# Analysis of lung cancer incidence in the nurses’ health and the health professionals’ follow-up studies using a multistage carcinogenesis model

## Authors

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DOI: 10.1007/s10552-007-9094-5

- Cite this article as:
- Meza, R., Hazelton, W.D., Colditz, G.A. et al. Cancer Causes Control (2008) 19: 317. doi:10.1007/s10552-007-9094-5

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## Abstract

We analyzed lung cancer incidence among non-smokers, continuing smokers, and ex-smokers in the Nurses Health Study (NHS) and the Health Professionals Follow-Up Study (HPFS) using the two-stage clonal expansion (TSCE) model. Age-specific lung cancer incidence rates among non-smokers are identical in the two cohorts. Within the framework of the model, the main effect of cigarette smoke is on the promotion of partially altered cells on the pathway to cancer. Smoking-related promotion is somewhat higher among women, whereas smoking-related malignant conversion is somewhat lower. In both cohorts the relative risk for a given daily level of smoking is strongly modified by duration. Among smokers, the incidence in NHS relative to that in HPFS depends both on smoking intensity and duration. The age-adjusted risk is somewhat larger in NHS, but not significantly so. After smokers quit, the risk decreases over a period of many years and the temporal pattern of the decline is similar to that reported in other recent studies. Among ex-smokers, the incidence in NHS relative to that in HPFS depends both on previous levels of smoking and on time since quitting. The age-adjusted risk among ex-smokers is somewhat higher in NHS, possibly due to differences in the age-distribution between the two cohorts.

### Keywords

Lung cancer epidemiologyLung cancer age-specific incidenceNever smokers lung cancer riskSmokers relative riskEx-smokers relative riskMultistage carcinogenesisTwo-stage clonal expansion model## Introduction

The Nurses Health Study (NHS) and the Health Professionals Follow-Up Study (HPFS) constitute outstanding dataset, to investigate in detail the relationship between smoking and lung cancer, and to evaluate the influence of gender both on background and smoking-induced risks. We analyze the consequences of smoking and smoking cessation on the lung cancer incidence rates in the NHS and HPFS using multistage carcinogenesis models. This approach allows us to explicitly consider the entire smoking histories of individuals in these cohorts, including complex time-related factors, such as ages at start and quit, and changes in smoking habits.

We use likelihood-based methods to estimate the parameters of the two-stage clonal expansion (TSCE) model. Using the model with the estimated parameters, we construct age-specific incidence curves for non-smokers, and for smokers and ex-smokers with pre-specified histories of smoking. We investigate also the roles of daily intensity of smoking and of duration of smoking on lung cancer risk. In particular, for a given level of smoking, we examine the impact of duration of smoking on the relative risk (RR).

The question of whether, for a given level of smoking, females are at greater risk than males of developing lung cancer has generated a great deal of debate [1–6]. The NHS consists entirely of females and the HPFS consists entirely of males. Our methods allow us to analyze the NHS and HPFS simultaneously using a common model, hence we can evaluate in a single-framework similarities and differences in the lung cancer risk in females and males.

Finally, we use our fitted models to project lung cancer risks for various smoking scenarios.

## Methods

### The nurses health and the health professionals follow-up studies

Classification according to status at baseline (NHS-1976, HPFS-1986)

Total | Never | Former | Smokers | |
---|---|---|---|---|

NHS | ||||

Subjects | 104,493 | 51,121 | 24,474 | 28,898 |

Lung cancer cases | 1,165 | 130 | 134 | 901 |

Avg. follow up | 23.15 years | |||

HPFS | ||||

Subjects | 46,050 | 22,431 | 19,632 | 3,987 |

Lung cancer cases | 461 | 58 | 247 | 156 |

Avg. follow up | 14.93 years |

It is important to mention that although there was a decade between the beginning of these studies, the age, and birth year distributions of both cohorts are quite similar.

