Modeling the Mortality Reduction due to CT Screening for Lung Cancer

Abstract

Background

The efficacy of CT screening for lung cancer remains controversial as results from the National Lung Screening Trial (NLST) are not yet available. In this study, we use data from a single-arm CT screening trial to estimate the mortality reduction using a modeling-based approach to construct a control comparison arm.

Methods

In order to estimate the potential lung cancer mortality reduction due to CT screening, a previously developed and validated model was applied to the screening trial to predict the number of lung cancer deaths in the absence of screening. Using age, gender, and smoking characteristics matching the trial participants, the model was used to simulate 5000 trials in the absence of CT screening to produce the expected number of lung cancer deaths along with confidence intervals, while adjusting for healthy volunteer bias.

Results

There were 64 observed lung cancer deaths in the screening cohort (n=7995), while the model predicted 117.7 (95%CI: 98, 139) indicating a mortality reduction of 45.6% (p<0.001). When a more conservative healthy volunteer adjustment is applied, 111.3 lung cancer deaths are predicted (95%CI: 91, 132) for a lung-cancer-specific mortality reduction of 42.5% (p<0.001).

Conclusions

These results indicate that CT screening along with early stage treatment can reduce lung cancer-specific mortality. This mortality reduction is greatly influenced by the protocol of nodule follow-up and treatment, and length of follow-up.

Introduction

Modeling has been effectively used to identify the effect of screening and early treatment on the mortality of a particular disease. Most recently, it was used to evaluate the effect of screening and adjuvant therapy on mortality from breast cancer (1). This report resulted from the collaborative efforts of a consortium of investigators, The Cancer Intervention and Surveillance Modeling Network (CISNET), sponsored by the National Cancer Institute.

The CISNET collaborators have also developed models to estimate the number of deaths for different cancers in the United States and validated them using a common national database. These models are useful in addressing the questions, which arise in evaluating screening for any cancer such as who should be screened, the frequency of the screening and the estimated mortality reduction, if any, as a result of screening.

We used a lung cancer (LC) mortality model developed within the CISNET collaboration to address the potential mortality reduction in a cohort that has undergone CT screening for lung cancer. We used the model to simulate the expected number of LC deaths that would be found in the absence of screening in a cohort that had actually received CT screening. The simulation thus provided a control comparison to estimate the LC mortality reduction due to screening.

Methods

We developed and applied a model (2) for determining the number and timing of deaths from lung cancer based on the smoking history and age of the person when they had their first, baseline low-dose CT scan of the chest. We applied the model to a cohort of volunteers who underwent CT screening for lung cancer (3–6) in New York State (NYS) for whom mortality follow-up using the National Death Index was available.

The model

Predictions and simulations of lung cancer mortality are carried out using a two-stage clonal expansion (TSCE) model (7), previously used in the lung cancer context (8–10), and modified and validated by us as part of the CISNET Lung Group’s Smoking Base Case project (2). The TSCE model is depicted in Figure 1.

Figure 1.

Two-stage Clonal Expansion Model. NC: normal cells; IC: intermediate cells; MC: malignant cells.

The TSCE model assumes that a normal cell (NC) mutates into an initiated cell (IC) in the first transition, according to a Poisson process with intensity ν(t), where t denotes the age. There are X normal cells in the tissue at birth or maturity, depending on the tissue. Then the initiated cell can duplicate or die according to a birth-death process with parameters α(t) and β(t), respectively, or further mutate into a malignant cell (MC) for the second transition with rate µ(t). After a time lag, this malignant cell is assumed to develop into a cancerous tumor with probability one. The parameters of the TSCE model are piece-wise constant over time and the model depends on the entire smoking history through these parameters. Under piece-wise constant parameters the survival function of time to the first malignant cell can be calculated exactly using recursive formulas outlined by Heidenreich (11).

This TSCE model was fit using a resampling based method allowing for estimation of risk factor dependent parameters from the combination of case-control data and prospective mortality rate data. The data for fitting smoking related parameters came from an M.D. Anderson case-control study of lung cancer (12) and the lung cancer incidence/mortality rates came from CPS-I (13) and the Nurses’ Health Study (8), for males and females respectively. The following parameters define the TSCE model depending on smoking measured in packs per day (ppd) and age t under a fixed lag-time of 6 years (2).

$$\begin{array}{l}X={10}^7\\ \nu (t)={\nu }_{0}X(1+a_1\times \sqrt{ppd})\\ \mu (t)={\nu }_0(1+a_1\times \sqrt{ppd})\\ \alpha (t)={\alpha }_0(1+a_2\times \sqrt{ppd})\\ \gamma (t)=\alpha (t)-\beta (t)-\mu (t)={\gamma }_0(1+a_2\times \sqrt{ppd})\end{array}$$

Estimates of the relevant parameters are collected in Table 1.

