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Cancer. Author manuscript; available in PMC 2011 January 1.

Published in final edited form as:

PMCID: PMC2807892

NIHMSID: NIHMS151113

Correspondence: Email: ude.ecir@4002gld (DG)

The Mayo Lung Project (MLP) was a randomized clinical trial designed to test whether periodic screening by chest Xray reduces lung cancer (LC) mortality in high-risk male smokers. Among MLP participants, more LC deaths were found in the screening arm both at the trial’s end and after long-term follow-up. Overdiagnosis is widely cited as an explanation for the MLP results whereas a role of excess LC risk attributable to undergoing numerous chest Xray screenings has been largely un-examined. We examine the consistency of the MLP data with a modified two-stage clonal expansion (TSCE) model of excess LC risk.

Using a simulation model calibrated to the initial MLP data, we estimate the statistical variance of LC incidence and mortality between the screening and control arms. We derive and apply a Bayesian estimation framework using a modified version of the TSCE model to evaluate the role of excess LC risk attributable to chest Xray screening.

Based on our simulations, we find that the overall difference in LC deaths and incidence between study and control arms is unlikely (p=0.0424, p=0.0104) assuming no LC excess risk. We estimate that the 10-year excess LC risk for a 60-year old male smoker having received 10 chest Xray screens is 0.574% (p=0.0021).

The excess LC risk observed among screening arm participants is statistically significant with respect to the TSCE model framework, due in part to the incorporation of key risk correlates of age and screen frequency into the estimation framework.

The Mayo Lung Project (MLP) was a randomized clinical trial (RCT) designed to test whether a mortality benefit attributable to screening for lung cancer (LC) by chest radiography exists. The MLP is considered a watershed trial in that it altered views regarding the role of early detection by chest radiography in screening for LC; the interpretations of its findings are still debated. When the MLP began recruiting participants in 1971, the Mayo Clinic endorsed annual chest radiograph screening for smokers. However, in the MLP, despite the detection of a higher number of early stage cancers in the screening arm, there were more LC deaths in the screening arm than in the control arm^{1}^{,}^{2}. After a follow-up study with a median of 20.5 years, an even greater excess of LC deaths were discovered in the screening arm^{3}. After a second follow-up study with a median duration of 23.5 years, the difference in the total number of incidence cases also increased^{4}. The interpretation of these MLP findings by the medical community was at best that they were inconclusive, and at worst, that they contradicted any benefit of screening. Due to the risks associated with early intervention based on a positive and, potentially, false positive screening result, no national cancer advisory source currently endorses LC screening in the broader population^{5}^{,}^{6}.

It has been proposed that the MLP results are consistent with high rates of overdiagnosis^{3}^{,}^{4}^{,}^{7}^{,}^{8}. Overdiagnosis occurs in the event that, through early detection, a disease state is identified, which does not shorten the patient’s life expectancy. However, a pathologic review of cases detected in the MLP confirmed the histologic diagnosis of cancer in all cases it studied although a higher rate of carcinoma in situ detected in the screening arm was noted^{9}. Other studies indicate that the power of the MLP may have been lower than initially planned, and that the initial findings of the MLP were not inconsistent with a model of moderately aggressive tumor progression and a modest mortality benefit^{10}^{,}^{11}. The inconclusive findings of the MLP have led to debate as to whether randomized clinical trials are an efficient way to study the benefits of screening^{12}^{,}^{13}.

A flaw in the argument that the observed MLP results are consistent with overdiagnosis is that overdiagnosis does not explain the greater number of LC deaths in the screening arm nor does it explain the greater cumulative LC incidence in the screening arm after extended follow-up. These findings hint at the presence of a systematic source of excess risk that pre-disposes the screening arm participants to higher rates of LC. Radiation is a known epidemiologic risk factor for many cancers, including LC. The MLP regimen prescribed chest radiographic screening three times a year for a period of six years, a total of eighteen screens. In practice, some screening arm participants received more than the prescribed number; if a screen was inconclusive the participant would often return for a follow-up screen prior to the next scheduled screen.

The aim of this paper is to confront the findings of the MLP study, as well as the hypothesis of overdiagnosis, with independently obtained estimates of the effect of chest Xray exposure, via mathematical modeling.