### Smoking histories

*d*(

*t*), are piecewise constant functions representing the number of cigarettes per day smoked by each subject at any particular age,

*t*. We construct the smoking histories in the following way. Clearly

*d*(0) = 0 and we keep this constant until the age at start of smoking. Subjects in both cohorts report their smoking intensities at different time points in the following categories: 0–4 cig/day, 5–14 cig/day, 15–24 cig/day, 25–34 cig/day, 35–44 cig/day, >45 cig/day. We assign the midpoint of each category as the corresponding intensity for that category, or 50 if the intensity is >45 cig/day. Once we have done this, we compute the ages at which subjects changed their smoking intensities (change points of

*d*(

*t*)) and assign the corresponding intensity value to

*d*(

*t*). In particular, we use the smoking information reported in the initial questionnaire to calculate the change points up to the age at entry into the study. In the initial questionnaire, participants responded to questions about their past smoking habits. The information provided at entry differs between the cohorts. In the NHS, the nurses reported the age at which they started smoking if they did, their average smoking rate and the quitting age for ex-smokers. Thus, for the NHS subjects, there are at most two ages of interest before the age at entry, namely the age at start of smoking and the age at quitting. In contrast, the subjects in the HPFS reported their average smoking rate during specific age-periods before their age at entry (<15, 15–19, 20–29, 30–39, 40–49, 50–59, >60 years). In this case, we only consider the information of the age-periods with right end point lower than their age at entry to the study. In addition, we only take the information in the >60 age-interval if the age at entry to the HPFS is at least 70-year-old. We assume that the age at start of HPFS smokers is given by the mid-point of the first age-period with a positive smoking rate. In case their first positive exposure occurs in the <15 or >60 age-interval, then we use 13 or 65 years old as the starting ages, respectively. Finally, if there is a change in the smoking dose or status between two consecutive age-periods, we assume that the change occurred in the midpoint year in between them and assign the corresponding age as a change point of the smoking history. The final step is to calculate the change points after the age of entry to the studies. This is done in a simple way, since the subjects in both cohorts report their smoking status and dose every two years after their entry into the study. In particular, we compare the smoking intensities between consecutive questionnaires and if they differ, we assume that the change occurred at the beginning of the mid-point year and assign the corresponding age as a change point of the smoking history. Typical smoking histories for members of the NHS and HPFS are shown in Fig. 1.

We use likelihood-based methods to estimate parameters of the TSCE model, which are functions of the smoking history. A brief description of the model and details of the likelihood construction are presented below.

### The two-stage clonal expansion model

For our analyses, we use a multistage model that acknowledges three phases in the process of carcinogenesis. In the first phase (initiation) a susceptible stem cell acquires one or more mutations resulting in an initiated cell, which has partially escaped growth control. In the second phase (promotion) initiated cells undergo clonal expansion, either spontaneously or in response to endogenous or exogenous promoters. Promotion is an extremely efficient way to bring about malignant conversion because clonal expansion of initiated cells creates a large population of cells that have acquired some of the genetic changes required for malignant transformation. Finally, in the third phase (malignant conversion) one of the initiated cells acquires further mutational changes leading to a malignant cell. The simplest model incorporating these three phases is the TSCE model [7, 8]. A schematic representation of the model is shown in the Appendix.

The TSCE model assumes that normal stem cells become initiated according to a Poisson process with intensity μ_{0}*X*, where *X* is the number of susceptible stem cells. Initiated cells expand clonally (promotion) via a linear birth and death process with rates (α,β). This means that each time that an initiated cell divides, it can produce two initiated cells (with birth rate α) or die/differentiate (with death rate β). Initiated cells can also divide into one initiated and one malignant cell (with rate μ_{1}). The time between the first malignant cell and diagnosis is modeled either as a constant or gamma-distributed lag.

*d*(

*t*) denotes the cigarette consumption of an individual at age

*t*. We assume that each of the identifiable parameters of the model (see Table 2) has a dose–response given by

_{c}and θ

_{e}are the dose–response coefficients. Previous analyses using the TSCE model [9, 10] of the relationship between smoking and the lung cancer rates suggested that power laws are good models for the smoking dose–response [9]. We estimate the background rates and the cigarette dose–response coefficients for each identifiable parameter in the model.