Table 1.

Parameter estimates of the TSCE lung cancer model fitted to mortality rates from Cancer Prevention Study 1 (CPS-I) for males and Nurses’ Health Study (NHS) for females.

Parameter	α0	γ0	ν0X	a1	a2
Males (CPS-I)	2.99	0.069	2.17	2.66	0.35
Females (NHS)	4.6	0.071	1.93	2.3	0.35

Healthy volunteer adjustment

Consideration was given as how to account for “healthy volunteer bias”, as demonstrated by Thomson et al. (14), and Pinsky et al. (15). This is a term used to describe an effect often seen in volunteer based studies where volunteers might be in better health than the general population, usually due to specific eligibility criteria. The effect results in the observed incidence of disease being lower than that in the population. This effect has been demonstrated in smokers (14) and in a screening trial (15). As the eligibility requirements for this screening study include that participants be asymptomatic at enrollment, we expect such a bias to exist. Symptoms of LC as defined in the eligibility requirements were hemoptysis (bloody cough), persistent hoarseness with worsening cough, and unexplained weight loss.

The previously described model is thus adjusted using a method we previously developed to exclude people who would have presented with symptoms prior to their age at entry, in other words, condition the simulation on individuals being asymptomatic at the time of entry into the screening study. An exponential distribution is used to approximate the empirical distribution of the time interval from clinical lung cancer (or onset of symptoms) to death from lung cancer. The mean of this exponential distribution was found using survival time data on 1190 newly diagnosed lung cancer patients at MD Anderson Cancer Center. An overall Kaplan-Meier (KM) survival curve was created from this data by re-weighting the stage-specific (AJCC I–IV) KM curves by the observed incidence proportions obtained from SEER 17. The overall KM survival curve indicated a median survival time of 17 months from lung cancer diagnosis to death. This distribution was approximated by an exponential distribution with a mean λ of 2.0 years found through the following formula, λ = (1 / ln(2)) x_med. This distribution is used in the LC mortality simulation routine as described in the next section in order to adjust for any healthy volunteer effect. As part of a sensitivity analysis, λ was varied to determine the effect of this assumption on the prediction of LC deaths.

Simulation of Lung Cancer Mortality

The probability that an individual will not die of lung cancer by age t, is defined as the survival probability denoted as S(t). In this model S(t) depends on an individual’s smoking history, d, with age at initiation, age at cessation, and number of cigarettes smoked per day, and will be referred to as S(t;d). Expected lung cancer mortality for the study is simulated based on the individual-level data on smoking history, as well as, the age at enrollment, t₀, and age at the end of follow-up, t₁, provided for the NYS cohort. Lung cancer mortality is simulated using the following routine.

For each individual a uniform(0, S(t₀; d)) random variable, u, was drawn.

1. If u ≤ S(t₁) then no lung cancer death occurs during follow-up and the simulation is retired.

2. If u > S(t₁) then lung cancer death occurs during follow-up at age, t*, computed by inverting the survival function, u = S(t*). Then, in order to adjust for healthy volunteer effect, the length of time between lung cancer diagnosis (or symptom onset) and death is simulated (exponentially distributed with a mean of 2 years) and an age at LC diagnosis is calculated by subtracting from the age at death.

   1. If the age at LC diagnosis is greater than the age at enrollment the simulation is retired.

   2. If the age at LC diagnosis is less than the age at enrollment the simulation is rejected and the individual is simulated again.

The cumulative and yearly number of lung cancer deaths per follow-up year is then calculated for each simulated study. The simulation is repeated 5000 times to compare expected lung cancer mortality and produce confidence intervals. The confidence intervals are estimated using the 2.5% and 97.5% quantiles of the 5000 simulated studies.

