Modeling carcinogenesis for smokers and never smokers
As detailed in the Results, we separately fitted carcinogenesis models for current and never-smokers. The underlying philosophy was that individuals who develop lung cancer without active smoking histories, that is, at much lower levels of exposure, may have a very different genetic background from those who required long-term exposure to develop the disease. Indeed, as suggested by , relative lung cancer risk associated with supoptimal DRC decreased with increased smoking exposure. This can be explained by the fact that conditional on a person developing lung cancer with little or no smoking exposure, this person’s relative risk associated with impaired DRC, logically is increased. Vice versa, with heavy smoking exposure, the relative risk associated with other factors is decreased, because smoking overwhelms even a relatively resistant phenotype.
One might expect that this would be reflected in baseline mutation rates being higher for never smokers with lung cancer than for smokers before smoking initiation. These latter mutation rates are not directly represented in our response functions. However, if the coefficients a2
were negative, this would suggest such an effect. As seen in , the estimate of a3
was indeed negative, but not significantly so, making the interpretation difficult. The fact that neither a2
were negative represents the tradeoff between trends before and after smoking initiation, which were jointly represented in the model. Meza et al
found that a joint model for smokers and never-smokers resulted in estimates not very different from those based on 2 separate models.
Biological interpretation of the parameters
DRC may have an effect on carcinogenesis at the initiation and/or malignant transformation phases, because at these transitions, mutations are required. Positive values of a1 and a4 indicate an association between suboptimal DRC and earlier onset of lung cancer. In the presence of cigarette smoking, the transition rates can be altered. In our model, parameters a2 and a3 referred to such changes (see also the definitions of the first and second variants of response functions). The impact that cigarette smoking had on initiation and malignant transformation can be either that the 2 transitions were accelerated or a new competing carcinogenesis pathway emerged as a result of exposure to high doses of carcinogens. Note that in the second variant of response functions, the terms a2 and a3 cannot be used to distinguish between these two possibilities. The parameters a2 and a3 were jointly estimated from the period before and after initiation, and therefore, there was a tradeoff between the background rate and the rate of the response to smoking. One can hypothesize that in the absence of smoking, the carcinogenesis process via path 2 () has a much lower probability of occurring than that via path 1, due to an extremely low malignant transformation rate and slow proliferation of IC2. However, still there could be generation of IC2 from NC, and it is possible that this process is faster than transition from NC to IC1 even before cigarette smoking starts. After initiation of smoking, the malignant transformation from IC1 to MC could be suppressed and most MCs come from path 2.
Cigarette smoking also affected the clonal expansion of initiated cells in our analysis. The TSCE models the proliferation of initiated cells as a birth–death process and its derived survival probability function largely depends on the net growth parameter α – β. Parameter a5*(log(40) − log(20)) represents the change in the net growth rate when increasing the smoking intensity from 20 cig/day to 40 cig/day.
Male never and current smokers
For male never smokers, the effect of suboptimal DRC on initiation and malignant transformation rates was significant (a1 = 3.02, 95% CI: [2.7, 3.9]) (). The cumulative lung cancer risk for never smoker men with suboptimal DRC was almost 6 times that for those with optimal DRC. For current smokers, the estimated coefficient a5 showing the effect of smoking intensity was about 0.16, significantly greater than zero.
For current smokers, the initiation rate was significantly higher than that in never smokers (a2 = 3.67, CI: [0.23, 13.73]). In contrast to the initiation rate, the malignant transformation in current smokers occurred at a significantly reduced rate when compared with never smokers (a3 = −0.69, CI: [−0.91, −0.19]). Again, this is a result of the lower transformation rate during either non-smoking or smoking period, or both. However, it is unlikely that cigarette smoking slowed down the malignant transformation process. Therefore, it was the background malignant transformation rate in current smokers that was likely to be much lower than that for never smokers. Despite the slower malignant transformation, smokers still carried a considerably higher risk of developing lung cancer when compared with never smokers, as the promotion effect of cigarette smoking dominates the initiation and malignant transformation effect.