Parameter estimates [MLE (MCMC 95% CI)]

| Parameter | NHS | HPFS |
---|---|---|---|

Fixed parameters | Stem cell population | 10 | |

Initiated cells’ division rate α | 3 | ||

Gamma-distributed lag time mean | 5 | ||

Background rates | Initiation & malignant-conversion rate μ | 8.14e-8 (5.51e-8,1.27e-7) | |

Initiated cells’ promotion rate | 0.0956 (0.0772, 0.1106) | ||

Gamma-distributed lag time std | 3.28* | ||

Tobacco coefficients | Tobacco promotion rate coefficient\(^{\dag}\,\,g_{c}\) | 0.1458 (0.1010,0.1752) | 0.1123 (0.0802,0.1500) |

Tobacco promotion rate power\(^{\dag}\,\,g_{e}\) | 0.5171 (0.4703,0.5945) | ||

Tobacco malignant-conversion coefficient μ | 0.2095 (0.1565,0.6691) | 0.5339 (0.2876,1.6972) | |

Tobacco malignant-conversion power μ | 0.4684 (0.1083,0.5483) | ||

Loglik | 11696.40 |

### Likelihood function

*ae*

_{i}). Subjects are censored in case of death by any other cause or in case they survive and were never diagnosed with lung cancer until the end of follow-up (year 2000 for our analysis). In addition, we also censor any individuals who were diagnosed with other types of cancer, except non-melanoma skin-cancer. Let

*al*

_{i}be the censoring or failure (lung cancer diagnosis) age. The individual likelihoods are

*t*of an individual with smoking history

*d*

_{i}, and \(\bar{\theta}(d_i)\) denotes the vector of identifiable model parameters given the smoking history

*d*

_{i}(Note: the prime denotes derivative with respect to

*t*). The overall likelihood is then

### The survival function

*f*(·) is the gamma density.

### Ten-year risk predictions

Models optimized for subjects in the NHS and HPFS cohorts are used to predict a 10-year risk estimates for lung cancer incidence. Competing causes of mortality are adjusted using standard actuarial methods for multiple decrement life tables. All cause annual risk estimates are extracted from the National Center for Health Statistics [12]. We use the 1989–1991 life tables for both cohorts. About 95% confidence intervals (CI) are calculated by sampling model variables from a Markov Chain Monte Carlo (MCMC) simulation using the Metropolis-Hastings algorithm.

### Ratio of age-adjusted hazards

For any particular smoking history, we use the ratio of age-adjusted hazards as a measure of the lung cancer relative risk between the NHS and HPFS. This ratio is calculated as follows. We compute the TSCE model age-specific incidence (ages 40–80) in each cohort using the corresponding maximum likelihood estimate (MLE) parameters and the specific smoking history of interest. We then adjust for age in each cohort using the 1990 US total white population and compute the ratio of age-adjusted hazards. In order to calculate a 95% CI of the estimated ratio, we obtain independent samples of the model parameters (model described in Joint Model section) via Markov Chain Monte Carlo (MCMC) simulations with the Metropolis Hasting algorithm [13]. For each set of parameters in the MCMC run, we compute the TSCE hazard in the NHS and HPFS (using the specific smoking history of interest), adjust for age in each cohort and compute the relative ratio between females and males. We then calculate the 95% CI of the ratio of age-adjusted hazards.

### Estimation procedure

Estimation of the parameters is done via maximum likelihood methods. The background rates and the dose–response relationships are estimated by maximizing the likelihood for the observed cancer incidence using the piecewise constant exposures of cigarette for each individual. The likelihood function calculation and its maximization is done by High Performance Fortran routines. The Nelder–Mead simplex and the modified Davidon-Fletcher-Powell algorithms are used for the optimization. Gauss-Legendre quadratures are used for the integration required for the computation of the survival function when the gamma-distributed lag time (time from malignant transformation to diagnosis) is used.

We used two estimation procedures. In the first, we fit the background parameters to the never-smokers only and then keeping them constant, fit the model to the entire cohort to optimize the dose–response parameters. Second, we fit the model to the entire cohort and estimate all the parameters simultaneously. We find that both approaches lead to similar fits in terms of the likelihood function. However the first provides better fits to the number of cancer cases in each sub-group, so it is preferred to the later.^{1} All the results presented here are based on the first estimation procedure.

## Results

^{2}In addition, we find that using a gamma-distributed lag time improves the model fit significantly in both cohorts.

^{3}Table 2 shows the reduced set of parameters. The corresponding 95% CI are constructed via MCMC simulations with the Metropolis Hasting algorithm [13]. The TSCE model describes lung cancer incidence in both cohorts well, as can be seen from Fig. 2.