The process of carcinogenesis is known to consist of multiple stages. Mathematical models of this multi-stage process have been formulated and fit to epidemiological data, offering a mechanistic explanation of age and exposure-related patterns of cancer incidence. According to the two-stage clonal expansion (TSCE) model, the process of carcinogenesis is governed by two rate-limiting stages^{14}. A normal cell (NC) must first transform to become an intermediate cell (IC), an irreversible step (initiation). Next, an IC must give rise to a malignant cell (MC), which gives rise to cancer with certainty (transformation). The TSCE model parameterization also accounts for the clonal expansion of IC (promotion), a key model feature used to account for exposure effects such as smoking in carcinogenesis models of lung cancer^{15}. Extensions of the TSCE model include a wide range of multi-stage stochastic models of carcinogenesis accounting for initiation, promotion, and progression^{16}^{,}^{17}. An earlier, distinct mathematical model of carcinogenesis by Armitage and Doll allows for several rate-limiting stages, but not clonal expansion of IC^{18}.

Estimates of excess LC risk attributable to radiation from medical imaging are largely based on models derived from data on Japanese atomic bomb survivors from Hiroshima and Nagasaki, collected as part of the extended Life Span Study (LSS). These estimates are approximately two orders of magnitude lower than needed to explain the LC incidence trends in the MLP^{19}^{,}^{20}. Current estimates of chest x-ray lung organ dose range from 0.06 – 0.25 mSv^{21}^{,}^{22}, whereas dose estimates reported at the time of the Mayo Lung Project were higher (approximately 0.7 mSv^{23}). Estimates of excess LC risk attributable to chest x-ray rely on linear scaling of estimated ERR/Sv^{24}; if the true model is somewhat less than linear, then estimates of excess LC risk based on these models will be higher. Moreover, the excess LC risks derived from the LSS may be substantially underestimated with respect to the MLP cohort, due primarily to the MLP participants’ older ages and therefore, longer smoking histories at the time of enrollment.

According to the TSCE model, if the pool of NC remains constant in adults and radiation acts only to transform normal cells to IC, the absolute excess LC risk attributable to radiation exposure should not increase with age-at-exposure. Several analyses of the LSS data have found it to be consistent with a TSCE model parameterization that assumes radiation acts only to induce NC to become IC^{25}^{,}^{26} (initiation effect). An age-at-exposure effect on radiation-induced initiation rates is rejected despite evidence that birth cohort effects are significant in estimating the parameters of the TSCE model^{25}. A study using the Armitage-Doll model also supports the absence of an age-at-exposure effect on stage transition rates for most solid cancers^{27}. An analysis that merges data on smoking history and radiation exposure suggests that the observed higher excess relative risk among older LSS individuals is a spurious finding that reflects differences in smoking histories by birth cohort and finds the joint effect of radiation exposure and smoking is consistent with an additive but not a multiplicative effect^{28}. This latter result supports a model in which both radiation exposure and smoking act synchronously to increase the pool of IC (via initiation), but radiation does not act on the IC directly (via promotion or transformation).

The original publication of the LSS data reports that the excess LC relative risk is nearly three times higher in individuals whose age-at-exposure is greater than 40 compared to individuals whose age-at-exposures are between 25 and 39 years and persists over time^{29}^{,}^{30}. As discussed, this finding has been attributed to birth cohort differences in smoking histories among LSS participants^{28}^{,}^{30}. However, a close inspection of the LSS data incorporating smoking histories indicates that this data subset is approximately half the original size with an age-at-exposure distribution shifted to the left due to the requirement that cohort members be alive at the time smoking histories were collected. The excess LC mortality risk observed in the MLP is restricted to the group of individuals over the age of 60 at the conclusion of the MLP, a group with virtually no representation in the combined smoking and LSS dataset^{3}^{,}^{28}.

Other modeling studies have suggested that the LSS data is more consistent with a radiation effect on both promotion and initiation^{31}^{,}^{32} than with an initiation effect alone. Furthermore, due to a delay in data collection after the bombings: “second-hit” lung cancers arising during the earliest time window are necessarily absent from the dataset. Additionally, several case-control studies examining the risk of second cancers following radiation treatment for a primary cancer do suggest a significant super-additive effect of smoking and radiation^{33}^{,}^{34}^{,}^{35}.

