Wu et al. reply

We recently reported a strong correlation between the incidence of cancers and the number of stem-cell divisions in the corresponding normal tissues1. We interpreted this correlation to mean that random genomic alterations (termed replicative or intrinsic) arising during DNA replication, as well as mutations that arise owing to environmental (extrinsic) and inherited factors, have important roles in tumorigenesis1–3; however, we did not quantify the contribution of intrinsic versus extrinsic factors to any cancer type1. In their study, Wu et al.4 estimated an upper bound for the contribution of intrinsic factors to many cancer types, concluding that intrinsic factors account for “less than 10–30%” of cancer cases. We believe that several of the assumptions made by these authors led them to underestimate the role of intrinsic factors, and we further show that one of their methods leads to the conclusion that extrinsic factors account for > 85% of the risk in situations in which extrinsic factors have no role. There is a Reply to this Comment by Wu, S., Zhu, W. & Hannun, Y. A.  (2017). On the basis of the data in ref. 1, Wu et al. chose seven cancer types to obtain a ‘lower bound intrinsic risk’ (LBIR) line, representing cancers that they assumed to carry a zero extrinsic risk (figure 3a in ref. 4). Instead of using the cancer types at the bottom of figure 3a in ref. 4 to define an LBIR line, one could analogously use cancer types at the top of figure 3a in ref. 4 to define an ‘upper bound extrinsic risk’ (UBER) line (Methods). 74% of the seven cancer types nearest this line are preventable (http://www.cancerresearchuk.org/cancer-info/cancerstats/causes/preventable) and 90% would therefore be a conservative estimate for the extrinsic risk in the cancers on this line. Using this UBER line to determine the risk of the 24 other cancer types, on average, 80% of the total risk can be calculated to result from intrinsic factors . In contrast, using the LBIR line, on average, only 7% of the total risk is calculated to result from intrinsic risks (extended data table 1 in ref. 4). If one assumes values of extrinsic risk for the UBER line that are inconsistent with epidemiologic evidence (for example, extrinsic risk < 25% or ≥ 99%), the risks attributable to intrinsic factors are either extremely high or extremely low . Boundary-based approaches can therefore yield widely variant conclusions simply depending on whether an upper or lower boundary is chosen and the fraction of extrinsic risk the boundary is assumed to represent. The estimates for the lifetime number of stem-cell divisions are noisy given the many different and complex biologic experiments required for their determination. In our original paper, we performed a robustness analysis by assessing the effect of noise on all cancer types analysed1. Because the lifetime number of stem-cell divisions in each organ is critical for the definition of the LBIR line, and for the distance of a cancer type from the LBIR line, noise in the stem cell estimates could strongly affect estimates of extrinsic risk. Wu et al. recognized this problem and performed a robustness analysis. However, we believe that the effects of noise were not taken sufficiently into account for defining the LBIR line; this line forms the baseline to which all other cancer types are compared. We performed simulations to evaluate the effect of noise on the data used to obtain the LBIR line and on the conclusions reached by Wu et al. . A typical simulation in which the extrinsic risk was assumed to be 10% is shown in Fig. 2a. The introduced noise transforms the green dots, representing the true values, into the red dots. The positions of all the red dots not on the green line in Fig. 2a are artefacts of noise. The histogram  2b shows the aggregate results of 10,000 such simulations. The LBIR approach overestimated the fraction of risk attributable to extrinsic factors; the median extrinsic risk was estimated to be 86% in these 10,000 simulations, although the assumed true risk was 10%. In fact, the median extrinsic risk was incorrectly estimated at 86% of the total risk, regardless of whether the true extrinsic risk was 0%, 100%, or any value in between. Our reading of the methods adopted by Wu et al. indicates that they assumed a linear relationship between cancer incidence and stem-cell divisions among cancer types with the same extrinsic risk. A corollary of this assumption is that cancer incidence in a tissue can be determined exclusively by the number of stem-cell divisions in the tissue and the degree of extrinsic risk. We do not believe that this assumption of linearity is justified because it disregards other factors that could influence incidence, such as the number of required mutations. Suppose, for example, that cancer types ‘A’ and ‘B’ have identical extrinsic risks and identical stem-cell divisions. The linearity assumption mandates that the incidences of cancer types A and B would be identical. However, figure 4 of ref. 4 demonstrates that if cancer type A requires two mutations to progress to malignancy, and cancer type B requires three mutations, then the incidence of cancer type A will be orders of magnitude higher than cancer type B. We believe that three other approaches used by Wu et al. to find a bound for the role of intrinsic risk were non-conservative, as explained in the following. First, in their analysis of Surveillance, Epidemiology, and End Results Program (SEER) cancer incidence data, Wu et al. assumed that all of the variation above the lowest value was due to extrinsic factors. But it has been documented that these incidences are affected by a variety of biological and methodological factors that are not linked to extrinsic risk—as well as by omnipresent noise (refs 5–9 and http://www.cancer.gov/research/progress/snapshots/kidney).