### Independent models

First, we fit our models to both cohorts independently. In both cohorts we find that the primary etiological mechanism for lung cancer appears to be smoking-related promotion (increased clonal expansion rate). The fitted models have a highly significant sub-linear dose–response on the promotion of premalignant lesions. These results are in agreement with a previous joint analysis of the lung cancer mortality in the British doctors’ and the American Cancer Society CPS-I and CPS-II cohorts [10]. Interestingly, the results are closer to the fits to the CPS-II cohort, which was roughly contemporaneous with NHS and HPFS, than to fits to the earlier CPS-I and British doctors’ cohorts. The NHS, HPFS and CPS-II cohort had an increased dose–response of tobacco on promotion than the earlier cohorts, but a reduced effect on initiation. These differences may in part be explained by changes in cigarette composition, with higher levels of nitrosamines in the newer cigarettes acting as promoters, while the lower tar levels may be associated with the lower apparent initiation rate. We also find a significant dose–response in the malignant conversion of premalignant lesions in the NHS and HPFS. This was not seen in CPS-II, possibly because the data did not include follow-up for changes in smoking intensity. A dose–response on malignant conversion has relatively short term effects on incidence rates.

Interestingly, all parameter estimates are similar in the NHS and HPFS cohorts, suggesting that a common model could describe the incidence in both.

### Joint model

There are reports in the literature suggesting that, for a given level of smoking, women are at higher risk of lung cancer than men [1–3, 5, 6]. However, a recent analysis of the NHS and HPFS by Bain et al. [4] found no statistically significant gender differences in the lung cancer rates among smokers for a given level of smoking in the NHS and HPFS cohorts. In a later correction to the original publication, Bain et al. [14] reported a gender difference among ex-smokers with the risk in women being 1.5 relative to men. Wakelee et al. [15] suggested in a recent analysis of several large cohort studies, including the NHS and HPFS, that the lung cancer incidence among never smokers is higher in women. However, although their estimated age-adjusted lung cancer incidence among never smokers is slightly higher in the NHS than in the HPFS, they do not reject the equality of the never smoker lung cancer rates in the two cohorts.

In order to address the issue of gender differences, we explored a joint model in the two cohorts. Multistage models allow us to test for specific gender differences in the initiation, promotion and malignant conversion rates of lung cancer. Using likelihood-ratio tests, we cannot reject the equality of the background parameters between females and males, although we can reject the equality of all the model parameters. In particular, a model with different tobacco-induced promotion and malignant conversion coefficients between women and men is the over all preferred model. Table 2 shows the parameter estimates of the preferred joint model. All the figures in this article are obtained using the parameter estimates of the preferred joint model.

The NHS and HPFS cohorts contain information on never, current, and former smokers. Figure 2 shows the lung cancer incidence among never, former, and current smokers in both cohorts and the model predictions. The bottom panels in Fig. 2 show the number of lung cancer cases in the NHS and HPFS as a function of years since quitting.

## Discussion

Methods of analyses are based on ideas of multistage carcinogenesis are fully parametric and allow complex patterns of exposure to multiple covariates to be explicitly considered [9]. In the analyses reported in this article, we have explicitly considered individual smoking histories, including age at start of smoking, changes in levels of smoking, and age at quitting among ex-smokers. Models incorporating detailed smoking information on the individual level are useful in exploring the consequences of intervention strategies to modify smoking habits. Moreover, being biologically based, multistage models allow the investigation of the effects of smoking on lung cancer initiation, promotion and malignant conversion. Hence, multistage models provide a natural framework to evaluate the potential benefits of chemo-prevention and pharmacological intervention strategies based on mode of action of the intervention. Finally, analyses based on multistage models begin with a completely different set of assumptions and therefore complement the traditional approaches. In particular, these analyses do not assume proportionality of hazards, a very strong assumption that appears to be inappropriate in the case of lung cancer and smoking [16].

