To our knowledge, this is the first study to estimate the population health impact of introducing RRPs in Germany by SEG. Depending on the Scenario, the health gains would have reached 34–83% of that from immediate smoking cessation, regardless of the SEG. For each of Scenarios 3, 6 and 7, the gains in the lower SEG population (B) compared with those in the higher SEG population (A) would have been more than twice as high for DD and more than 1.5 times as high for YLS. Depending on the Scenario, these excess gains in B than in A corresponded to a greater DD by 27,004 to 62,262 and a greater YLS by 215,000 to 526,000.
In our companion paper, which took no account of the SEG, we estimated that, in Scenarios 1 (Complete cessation), 3 (Complete switch to RRPs — 50% HnBs, 50% ECigs), 6 (Conversion), and 7 (Full Conversion), the DDs for the sexes combined and all four diseases combined would have been, respectively, 216,650; 179,470; 75,597; and 81,293. According to the results in Tables 5 and 6 in this paper, which did take into account the SEG, the corresponding estimates were quite similar (220,409; 182,424; 74,395; and 78,300, respectively) to those in our companion paper. Our results suggest that taking SEG into account had little effect on the overall estimated DDs. They also show that substantial DDs were seen in both SEG groups, A and B, with the drops being about twice as high in B as in A.
The estimates of population health impact in both SEGs are likely to be conservative for the three main reasons discussed in our companion paper — that deaths were only counted for four diseases, that only a 20-year follow-up period was considered, and that we failed to account for the possibility that cigarette smokers who took up HnBs and ECigs might subsequently be more likely to quit cigarettes than those who continued as exclusive smokers. We also note that the RRs we have used for current and former smoking (on the basis of published meta-analyses) are lower than those used by others (on the basis of specific studies) when estimating deaths attributable to smoking in Germany . Using higher RR estimates would have increased our DD estimates. However, our estimates might be optimistic if the rates of uptake of HnBs and ECigs are lower than what we have assumed, or if, in fact, taking up HnBs and ECigs makes smokers less likely to quit or increases their cigarette consumption. There is little real-life evidence, however, that the latter is the case.
While there is mounting scientific consensus that RRPs like ECigs and HnBs represent less risk than cigarettes [26, 27], there has been debate on whether smoking-related health inequalities between SEGs could be reduced by smokers switching to RRPs . Some studies have found more advantaged smokers to be more likely to use ECigs in the UK  or HnBs in Germany , whereas others have recently observed that ECigs might be helping disadvantaged smokers quit . ECigs might have contributed to some of the highest UK smoking cessation rates so far, with parity across SEGs . This suggests that ECigs worked as quitting aids for low SEG smokers previously not reached by conventional methods and can be explained by the high acceptability of RRPs as substitutes for cigarettes, as witnessed from ECigs being the most popular quitting aids in the UK  and Germany [17, 32]. It is notable that conventional pharmacotherapies for smoking cessation are more commonly used in Germany by smokers with higher incomes [17, 32], thus possibly increasing health inequalities. The question whether this is linked to the affordability of pharmacotherapies or to factors related to education has not been conclusively answered. While a recent study found higher income of German smokers to be associated with more frequent use of pharmacotherapies, neither income nor education affected quit success . On the other hand, use of the most popular quitting aid ECigs was not associated with income or education, underlining that RRPs could be a promising addition to public health strategies aimed at providing equal chances for smokers from different SEGs to exit out of cigarettes .
Data from several individual countries have shown that lower social grades and level of education are significantly linked to inaccurate harm perception of ECigs [26, 33]. Currently, 61% of German smokers falsely perceive ECigs as equally harmful or more harmful than cigarettes, with only 5% correctly perceiving them as much less harmful . Given that ECigs are more likely to be used for smoking cessation if they are perceived as less harmful than cigarettes , misperceptions might well be discouraging many cigarette smokers from trying RRPs. Improving current perception is particularly important for disadvantaged populations of smokers, such as those in lower SEGs, who could benefit more from RRPs as a harm reduction tool.
Uptake of RRPs by smokers is also affected by other factors such as taxation , affordability , moral concerns around addiction , and consumer choice regarding ECig flavors . To reduce smoking-related health inequalities, an integrated strategy has been proposed which combines targeted cessation programs, tobacco control measures, and educational media campaigns, all applied within wider attempts to address inequalities in health . Clear communication of relative risks, delivered through targeted public health educational campaigns, could help realize the potential of RRPs for harm reduction among lower SEGs.