Theoretical considerations of the TSCE model may help reconcile the conflicting studies on excess LC risk. If radiation acts on both rate-limiting stages, its observable effect on the second stage will be negligible in younger individuals due to the small number of IC^{14}. As individuals age, the effect of radiation on the second stage will increase due to the growing population of IC. Smoking will tend to enhance this effect of age, due to its role in promotion and initiation. Consequently, the absence of an age-at-exposure effect and an observed additive relationship between smoking and radiation are expected as long as the accumulated number of IC is small. Current models derived from the LSS data assume that either excess LC risk or excess LC relative risk depend on gender and smoking history but not on age-at-exposure^{19}^{,}^{20}, most consistent with a relatively young exposure group such as the LSS data subset from which they are derived^{28}.

The original TSCE model parameterization assumes that if an acute exposure acts on the second transition rate, then the excess risk will be evident after a short lag time following the exposure. A literal interpretation of the TSCE model is that IC comprise a homogeneous group of cells that have all accumulated a single mutation. The “second-hit” occurs when the complementary gene is mutated, resulting in a loss of function phenotype. We allow for the population of IC to be heterogeneous, while sharing a common growth advantage as well as an increased probability of acquiring a subsequent mutation. However, the number of mutations in any particular IC is random as are the number of total mutations needed to result in a cancer phenotype. It follows that an acute radiation exposure may act on an existing population of IC to either directly induce a second hit or to irreversibly increase the probability of the second transition.

The MLP was initiated in 1971 and completed on July 1, 1983^{1}^{,}^{2}. A summary of the MLP findings is presented in Table 1. The original data collected during the MLP trial were made available to CISNET participants on its website. These data contain individual patient medical and smoking histories at the time of enrollment, annual follow-up questionnaire results, chest Xray visit dates and findings, cytology results as well as death records. Data from the two follow-up studies was provided by Pamela Marcus, PhD, of the National Cancer Institute^{3}^{,}^{4}. We merged the original MLP data with the follow-up data to form a unified MLP dataset.

A mathematical model of the natural course of LC in a screened population was previously described and calibrated to the initial seven years of MLP data^{10}. We modify the model of the natural course of LC in two ways. We use a table of smoking-history and age-dependent annual hazard rates to simulate the age at death by other causes than LC. This hazard table was developed by Marjorie Rosenberg, PhD and provided as a CISNET resource (www.cisnet.cancer.gov). Furthermore, we sample age at enrollment from the empirical distribution of MLP participants. We calibrate to the observed early stage incidence, late stage incidence, LC deaths, and other-cause deaths in the first seven years of the MLP (N=2,500).

We project LC mortality and incidence in the follow-up period, extending the time frame of the simulation from seven to 24 years. We separately employ two different models of screening frequency in the follow-up period. The first model assumes that, upon completion of the MLP, the screen frequency of adherent screening arm participants reverts to baseline levels of random periodic screening. The second model assumes that, upon completion of the MLP, screening arm participants receive annual screening for a period of random duration, averaging ten years, after which they revert to baseline levels of random periodic screening.

We describe a biological framework for estimating excess LC risk resulting from repeated chest Xray screens. As in the TSCE model, we assume two rate-limiting steps in the carcinogenesis process, namely the transition from NC to IC and the transition from an IC to the first MC. Due to their smoking histories, we assume that by age 40, MLP participants have accumulated *x*_{0} IC, which is an exponential random variable with parameter λ: *x*_{0} ~ exp(λ). We assume a minimum number *z* of IC has accumulated in an individual by age 40, so that *x*_{0} has a lower bound of *z*. Whereas the total number x_{0} of IC at age 40 is stochastic, we assume that subsequently, the number of IC increases deterministically each year by a common factor {*c _{i}*}, where

In our model, radiation acts directly upon the IC to increase their genetic instability. For the periods during and prior to the MLP, we assume that the distribution of age of LC onset is not influenced by radiation exposure due to screening. However, after the MLP has concluded, the probability that an IC becomes a MC increases to μ_{s} + *k*μ_{r}, for an individual having received *k* screens. Consistent with the assumption of deterministic growth of IC, the number of IC is assumed to be sufficiently large such that radiation exposure does not influence the total number of IC nor their annual growth rate.