Female never and current smokers
For female never smokers, DRC also significantly contributed to initiation and malignant transformation rates (a1
= 3.36, 95% CI: [2.99, 4.00]) (). Its contribution was even higher in current smokers (a4
= 11.46, 95% CI: [7.97; 15.14]) (). Cigarette smoking not only significantly increased the proliferation rate of initiated cells (a5
= 0.38, 95% CI: [0.21, 0.65]) () but also elevated the initiation rate in current smokers (a2
= 3.53, 95% CI: [0.15–7.42]) (). The promotion effect coefficient a5
was more than twice that of males, suggesting increased smoking intensity confers a higher lung cancer risk for women when compared with men. Unlike men smokers, in whom the a3
coefficient was significantly negative, in women a3
was not different from zero (a3
= −0.34, 95% CI: (−0.74, 1.68), ), suggesting (i
) a higher malignant transformation rate in smoking women than men and (ii
) no difference between the malignant transformation rate in women smokers and never smokers. This finding is in agreement with a number of studies that suggested a greater smoking-associated lung cancer risk in women than men.24–27
However, other studies did not show this effect.28–30
Previous analyses of lung cancer data using the TSCE have also reported some gender differences in the smoking-related parameters of the TSCE model.23,31
In particular, in the NHS/HPFS analysis, Meza et al
also found a higher smoking-related promotion among women. However, contrary to the findings reported here, they found a lower smoking effect on malignant conversion among women.
Limitations of the method
For multistage expansion modeling including TSCE models, alternative models with different assumptions for the biological process may yield similar fit and dose-response relationships. In addition, other empirical models may fit these data equally well. For instance, the Doll and Peto model, a multiplicative power model, and its extended version produced a slightly better fit than TSCE when used to assess lung cancer rates in CPS-I cohort.32
However, as a biological-based model, TSCE model has the potential to offer insights into the underlying mechanism while the formulation of other models was largely driven by data fitting. In our analysis, the model was formulated using parameters for smoking related dose-response on birth and death (parameters a5
). There are 2 smoking value bins (20 and 40 cig/day) and essentially any functional form can be used to relate 2 parameters to 2 dose values while achieving the optimal assignment. This does not constitute a difficulty as long as this response function is not extended beyond the 2 smoking value bins.
As already mentioned, in the second variant of response functions, the terms a2 and a3 cannot be used to distinguish between the two ways in which cigarette smoking may influence initiation and malignant transformation, that is, that either the 2 transitions are accelerated or a new competing carcinogenesis pathway emerges. This limitation is a consequence of nonidentifiability of the TSCE model.
There are some limitations concerning the data used. First, causal relationship between lung cancer development and suboptimal DRC has not been established yet. However, the fact that DRC does not depend on stage10–12
suggests that DRC is a risk factor rather than a disease marker. Future research is needed to draw causal inference in a prospective study setting. Second, our conclusions are subject to sampling error as the sample size of the case–control data is not large after stratification by gender and smoking status. Furthermore, a violation of the assumption that the data from the CPS-II study and the M.D. Anderson study are compatible may result in different conclusions as well.
Relation to other models
This study builds the response function using the original biological parameters as a function of risk factor measurements. This makes the interpretation of the estimated parameters more straightforward. Unlike our model, some studies include an extra variable, the waiting time from the first malignant cell to a detectable tumor. Because of the nonidentifiability problem, we decided not to adopt this approach because adding an extra parameter produces additional variation to the final parameter estimates. Despite some differences in the model assumptions and parameter set-up, our model results show that cigarette smoking increases the proliferation rate, which corroborates previous findings.16–18
However, whether or not smoking impacts the malignancy transformation is inconclusive in earlier studies. Our model suggests that among men the malignant transformation rate for current smokers is lower when compared with that for never smokers. For women, there is no significant difference.