The strengths of our study include the use of nationally representative data and the hindcasting approach, which helps avoid problems in accounting for the unknown future effects of other factors, such as medical advances, infections, wars, and global warming, on future death rates. Our methodology also allows the population health impact of RRP introduction to be estimated under a variety of different assumptions.
There are, however, a number of potential limitations that need to be considered in interpreting our estimates. Issues regarding our failure to consider other sources of nicotine or environmental tobacco smoke, the possible limitations in our negative exponential model, the choice of effective doses, limiting our attention to deaths at ages 30–79 years, and the choice of appropriate uptake rates of HnBs and ECigs have been discussed in our companion paper and are not considered further here. Also failure to take into account the reduced mortality in the Alternative Scenarios compared to that in the Null Scenario was shown to have very little effect on the results.
Some issues specifically relating to estimation of population health impact by SEG are, however, worth consideration. One is that the age- and sex-specific prevalence data for current and former smoking in Germany by SEG was only available for 2 years (2002 and 2012); therefore, annual data had to be estimated by a combination of interpolation/extrapolation and smoothing (as described in Additional File 1). More detailed source data might have led to some revision of our estimates, but it seems unlikely that they would have made much difference, given that the adjustment for SEG had little effect on the unadjusted estimates.
Similar considerations apply to the derivation of TPs by SEG in the Null Scenario, which, as described in Additional File 2, are calculated based on the distribution of smoking habits in the same birth cohort 5 years apart. Errors in the distributions would have led to errors in the estimated TPs, and inspection of the TPs in Table 3 shows that though the general patterns by SEG and age look plausible, there are a few exceptions. For example for SEG A period 1–5 years, the estimated initiation rates in men rise between ages 25–29 and 30–34 years, while at age 15–19, but not at other ages, quitting and re-initiation rates were much higher in women than men. Given that the changes in the distribution of smoking habits over time generated by the model using the TPs matched quite well observed distributions in Germany, it is unlikely that any further attempt to improve estimation of these TPs would have materially affected our conclusions.
Another issue is that data on transfer between SEG groups A and B were not available for Germany, and the data used here (as described in Additional File 4) were derived partly from the current smoking prevalence rates in the USA coupled with assumptions about the age-specific level of transfer from A to B. In fact, weaknesses in these data seem unlikely to be very relevant because re-running the analyses for Alternative Scenario 6 by disallowing the possibility of transfer had little effect on the overall estimates and only slightly reduced the estimated DDs shown in Table 5 (19,007 [A men]; 37,256 [B men]; 5,003 [A women]; and 13,129 (B women) to 18,738 [A men]; 37,193 [B men]; 4,962 [A women], and 12,999 [B women]. (Detailed results not shown.)
One other issue relates to how we classified the SEGs. As noted earlier, our classification used a previously described standard method  based on a combination of net annual income and mean years of education. Using methods that also took occupation into account or classified individuals into more than two groups would have been possible, but it is doubtful that it would have affected the conclusion that switching to RRPs would have reduced the risk and been more beneficial in groups that smoke more.
A further issue is that, for any given year, disease, sex, or age group, the estimated number of deaths by SEG was derived from the reported number for the combined SEG by multiplying this number by the estimated proportions in A and B for that year, sex, and age group. This assumes that the mean risk of death is identical in SEG groups A and B. While data are available from the NEM on the average RR (relative to never smokers) in each SEG group, no data are available on the absolute risk separately in A and B and, therefore, a precise test of this assumption is not possible. However, some idea of the potential effect of allowing for variation in risk by SEG can be gained from an example based on the data for men and all diseases combined. Overall there were 1,901,972 deaths, and, if one assumes that the risks per individual in A and B are the same, we can estimate on the basis of age-specific proportions in A and B that there would be 542,783 deaths in A and 1,359,189 in B. If, on the other hand, one assumes that the average risks in B are twice those in A, one can readily calculate that the deaths would be split as 316,562 in A and 1,585,410 in B. In Alternative Scenario 6, the assumed 542,783 deaths in A would drop by 19,007 (3.51%) and the 1,359,189 deaths in B would drop by 37,256 (2.74%), a total DD of 56,263. On the basis of these percentages and the revised numbers of deaths in A and B, the 316,562 deaths in A would drop by 11,085 and the 1,585,410 deaths in B by 43,437, a total DD of 54,542. Thus, even with this quite extreme assumption, the total DD is not changed that much, and there are still substantial DDs in both A and B, though the DD in A is decreased and that in B is increased.
Overall, our results clearly demonstrate that increasing uptake of HnBs and ECigs would reduce the adverse population health impact of cigarette smoking in both SEG groups A and B. They also show that adjustment for SEG makes little difference to the estimated impact in the total population.