What is statistical modeling?

Statistical models are mathematical representations of data that help scientists understand the relationships between different variables, ultimately make sense of the world, and predict what might happen in the future.

They are used in almost all fields of science—including physics, astronomy, biology, medicine, psychology, and sociology—in engineering, economics, and business. In everyday life, they are used to predict the weather, stock market prices, natural disasters, life expectancy, and much, much more.

All statistical models, whether they are physical, biological, or sociological, are simplified representations of parts of the world around us. They are based on assumptions, usually derived from observations of the world around us, and they can provide scientists with a solid foundation to forecast and project data into the future. The further into the future you predict, the less accurate the prediction will be.

What approach did we use?

We used the World Health Organization’s (WHO’s) approach1 to estimate the number of smoking-attributed deaths from the WHO’s data relating to: (a) information on smoking prevalence; and (b) number of deaths attributed by the WHO to smoking-related diseases. We estimated the number of smoking-attributed deaths in 53 countries representing 24 percent of the world’s population using data in the WHO Mortality Database.2 All estimations have limitations. The WHO’s method of estimation is no exception and there are many areas where we disagree with their approach. Nevertheless, it is commonly used by governments and public health organizations to form policy proposals. In the interest of finding common ground, we used the WHO’s approach for this hypothetical scenario to center discussions on what the estimations are, rather than whether the approach is accurate and appropriate or not.

For each country, sex, and age, we forecast future population sizes assuming that mortality in the future will be the same as today. We then estimated the number of smoking-related deaths based on the WHO’s information on smoking prevalence and the relative risk of dying of a smoking-related disease for smokers compared with non-smokers.

We took the estimates of mortality attributed to smoking yielded by the WHO’s approach and went on to predict the potential impact of switching all smokers to a hypothetical product that that we assumed to be 80 percent less risky than cigarette smoking. We subtracted 80 percent of the relative risk of smoking from the baseline produced by the WHO’s approach and then, using a previously published third-party method,3 improved the accuracy of the prediction to allow for the time lag in reduction of excess harm from smoking that would occur upon switching to the hypothetical smoke-free product.4,5,6,7,8 This gave us a prediction of the potential reduction in smoking-attributable deaths if smokers were to switch to the hypothetical product.

To compare this with the historically enacted tobacco control measures on their own, we took certain published estimates of their impact on smoking-attributable deaths.9

We chose 80 percent as the hypothetical smoke-free product risk reduction level as we believe this is a reasonable assumption based on the science. The real figure could be lower or higher. Even if it is lower than 80 percent, smoke-free products would still yield better outcomes than traditional tobacco control measures on their own. If the risk reduction level is higher, then the positive impact of smoke-free alternatives could be greater still.


Traditional tobacco control measures can gradually reduce smoking, smoking-associated diseases, and therefore, mortality.9 However, we estimate that if all current smokers switched to a hypothetical smoke-free product that is assumed to be 80 percent less risky than smoking, over their lifetime, there could be a 10-fold reduction in smoking-attributable deaths compared with historical tobacco control measures on their own. 

Of course, the best thing for all smokers is to quit altogether but for those who don’t, enabling access to smoke-free products has a real potential to deliver much faster public health results than relying on traditional tobacco control measures on their own.

What is the German model?

We developed, validated, and published our own Population Health Impact Model using well-established methods in epidemiological modeling and simulation analysis.10 We used this model and applied it to Germany.11 To do this we used age-specific data on number of deaths from lung cancer, chronic obstructive pulmonary disease, ischemic heart disease, and stroke specific to Germany and derived from the WHO Mortality Database.12 Together, these diseases account for an estimated three quarters of all smoking-related diseases. We used population size estimates by sex and age group from the United Nations website for the years 1966–2035.13

For each scenario, and for a given sex, disease, and age group, we estimated the relative risk of mortality for each individual at each year of follow-up. The proportion of deaths associated with tobacco use was then estimated.

For each scenario, and for a given sex, disease, and age group, we estimated the relative risk of mortality for each individual at each year of follow-up. The proportion of deaths associated with tobacco use were then estimated.

Our model showed that if smoke-free alternatives to cigarettes had been introduced into the tobacco market in Germany in 1995, this would have led to substantial reductions in smoking-related deaths over the following 40 years. The reductions would likely have been larger than those associated with introducing any of the four tobacco control measures considered (single price increase, marketing ban, plain packaging, and raising the minimum legal age of smoking to 21 years) if they had also been introduced at the same time. Data from a recent study (the DEBRA study,)14 which started measuring prevalence in 2016, suggests that smoking prevalence in Germany in recent years may be markedly higher than our model suggests. If so, the benefits of smoking cessation, regulatory measures and switching to smoke-free products could be greater than we estimated.


Because any statistical model simplifies the world around us, and all are based on a set of assumptions, no model can ever be 100 percent accurate. We also used data from the WHO and other third parties to create a common benchmark for the hypothetical model, but this does not mean that we agree with the accuracy, reliability or appropriateness of the data or the methodology used by these organizations.

No model can capture every single detail of the relationships they are aiming to describe, but they can provide us with a useful tool to help us predict what might happen in the future.

Are there models which can more accurately predict the potential reductions in smoking-attributable deaths associated with introducing smoke-free alternatives than the ones we have used? The answer is probably “yes.” And we invite scientists to share their approaches to help inform public policy on smoke-free products.

Question:  Why don’t you have estimates for all the countries in the world?

Answer: We estimated the number of smoking-attributed deaths in 53 countries using data in the WHO Mortality Database. Specifically, we selected those countries that have causes of death data in the WHO Mortality Database. There may be other datasets which contain information on more countries.

1 https://www.who.int/publications/i/item/9789241564434
2 https://www.who.int/data/data-collection-tools/who-mortality-database
3 https://www.sciencedirect.com/science/article/pii/S0273230012001195?via%3Dihub
4 https://www.sciencedirect.com/science/article/pii/S0273230013000871
5 https://www.sciencedirect.com/science/article/pii/S0273230013002213
6 https://www.sciencedirect.com/science/article/pii/S0273230012001195
7 https://www.sciencedirect.com/science/article/pii/S0273230013002146
8 https://www.cancer.org/research/population-science/cancer-prevention-and-survivorship-research-team/acs-cancer-prevention-studies/cancer-prevention-study-2.html
9 https://tobaccocontrol.bmj.com/content/27/1/50.long
10 Weitkunat, R., P.N. Lee, G. Baker, Z. Sponsiello-Wang, A.M. González-Zuloeta Ladd, and F. Lüdicke: A Novel Approach to Assess the Population Health Impact of Introducing a Modified Risk Tobacco Product; Regul.Toxicol. Pharmacol. 72 (2015) 87–93. DOI: 10.1016/j.yrtph.2015.03.011
11 Rytsar, Romana, Djurdjevic, Smilja, Nussbaum, Alexander K., Kaul, Ashok, Bennewitz, Emanuel, Lee, Peter N. and Fry, John S. "Estimated Public Health Gains From German Smokers Switching to Reduced-Risk Alternatives: Results From Population Health Impact Modelling" Contributions to Tobacco & Nicotine Research, vol.31, no.1, 2022, pp.35-51. https://doi.org/10.2478/cttr-2022-0004
12 https://platform.who.int/mortality/themes/theme-details/MDB/
13 United Nations Department of Economic and Social Affairs Population Division: World Population Prospects 2022; United Nations, New York, NY, USA. Available at: World Population Prospects - Population Division - United Nations
14 https://www.debra-study.info/