To summarize our estimation methodology, we first optimize the fit of the triangular LC age of onset distribution to the control arm data. This step entails updating the probability that a single IC transforms to an MC in a given year to μ′_{s} = μ_{s} + μ_{adj}, and estimating the ratio *r _{a}* = (μ

The annual probability of LC onset at age *i* in the absence of radiation exposure, *k _{i}*, can be expressed as a function of the model parameters as follows:

$${k}_{i}={\displaystyle \underset{z}{\overset{\mathrm{\infty}}{\int}}{(1-{\mu}_{s})}^{{\displaystyle \sum _{t=40}^{i-1}{x}_{0}{c}_{t}}}[1-{(1-{\mu}_{s})}^{{x}_{0}{c}_{i}}]\lambda {e}^{-\lambda ({x}_{0}-z)}{\mathit{\text{dx}}}_{0},\phantom{\rule{thinmathspace}{0ex}}i=40,\dots ,85}$$

(1)

Solving the integral in (1), we obtain:

$${k}_{i}=\frac{-\lambda {(1-{\mu}_{s})}^{z{\displaystyle \sum _{t=40}^{i-1}{c}_{t}}}}{({\displaystyle \sum _{t=40}^{i-1}{c}_{t}})\phantom{\rule{thinmathspace}{0ex}}\text{ln}(1-{\mu}_{s})-\lambda}+\frac{\lambda {(1-{\mu}_{s})}^{z{\displaystyle \sum _{t=40}^{i}{c}_{t}}}}{({\displaystyle \sum _{t=40}^{i}{c}_{t}})\phantom{\rule{thinmathspace}{0ex}}\text{ln}(1-{\mu}_{s})-\lambda},\phantom{\rule{thinmathspace}{0ex}}i=40,\dots ,85$$

(2)

Since *c*_{40}=*1*, {*c _{i}*:

$$\lambda =\frac{{\mu}_{s}\phantom{\rule{thinmathspace}{0ex}}(1-{k}_{40})}{{e}^{-{\mu}_{s}z}-(1-{k}_{40})}$$

(3)

It follows from (2) that $\sum _{t=40}^{i}{k}_{t}}=1+\frac{\lambda {(1-{\mu}_{s})}^{z{\displaystyle \sum _{t=40}^{i}{c}_{t}}}}{({\displaystyle \sum _{t=40}^{i}{c}_{t}})\phantom{\rule{thinmathspace}{0ex}}\text{ln}(1-{\mu}_{s})-\lambda$. Setting ${x}_{i}={(1-{\mu}_{s})}^{z{\displaystyle \sum _{t=40}^{i}{c}_{t}}}$ and assigning a value to μ_{s}*z*, we can apply Newton’s method to solve for each *x _{i}* in the equation $\sum _{t=40}^{i}{k}_{t}-1=\frac{\lambda {\mathit{\text{zx}}}_{i}}{\text{ln}\phantom{\rule{thinmathspace}{0ex}}{x}_{i}-\lambda z}$, and thereby obtain solutions for {

$$k{\text{'}}_{i}\approx \frac{-\lambda z{({x}_{i-1})}^{{r}_{\mathit{\text{adj}}}}}{{r}_{\mathit{\text{adj}}}\phantom{\rule{thinmathspace}{0ex}}\text{ln}({x}_{i-1})\phantom{\rule{thinmathspace}{0ex}}-\phantom{\rule{thinmathspace}{0ex}}\lambda z}+\frac{\lambda z{({x}_{i})}^{{r}_{\mathit{\text{adj}}}}}{{r}_{\mathit{\text{adj}}}\phantom{\rule{thinmathspace}{0ex}}\text{ln}({x}_{i})-\lambda z}$$

(4)

However, our model assumes that excess LC cases attributable to screening exposure are expected only after the MLP has concluded, resulting in a further modification of (4). We define *r _{r}* = (μ′

$$k{\text{'}}_{i}\approx \frac{-\lambda z({x}_{a}^{{r}_{\mathit{\text{adj}}}}){({x}_{i-1})}^{{\mathit{\text{rr}}}_{(a,i-1)}}}{{r}_{\mathit{\text{adj}}}\phantom{\rule{thinmathspace}{0ex}}\text{ln}({x}_{a})+{\mathit{\text{rr}}}_{(a,i-1)}\phantom{\rule{thinmathspace}{0ex}}\text{ln}({x}_{i-1})-\lambda z}+\frac{\lambda z({x}_{a}^{{r}_{\mathit{\text{adj}}}}){({x}_{i})}^{{\mathit{\text{rr}}}_{(a,i)}}}{{r}_{\mathit{\text{adj}}}\phantom{\rule{thinmathspace}{0ex}}\text{ln}({x}_{a})+{\mathit{\text{rr}}}_{(a,i)}\phantom{\rule{thinmathspace}{0ex}}\text{ln}({x}_{i})-\lambda z},\forall i>a$$