### Previous analyses using multistage models

The Two-stage Clonal Expansion Model has been used to describe the lung cancer incidence and mortality in several cohort and case–control studies [9, 10, 17–19]. In all of them, smoking-related promotion has been found to be the primary etiological mechanism of lung carcinogenesis. Interestingly, analyses of older datasets have shown also an effect of smoking on lung cancer initiation and no effect on malignant conversion [9, 10]. However, exactly the opposite has been found in more recent dataset [18, 19]. In particular, Heidenreich et al. [18] found in a case–control study in Germany that smoking has significant effects on promotion and malignant conversion and no effects on initiation. More recently, Schollnberger et al. [19] found similar patterns in a large cohort study carried out in 10 European countries. Interestingly, Schollnberger et al. reported that a common model described lung cancer incidence in males and females in the European Prospective Investigation into Cancer and Nutrition (EPIC). They concluded that gender differences in lung cancer risk are due entirely to differences in smoking habits. Hazelton et al. [10] also found a limited effect of tobacco on the lung cancer initiation in the CPS-I study, however, no effect on malignant conversion was seen in that cohort. These differences may in part be explained by changes in cigarette composition, with higher levels of nitrosamines in the newer cigarettes acting as promoters, while the lower tar levels may be associated with the lower apparent initiation rate. Additionally, the smoking information available in the older cohorts may not have been detailed enough to detect an effect on malignant conversion.

### Incidence among life-long non-smokers

### Incidence among continuing smokers

Figure 3a shows the age-specific incidence curves generated by the joint model for female and male smokers of 20 and 40 cigarettes per day. The second panels of Fig. 2 show the age-specific incidence rates among continuing smokers in both cohorts along with the incidence curves generated by our model.

The relative hazard associated with smoking 20 and 40 cigarettes per day in each cohort is shown in the top panels of Fig. 3b. It is clear from this figure that the relative risks associated with smoking are strongly modified by duration of smoking. That this observation is not an artifact of our model can be seen from the directly computed rate ratios in the Cancer Prevention Study I (Burns et al. [20] , Table 11), which show a similar concave-down picture not only for lung cancer but also for other causes of mortality associated with cigarette smoking. The initial increase in RR with duration of smoking can be directly attributed to the strong influence of tobacco on promotion. The later decline can be attributed to the strong increase in non-smoker incidence rates of lung cancer with age with a concomitant leveling off of the incidence rates among smokers predicted by the model. The strong modification of RR by duration of smoking suggests that the proportional hazards model may not be the appropriate tool for analyses of these data.

^{4}and is not statistically significant, a finding that is consistent with that reported in Bain et al. (2004). For smokers of 40 cigarettes per day, the ratio of age-adjusted female to male rates is 1.2 (95% CI = 0.80–1.64).

### Incidence among ex-smokers

The bottom panels of Fig. 2 show the incidence rate among ex-smokers as a function of time since quitting. The model predictions describe the data well in both cohorts except for the first few years after quitting. We attribute this discrepancy in the first few years to quitters who stopped smoking because they had developed symptoms of lung cancer. This phenomenon is well known [23, 24]. The effect of smoking on the rate of malignant conversion implies a rather quick decrease in risk after quitting, and the effect on the rate of promotion implies a continuing decrease in risk over a prolonged period of time as seen in previous analyses of mortality data (Hazelton et al. [10]). Bottom panels of Fig. 3b show the decrease in lung cancer incidence among ex-smokers relative to that among continuing smokers. The pattern of decrease in both cohorts is consistent with that reported for mortality by Hazelton et al. [10], by Peto et al. [25] and by Rachet et al. [16].

Figure 4 shows the female to male hazard ratio for ex-smokers. This ratio is higher than the ratio of hazards for continuing smokers (left panels of the figure). The hazard ratio quickly increases to about 1.5 and remains approximately constant. It is important to mention that these calculations also depend on the assumed age at start (age 20) and age at quitting (age 50). The confidence bounds on the ratio indicate that it is border-line significant consistent with the report by Bain et al. [14]. For ex-smokers of 20 cigarettes per day, the ratio of age-adjusted female to male rates is 1.35 (95% CI = 0.99–1.56). For ex-smokers of 40 cigarettes per day, the ratio of age-adjusted female to male rates is 1.48 (95% CI = 1.08–1.90).

The estimated benefits of smoking cessation depend largely on the available information at older ages, where longer durations of both abstinence and smoking are observed. The age-distribution of individuals differs between the two cohorts, with a larger proportion of older individuals present in the HPFS. Therefore, it is plausible that the lower risk among the ex-smokers in the HPFS predicted by the model is attributable, at least in part, to the difference in age-distribution.