This approach was validated against the heavy-smokers control arm (non-asbestos-exposed) of the Carotene and Retinol Efficacy Trial (CARET) (16) including 6877 individuals (3797 males and 3080 females). The CARET study was a double-blind, placebo-controlled trial on the effect of beta-carotene and retinol in the prevention of cancer. The TSCE model and healthy volunteer adjustment were able to closely predict 357.9 LC deaths over the course of follow-up versus the observed 364 LC deaths. Since CARET consisted of heavy-smoker participants who are similar to those found in the NYS cohort, we expect the model and adjustment to provide reasonable estimates of risk in the NYS group.

The New York State (NYS) cohort (N=7995)

The NYS cohort consisted of 7995 asymptomatic volunteers with no prior history of lung cancer, who had no asbestos exposure and were 50 – 84 years of age (average 66 years) at enrollment with a history of cigarette smoking (average of 48 pack-years). The average age at initiation of smoking was 17.7 years in the cohort consisting of 2756 current-smokers and 5239 former-smokers. All participants gave informed consent under IRB-approved protocols at their respective institutions. Baseline screenings were performed in 1993–2004 (median 2001). Of the 7995 participants, 5863 had a repeat screening within 7 to 18 months of the baseline screening. Age and smoking history were documented at the time of enrollment, 90% were Caucasian, and more than 50% had attended college.

If a participant in the NYS cohort was not confirmed to be alive on December 31, 2005, a National Death Index search was performed to determine whether he/she had died before that date; and, if so, the cause of death was ascertained from the death certificate. For each member of the cohort, the duration of follow-up was calculated from the time of enrollment to the latest closing date of follow-up or to death before that date, whichever came earlier.

Standardized mortality ratio

The standardized mortality ratio (SMR), defined as the ratio of total observed to total expected deaths in the NYS cohort, was calculated using the expected deaths obtained from the model, together with its lowest attainable significance level (p-value) and its 95% confidence interval (95%CI) (17).

Results

In the NYS cohort of 7995 volunteers, 64 participants died of lung cancer. Figure 2 depicts the cumulative number of expected and observed deaths from lung cancer in the NYS cohort with the 95% confidence interval. The expected number of LC deaths in the absence of screening is 117.7 and the 95%CI ranges from 98 to 139 using a healthy volunteer adjustment with a mean of two years. The number of cumulative LC deaths levels off after 5 years due to the decrease in person-years of observation as seen in Figure 3.

Figure 2.

Cumulative expected and observed number of deaths in the NYS cohort starting with baseline enrollment (time 0) with healthy volunteer adjustment with mean length of 2.0 years.

Figure 3.

Person-years of observation per follow-up year.

Another approach to determining the mortality reduction is to calculate the SMR. The SMR was significant even when the patients non-compliant with the screening schedule were included, 64/117.7 = 0.544, indicating a mortality reduction of 45.6% (95%CI: 34.7%, 54.0%, p< 0.001). Figure 4 shows a histogram of the total number of lung cancer deaths for the 5000 simulated NYS cohorts.

Figure 4.

Histogram of the total number of lung cancer deaths over 5000 simulated studies.

Since the healthy volunteer interval may be extended due to the eligibility requirement that patients be not just cancer-free, but also asymptomatic at the time of enrollment, a sensitivity analysis was done to analyze the effect of assumptions relating to the length of this interval. Data on symptom presence and duration of the 1190 lung cancer patients from MD Anderson was used to further estimate the length of the symptom-extended healthy volunteer interval. As described previously, KM curves were analyzed and an exponential distribution with estimated mean length of 2.3 years was found to describe the time between symptom onset and death from lung cancer. Using this adjustment, simulations were repeated but conclusions did not change with 111.3 predicted LC deaths (95%CI: 91, 132). The estimated SMR 0.575 still showed a highly significant (p< 0.001) LC-specific mortality reduction of 42.5% (95%CI: 29.7%, 51.5%). Figure 5 shows a graph of the cumulative number of LC deaths per follow-up year for each of the 2 healthy volunteer interval length adjustments.

Figure 5.

Cumulative LC deaths. Modeled data corrected for the healthy volunteer effect using two different values of the mean time from diagnosis to LC death (2 years, red; and 2.3 years, blue). Dotted lines denote the limits of the corresponding 95% confidence intervals. Observed cumulative deaths counts (purple) plotted for comparison.