(5)

We isolate the data from individuals who were alive at the end of the first seven years of the MLP trial and eligible for inclusion in the long-term follow-up analysis of LC mortality. Outcomes are coded to reflect three possibilities: the participant was alive at the end of the follow-up period, he died of LC, or he died of other causes. If a participant died of other causes, or was alive at the end of the follow-up period, then this record is censored with respect to LC onset. Given a censoring event at age *t*, age at enrollment *a*_{0}, we apply the Bayesian data-augmentation algorithm^{36} to generate an age of LC onset *x* from the distribution:

$$\text{Pr}[x=i|{a}_{0},(s+x)\ge ({a}_{0}+7)]=\frac{{k}_{i}\phantom{\rule{thinmathspace}{0ex}}\text{Pr}[s>(t-i)]{\mathrm{I}}_{\{{a}_{0}\le i<t\}}+{k}_{i}{\mathrm{I}}_{\{i\ge t\}}}{1-{\displaystyle \sum _{j=40}^{{a}_{0}-1}{k}_{j}-{\displaystyle \sum _{j={a}_{0}}^{{a}_{0}+6}{k}_{j}\phantom{\rule{thinmathspace}{0ex}}\text{Pr}[s\le ({a}_{0}+7-j)]}}}$$

(6)

The time of LC progression from LC onset to death, *s*, has a distribution which is a convolution of two exponential distributions^{10}. Using the augmented data, a likelihood function can be defined according to the following three scenarios:

- Censored data, LC onset at age
*i*after data-augmentation:$$\text{Pr}[x=i\phantom{\rule{thinmathspace}{0ex}}|\phantom{\rule{thinmathspace}{0ex}}{a}_{0},(s+x)\ge ({a}_{0}+7)]=\frac{{k}_{i}\phantom{\rule{thinmathspace}{0ex}}\text{Pr}[s>({a}_{0}+7-i)]{\mathrm{I}}_{\{{a}_{0}\le i\le {a}_{0}+6\}}+{k}_{i}{\mathrm{I}}_{\{i\ge {a}_{0}+7\}}}{1-{\displaystyle \sum _{j=40}^{{a}_{0}-1}{k}_{j}-{\displaystyle \sum _{j={a}_{0}}^{{a}_{0}+6}{k}_{j}\phantom{\rule{thinmathspace}{0ex}}\text{Pr}[s\le ({a}_{0}+7-j)]}}}$$ - Censored data, no LC onset after data augmentation:$$\text{Pr}[x=\mathrm{\infty}\phantom{\rule{thinmathspace}{0ex}}|\phantom{\rule{thinmathspace}{0ex}}{a}_{0},(s+x)\ge ({a}_{0}+7)]=\frac{1-{\displaystyle \sum _{j={a}_{0}}^{85}({k}_{j}\phantom{\rule{thinmathspace}{0ex}}\text{Pr}[s>({a}_{0}+7-j)]{\mathrm{I}}_{\{{a}_{0}\le j\le {a}_{0}+6\}}+{k}_{j}{\mathrm{I}}_{\{j\ge {a}_{0}+7\}})}}{1-{\displaystyle \sum _{i=40}^{{a}_{0}-1}{k}_{j}-{\displaystyle \sum _{i={a}_{0}}^{{a}_{0}+6}{k}_{j}\phantom{\rule{thinmathspace}{0ex}}\text{Pr}[s\le ({a}_{0}+7-j)]}}}$$
- LC death in original follow-up dataset at age
*t*:$$\text{Pr}[d=t\phantom{\rule{thinmathspace}{0ex}}|\phantom{\rule{thinmathspace}{0ex}}{a}_{0},(s+x)\ge ({a}_{0}+7)]=\frac{{\displaystyle \sum _{j={a}_{0}}^{t}{k}_{j}\phantom{\rule{thinmathspace}{0ex}}\text{Pr}[(t-j)<s<(t-j+1)]}}{1-{\displaystyle \sum _{j=40}^{{a}_{0}-1}{k}_{j}-{\displaystyle \sum _{j={a}_{0}}^{{a}_{0}+6}{k}_{j}}\phantom{\rule{thinmathspace}{0ex}}\text{Pr}[s\le ({a}_{0}+7-j)]}}$$

