Cells of Uncertain Significance or higher as the cytotogic thresholdfor a positive test and low-grade squamous intraepithelial lesions or higher as the histologlc threshold) at intervals of (from top to bottom) every5 (Pap q 5, second curve), 3 (Pap q 3, third curve), 2 (Pap q 2, fourth curve), and 1 (Pap q 1, bottom curve) years.
incidence between ages 50 and 65 years with a moregradual decline. Their modeling suggests that some ofthis difference results from increased incidences insuccessive birth cohorts. The curves with peaks at ear-lier ages were observed primarily for westernEuropean countries between 1950 and 1975. Thecurves showing a later peak incidence are from eitherthird-world countries or western countries in the 1930sand 1940s. Some of the difference in age-specific inci-dence may be due to differences in age at onset of sex-ual activity, number of partners, or overall prevalenceof HPV in the sexually active population. Since inci-dence in unscreened populations also is a function ofthe likelihood of presenting with symptoms, some ofthe observed differences may be due to variations inaccess to care, or willingness to seek care, across timeand place.
Our predicted distribution of cancer by stage alsowas similar to that reported in series of cases with noprior screening (35—38).
The incidence of HPV infection, the proportion ofrapidly progressive infections, and low-grade SIL pro-gression rates appear to have the largest impact on cer-vical cancer risk. This finding suggests the potentialimpact of primary prevention of HPV infection, byusing either barrier methods of contraception, vaccina-tion, or abstinence, on cervical cancer risk. Furtherrefinement of the model will enable modeling of theeffectiveness and cost-effectiveness of such strategies.The model also can be used to investigate the impactof testing for high-risk HPV types in screening strate-gies (49). It could even be adapted to model the impact
of the probability of specific mutations in HPV-infected cells on cervical carcinogenesis.
Because multiple parameters can affect the predictedincidence of cervical cancer, similar results could beobtained by combining the estimates for the variousnatural history probabilities differently. Because ourinitial goal in constructing the model was to use it toanalyze the cost-effectiveness of new technologies forimproving the sensitivity of cervical smears (16), wechose estimates that resulted in a predicted age-specificincidence that would favor improved sensitivity (earlyage of peak incidence, relatively high progressionrates). Given the range of reported estimates for naturalhistory probabilities, our estimates clearly will notreflect the natural history of HPV infection in all popu-lations. Our predicted prevalence patterns of HPV andSIL are similar to those reported in cross-sectional stud-ies of average-risk populations (46, 47). The modeldoes not predict a second peak in HPV in women laterin life, after age 35 years, as was suggested in somestudies (38, 50). Because cross-sectional data representthe prevalence in successive birth cohorts, it is likelythat at least some of this second peak may be due to agedifferences in onset of sexual activity or other risk fac-tors in different cohorts. We chose a cohort simulationfor computational simplicity and speed. The impact ofvarying specific parameters in different cohorts oncross-sectional data could be tested easily by using ourbasic model.
Many of the parameters, especially those related toregression and progression, are reported as means. AsCarson and DeMay (47) point out, the age-specific dis-
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tribution of low-grade lesions does not appear to beGaussian, a finding that our model recreates. Morecomplete reporting of distributions would enable moresophisticated modeling techniques that incorporate theactual distribution of parameter estimates, in turnallowing more precise estimates of the range of cervi-cal cancer risk.
The model can be used to predict individual risk ofcervical cancer given a patient's age and histologicdiagnosis (figure 8). Varying the model to incorporatethe distribution of various input parameters couldenable the risk to be expressed as a point estimate withconfidence intervals. Incorporation of patient prefer-ences for various treatment and follow-up optionscould make the model useful for patient counseling.
Another application is in testing the impact ofscreening and prevention strategies on cervical cancerincidence. For example, the dramatic effect of decreas-ing HPV incidence on cancer incidence (figure 4) sug-gests the potential impact of effective HPV vaccines.Assessing the effect of screening on age-specific inci-dence (figure 9) is another example.
A third application is in exploring the effect of deriv-ing incidence estimates from populations with varyingdegrees of screening, as is common in the United States.For example, the widely cited Eddy (9) Markov modelhas served as the basis for several cost-effectivenessanalyses (9, 51). Although Eddy's model parameterswere adjusted to fit international data (52), the incidenceof invasive cervical cancer in an unscreened US popu-lation was estimated by assuming that it would be threetimes higher than that observed in a partially screenedpopulation. However, this assumption does not accountfor the fact that 30-50 percent of US cancer cases occurin an unscreened population. Because the incidence ofcervical cancer in the United States reflects bothscreened and unscreened populations as well as theeffect of different cohorts with varying exposure toHPV, simply increasing the age-specific incidence bythreefold will overestimate the expected incidence inunscreened patients at younger ages. If the distributionof stages is not changed, then the ratio of incidence tomortality will be overestimated; the ratio of early-stagecases in the SEER registries is much higher in youngerwomen than in older women (66 percent localized inwomen less than age 50 years compared with 37 percentin women more than age 50 years) (2).