Discussion

For the NYS cohort, the model predicts 117.7 LC deaths over the 10 years of follow-up after adjusting for healthy volunteer effect, compared to the 64 observed deaths. This analysis suggests that CT screening protocol followed by its associated early treatment does provide a mortality benefit. In this analysis we chose to use an exponential distribution with a mean of 2.0 years to model the time between clinical lung cancer diagnosis and death based on survival time data from 1190 newly diagnosed lung cancer patients at MD Anderson Cancer Center. The underlying TSCE risk model and this exponential distribution were validated against the control arm of CARET where it was able to accurately predict the number of LC deaths.

Adjustments for healthy volunteer effect are important in the context of screening studies. Pinsky et al. (15) recently demonstrated substantially lower than expected overall mortality in both arms of the PLCO screening trial, which could only partially be explained by the demographic and risk profile differences between trial participants and the general population. The authors hypothesized that subjects with certain chronic diseases or conditions that strongly predispose to death over the next 5–10 years were unlikely to volunteer for the PLCO. Therefore, the PLCO trial population, as well as other screened populations (18–19), does not represent the general population in terms of mortality. However, the authors (15) noted that cancer incidence and mortality in the PLCO (excluding cancers for which the participants were screened) were closer to those in the general population than overall mortality, although standardized incidence and mortality ratios for individual cancers varied widely and were lower than in the general population. The study (15) does not report the SMR for lung cancer specifically (since lung cancer is one of the cancers for which the population is being screened) or the risk factor-adjusted SMR for all cancers combined. A healthy volunteer effect in the NYS study, resulting in part from the fact participants with suggestive LC symptoms are not eligible for the study, justifies the corrections applied in the current analysis. Importantly, our analysis takes into account the gender and smoking histories of study participants, which obviates the necessity of further risk factor adjustments. Since the exact magnitude of the healthy volunteer effect in the lung cancer context is not possible to estimate, this constitutes one of the limitations of our analysis. While assuming a healthy volunteer interval of 2 years may not be a fair generalization nationally, the choice of this longer interval results in exclusion of more simulated patients with LC, which in turn reduces the contrast between the expected and observed mortality and makes the comparison more conservative. Yet the SMR remained significant even when a longer time interval from symptoms to LC death estimated for the MD Anderson population was assumed. This time interval is likely to be longer than that for an average LC patient in the US.

Other modeling approaches have been used to evaluate the effectiveness of CT screening (20–21). McMahon et al. (20) used the Lung Cancer Policy Model (LCPM), a comprehensive microsimulation model of lung cancer development, progression, treatment, and survival. It compared model results in the absence of screening with the Mayo CT screening study (22) and found that a mortality reduction of 28% in cumulative lung-cancer mortality from 5 annual rounds of screening. Interestingly, when the model and methods presented in this paper are used to simulate LC deaths using gender and smoking history data from the Mayo CT cohort, it also predicts a 28% reduction in lung cancer mortality although the reduction was not statistically significant (95% CI: −11%, 48%). Another study comparing the mean sojourn times of 6 published CT screening studies estimated a potential 23% lung cancer mortality reduction under annual CT screening after 10 years of follow-up (21). A third study (23) used a model to estimate the mortality reduction of CT screening of 3210 participants in 3 studies and reported no mortality reduction. It is possible that Bach’s model (23) is not well applicable to the Italian Istituto Tumori study because of differences in the chemical composition of US and European cigarettes. Also, the Bach et al. study did show a mortality reduction in the Mayo Clinic study, which although not statistically significant seems consistent throughout the study duration (Fig. 1, panel K of Bach et al. 2007); however, this effect was lost when the 3 studies were combined. Finally, the higher risk of LC in the Moffitt Center study, due to high prevalence of patients with COPD, might not have been adequately taken into account. Further, the predicted confidence interval in the Bach et al. study was consistent with as much as a 30% reduction in lung cancer deaths.

The efficacy of CT scanning as a screening tool for lung cancer is an important and contested topic. As more data becomes available, it should become apparent whether it can be reliably used to lower LC mortality. If it is proven effective, then more analyses will be needed to determine which individuals should be screened, how often they should be screened, and how should the nodules detected be managed. The results from the randomized National Lung Screening Trial are anticipated but may not fully answer questions about efficacy because instead of being offered the standard care, with no screening recommended, the control group is being screened with x-ray, which will bias results towards underestimating any observed mortality benefit.