We estimate *r _{adj}* using Bayesian data augmentation as follows: 1) Augment control arm data n times according to (4) and (6) with the initial condition:

To estimate *r _{r}*, we augment the study arm data n times according to (5) and (6) with initial conditions:

We incorporate the parameter *r _{r}* into the original {

Table 2 compares the simulated LC incidence and deaths in the first seven years to the deaths and incidence observed in the MLP. Figure 1 illustrates the simulated mean annual incidence cases for both the stop-screen and ongoing-screen models and the simulated annual LC deaths for the stop-screen model over the duration of the median follow-up period of mortality and incidence. The difference in the simulated mean annual LC deaths between the stop-screen model and the ongoing-screen model is negligible and only the stop-screen model is shown. Table 3 summarizes these simulation results.

Simulated annual LC incidence, annual LC deaths and cumulative differences in LC incidence and LC deaths (screening-control) a) Mean counts of LC cases per year assuming a stop-screen model. b) Mean counts of LC cases per year assuming an ongoing screening **...**

Simulated LC incidence and deaths compared to MLP data in the 7-year period after prevalence screen.

We evaluated the stochastic variability of our simulation results with respect to the observed cumulative LC incidence and mortality differences (screening – control). Among the 2,500 individual trajectories in our simulations, we report the frequency of observing a difference in the cumulative LC incidence greater than or equal to 85 cases after 23.5 years of follow-up. In the stop-screen model, there were 10 (*p*=0.004) such trajectories whereas in the ongoing-screen model, there were 26 (*p*=0.0104) such trajectories. We also report the frequency of observing a difference in the cumulative LC deaths (screening – control) greater than or equal to 34 cases after 20.5 years of follow-up. In the stop-screen model, there were 132 (*p*=0.0528) such trajectories, and in the ongoing screen model, there were 106 (*p*=0.0424) such trajectories (Table 4).

Beginning with the initial value of *r _{adj}* = 0.925 in the augmentation procedure, we obtain a median MLE of

Incorporating the parameter *r _{r}* = 1.008 (p=0.0021) into the original age-at-onset distribution, we estimate that the 10-year excess LC probability for a 60-year old male smoker having received 10 chest X-ray screens is 0.574%. The relationship between 10-year excess LC probability, attained age, and screen frequency is depicted in Figure 2.

We repeat the MLP simulations after updating the annual probabilities of lung cancer onset {*k*′_{i}} with our obtained estimate of *r _{r}*. Within the spectrum of 1,000 individual trajectories in our simulations, we examined the frequency of observing a difference in the cumulative LC incidence (screening – control) greater than or equal to 85 cases after 23.5 years of follow-up. In the stop-screen model there were 42 such trajectories (

The usual interpretation of the MLP findings is that there is strong evidence that screening for LC is plagued by overdiagnosis. In particular, there was no reduction in LC mortality after the trial or after long-term follow-up^{3} and the cumulative incidence of total LC cases in the control arm did not “catch-up” to the cumulative incidence of total LC cases found in the screening arm^{4}. However, overdiagnosis does not explain the excess LC deaths in the screening arm or the steady increase in LC cases after the end of the MLP. At the end of 20.5 years of median follow-up, there were 34 more LC-attributed deaths in the screening arm compared to the control arm. There were 31 more reported LC cases in the screening arm versus the control arm at the end of the initial seven years of the MLP. At the end of 23.5 years of median follow-up, there were 85 more LC cases detected in the screening arm compared to the control arm.

We examined the stochastic variability within our simulation model encompassing the time frame of the long-term incidence and mortality follow-up and discovered that the observed long-term incidence and mortality results deviate significantly from the expected mean behavior. A difference in the cumulative incidence of 85 or more cases after 23.5 years of follow-up occurred in only 0.40% and 1.04% of our simulation trajectories in the stop-screen and ongoing screen models, respectively. A difference in the cumulative number of LC deaths of 34 cases or more after 20.5 years of follow-up occurred in only 4–5% of trajectories. While the observed data do lie within the range of variation that our model forecasts, their occurrence would be unlikely.