We were able to approximate the lifetime cervicalcancer risk of Eddy (2.5 percent) (9) by altering ourHPV incidence. However, the lifetime mortality riskpredicted by this model is 0.88 percent, substantiallylower than Eddy's estimate of 1.18 percent. We thenadjusted rates for progression between cancer stagesand symptoms to obtain similar incidence and mortal-
ity risks. By changing the progression rates to 90 per-cent in 2.5 years for stage I to stage II, 75 percent in 1year from stage II to stage m, and 100 percent in 1year for stage m to stage IV and changing the proba-bility of symptoms for stage III to 35 percent, weobtained a lifetime risk of 2.52 percent and a mortalityrisk of 1.14 percent. However, these progression ratesare inconsistent with those reported by Eddy.
Because detection of cervical cancer in youngerwomen included in the SEER data is more likely to bedue to screening and therefore occurs at both an earlierage and an earlier phase of progression than in olderwomen, survival rates are likely to be higher than forwomen who present with symptoms. The high inci-dence-to-mortality ratio of the Eddy model (9) may besecondary to extrapolations of distribution by stage inunscreened populations to the SEER data for youngerwomen. Use of our model to examine the effects ofdifferent screening intervals also supports this hypoth-esis: as screening intervals decrease, the proportion ofearly-stage disease increases, as does the proportion ofcases among younger women (figure 9), a finding thathas been reported in the British population (53). Thisprediction of the model is also consistent with the find-ing that in younger women, "rapid-onset" cervical can-cer tends to be early-stage disease (54). In addition, wehave been able to recreate observed SEER incidenceand mortality data by modeling a cohort with varyingproportions of screening intervals, from no screeningover a lifetime to annual screening (16).
These comparisons illustrate the difficulty in esti-mating the risk of cancer in unscreened populationswhen most available data represent both screened andunscreened populations. Previous models have usedestimates from case-control or cohort studies (33, 52).However, the consistency of the shape of the curve forage-specific incidence in unscreened women acrosspopulations (1, 45) facilitates calibration of the model.Other than the paper of Gustafsson and Adami (55),we are unaware of another model that takes a similarapproach.
Similarly, relatively few published models of cervi-cal cancer screening incorporate the HPV status ofnormal women (49, 56, 57), and one includes the HPVstatus of women infected with human immunodefi-ciency virus (58). Given the prevalence of HPV, thegrowing insight into its molecular biology, and thepotential role of HPV testing in preventive strategies,modeling cervical cancer prevention strategies in thefuture may well require some method for incorporatingHPV status.
Obvious limitations inherent in any model areuncertainty surrounding parameter estimates, assump-tions that can be reasonably debated, and the effects of
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changing epidemiologic parameters over time andspace. In addition, the specific parameters of ourmodel are based on US data. We used FederationInternationale de Obstetriques et Gynecologie stagingof cervical cancer and calculated survival rates on thebasis of published US data. Although use of thesestages improves the clinical relevance of the model,stage-specific survival may well vary in other settings.Similarly, the effect of hysterectomy rates, a particu-larly important parameter in assessing the efficiency ofscreening strategies, may not be as important in othersettings in which hysterectomy is not used as widely.
In summary, we have developed a model that syn-thesizes published data on HPV infection and cervicalcarcinogenesis and approximates reported patterns ofage-specific incidence and prevalence. The model isdesigned to be updated easily as new evidencebecomes available and enables modeling of bothhypotheses about the biologic behavior of HPV-relateddisease and the potential impact of various strategiesfor preventing cervical cancer. Strategies that reduceHPV incidence can reduce cervical cancer incidence atleast as much as strategies that improve the availabil-ity or sensitivity of cytologic screening. Given theimportance of models in understanding the biology,epidemiology, and policy implications of HPV infec-tion and cervical carcinogenesis, serious considerationshould be given to development of a consensus model,or a series of models, for general use.
ACKNOWLEDGMENTS
This paper is based on work performed under contract(no. 290-97-0014) to the Agency for Health Care Policy andResearch. The authors are solely responsible for its content.No agency endorsement of opinions or recommendationsexpressed herein should be stated or implied.
The authors thank Jane Kolimaga for overall project man-agement and Jean Slutsky for project support.
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