### Ten-year risk predictions

The 10-year risk projections for smokers who smoke for 25, 40, or 50 years and continue to smoke or quit at ages 55, 65, or 75 years based on models for White male and female smokers in the NHS and HPFS cohorts [% risk(95% CI)]

| 25 years | 40 years | 50 years | |||
---|---|---|---|---|---|---|

Quit | Still smoking | Quit | Still smoking | Quit | Still smoking | |

NHS: 20-cig smokers | ||||||

55 | 0.8 (0.6–1.2) | 1.7 (0.9–3.1) | 2.0 (1.6–2.7) | 3.8 (2.3–6.5) | * | * |

65 | 2.0 (1.5–2.7) | 3.8 (2.0–6.6) | 4.6 (3.7–5.7) | 7.9 (4.8–12.0) | 6.7 (5.6–8.0) | 10.7 (7.1–15.1) |

75 | 4.0 (2.9–5.2) | 6.8 (3.7–10.6) | 7.8 (6.3–9.5) | 12.0 (7.7–16.7) | 10.3 (8.5–12.6) | 14.9 (10.2–20.1) |

NHS: 40-cig smokers | ||||||

55 | 1.8 (1.3–2.7) | 4.2 (2.0–7.6) | 5.4 (4.0–7.0) | 10.4 (6.2–15.7) | * | * |

65 | 4.1 (2.9–5.7) | 8.4 (4.5–13.8) | 10.0 (8.3–12.15) | 16.9 (11.3–23.0) | 12.3 (9.6–15.7) | 18.8 (13.2–25.6) |

75 | 7.3 (5.4–9.4) | 12.7 (7.4–18.7) | 13.7 (11.2–16.9) | 20.4 (14.4–27.3) | 14.9 (10.6–20.7) | 20.8 (14.7–29.1) |

HPFS: 20-cig smokers | ||||||

55 | 0.7 (5.2–1.1) | 1.8 (0.8–3.1) | 1.5 (1.0–2.0) | 3.4 (1.6–5.4) | * | * |

65 | 1.7 (1.2–2.3) | 3.8 (1.8–5.9) | 3.2 (2.4–4.1) | 6.6 (3.6–9.4) | 4.3 (3.5–5.3) | 8.3 (5.3–11.2) |

75 | 3.1 (2.3–4.2) | 5.9 (3.2–8.6) | 5.2 (4.2–6.4) | 9.0 (6.1–12.2) | 6.5 (5.4–7.8) | 10.7 (7.9–14.1) |

HPFS: 40-cig smokers | ||||||

55 | 1.4 (0.8–2.2) | 3.8 (1.4–6.4) | 3.4 (2.1–4.7) | 7.9 (3.5–11.5) | * | * |

65 | 3.1 (1.9–4.2) | 7.1 (3.2–10.5) | 6.3 (4.5–7.8) | 12.4 (7.2–16.8) | 7.8 (6.1–9.6) | 13.9 (10.0–18.3) |

75 | 5.1 (3.5–6.6) | 9.6 (5.3–13.6) | 8.5 (6.9–10.5) | 14.2 (10.3–18.7) | 9.5 (6.4–12.2) | 14.7 (10.3–19.6) |

## Conclusions

We conclude that the risk of lung cancer is similar among non-smoking and smoking men in the HPFS and women in the NHS, but that the lung cancer risk among ex-smokers is higher in the NHS. Within the framework of the TSCE model, this difference can be attributed to higher smoking-related promotion in the NHS cohort. However, it is plausible that this is just an artifact produced by the difference in age-distribution between the two cohorts. In both cohorts, we find that the main effect of cigarette smoke is on the promotion of premalignant lesions. This is consistent with previous analyses of several cohort and case–control studies using the TSCE model [9, 10, 17–19]. The relative risk of smoking is strongly dependent on duration of smoking. For a smoker who begins to smoke before the age of 20, the RR increases to about age 70 and declines thereafter. This pattern is consistent with that observed in other studies [10, 20]. Among ex-smokers, the relative risk of former versus current smokers appears to decrease more strongly at higher smoking levels. This finding is consistent with the analysis of CPS-I, CPS-II and the British Doctors cohorts in Hazelton et al. [10] and with the analysis of a large case–control study in Rachet et al. [16].

## Acknowledgments

We thank the Cancer Intervention and Surveillance Modeling Network (CISNET) Group, Dr. Anup Dewanji and Dr. Jihyoun Jeon for useful suggestions. We acknowledge support from the NIH grants RO1 CA047658 and UO1 CA97415. Financial support: NIH grants RO1 CA047658 and UO1 CA97415.