While our simulation model forecasts the total number of LC deaths nearly exactly in the control arm, our model underestimates the number of LC incidence cases by 53 cases in the control arm, excluding any projected cases among participants having unknown LC status (Table 3). A key source of information used to assign a participant’s LC status was based on next-of-kin questionnaire information^{4}. The ability of next-of-kin to provide accurate information was determined by a sensitivity study based upon the ability of next-of-kin to correctly report LC in already known LC cases. Sensitivity was shown to be greater than 90%. However, a specificity study demonstrating the ability to correctly report the absence of LC was not performed. Low specificity may have resulted in an inflation of reported LC cases, thereby explaining the lack of consistency between reported LC incidence and mortality in the follow-up period.

We sought a mechanistic explanation for the observed excess LC risk among the screening arm participants. It has been suggested that the initial randomization procedures were flawed but this hypothesis has generally been discounted^{4}^{,}^{37}. The TSCE model predicts an age-at-exposure effect when the population of intermediate cells is large, such as expected in a population of high-risk smokers. The excess LC mortality in the study arm participants was restricted to trial participants older than 55 at the time of enrollment and was greatest in individuals over the age of 65 at the time of enrollment. Furthermore, among screening arm participants, a higher number of screens received during the MLP trial corresponded to a higher frequency of LC incidence and deaths reported in the follow-up period.

A Bayesian framework allows us to incorporate a single parameter of excess LC risk, namely *r _{r}*, into an existing distribution of age-at-onset based on the triangular distribution. An advantage of our model-based estimation methodology is the improved power compared to traditional statistical methods for estimating excess risk. The parameter

Incorporating excess LC risk into the simulation model of the natural course of LC increases the likelihood of observing the differences in cumulative incidence and mortality (screening-control) as high as those observed in the reported long-term follow-up. We note two discontinuities between our estimation procedure and the simulation model. First, because we consider the number of screens to be a pre-existing factor in our estimation data-set, we eliminate any LC deaths that occurred within the first seven years of the MLP, including the excess 12 LC and study-related deaths in the study arm. Second, our simulation model of the MLP incorporates an estimate of early-stage disease curability of 35% and forecasts a net mortality benefit of six to seven deaths by year twelve. In our estimation procedure, the null hypothesis assumes equivalent LC expected incidence and mortality in the screening and control arms following the conclusion of screening. This latter feature reflects the potentially conservative nature of our estimates of LC excess risk.

In our view, the MLP results reiterate the value of the randomized trial in providing a measure of net mortality benefit, given uncertainty of the nature and quantification of the risks and benefits associated with early detection. In contrast to previous papers, our study suggests that excess LC risk attributable to being a member of the screening arm of the MLP may provide a more satisfactory explanation of the MLP outcome than overdiagnosis. A reliance on an aggregate measure of trial efficacy to reflect one potential contributor of efficacy can be misleading. Our analysis further suggests the need for novel quantitative methods to directly estimate the stochasticity of tumor progression, and likewise, overdiagnosis.

As for the nature of the excess risk attributable to screening, a natural hypothesis invokes mutagenic effects of radiation. Our mathematical model has been formulated in such terms. However, other hypotheses might be invoked, such as a weakening of immunity by the stress of unknown nature caused by frequent screening. Since mutation rate results from a balance between DNA damage and repair, as well as removal of transformed cells, the net effects cannot be easily attributed to a single cause. Ideally, in the future, the risks associated with screening for LC can be fully understood and successfully managed in order to maximize the number of lives saved by early detection.

We thank Pamela Marcus for her help in supplying the necessary data for our analysis. Deborah Goldwasser thanks Christopher Amos for his mentorship throughout the R25 Cancer Prevention Research Training Program.

Grant Support: This work was supported by the National Cancer Institute CISNET grant U01CA097431. Deborah Goldwasser is supported by a National Cancer Institute cancer prevention fellowship awarded by the University of Texas M. D. Anderson Cancer Center's Cancer Prevention Research Training Program, R25 CA57730, Robert M. Chamberlain, Ph.D., Principal Investigator.

There are no financial conflicts of interest to report.

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