The smktrans package is the engine room for estimating
the probabilities that individuals will move between different smoking
states—specifically initiation, cessation, relapse, and death—within the
Sheffield Tobacco Policy Model (STPM).
This article outlines the philosophy behind these estimates, the methodology used to generate them, and their history of use in informing UK government policy.
Living Estimates: A Versioned Approach
It is important to understand that the transition probabilities
provided by smktrans are not static.
Smoking behaviour is dynamic, and our understanding of it evolves as new survey data becomes available and methodological refinements are made. Therefore, this package operates on a versioned basis:
- Updates: When new health survey data is released or when we refine our algorithms, the package version is incremented.
- Snapshots: Each version of the package produces a specific set of estimates.
- Access: You can download the specific probability estimates for England, Scotland, and Wales from the Articles tab on this website.
We recommend always checking the package version to ensure you are using the most current estimates for your modelling work.
Methodology
The estimates produced by smktrans are not the direct
result of calibration or fitting a standard statistical model (e.g. a
logistic regression for prediction). Instead, they result from applying
a mathematical algorithm that is based on a rearrangement of the
formula for the dynamics of smoking prevalence. See the Sheffield Tobacco Policy
Model Technical Documentation.
The Framework
The foundation of this methodology is the work by Holford et al. (2014) for the United States. They established a workflow for estimating smoking state transition probabilities from repeat cross-sectional survey data.
We have adapted this approach for the UK context. The core logic involves taking observed cross-sectional prevalence (the “stocks” of smokers and non-smokers at a specific time) and calculating the necessary flows (transitions) required to maintain or change those stocks, accounting for:
- Mortality: We integrate external information on disease-specific mortality rates to account for the differential survival of smokers, former smokers, and never smokers.
-
Relapse: We explicitly model the probability of
returning to smoking after quitting.
- Long-term (>1 year): Based on Hawkins et al. (2010) using the British Household Panel Survey.
- Short-term (<1 year): Derived from the placebo condition in Jackson et al. (2019).
Full technical details can be found in the STPM Technical Documentation and in the methodological vignette found in the articles tab of the smktrans website.
Impact and Policy Application
The estimates generated by smktrans have formed the
evidence base for major tobacco control policy decisions in the UK.
1. England: The Royal College of Physicians & The SmokeFree Generation
The transition probabilities were originally developed for England. Their first major application was informing the projections for Section 2.6 of the Royal College of Physicians’ 2021 report, “Smoking and health 2021: A coming of age for tobacco control?”
As the President of the RCP noted in the introduction:
> “Instead, modelling of current tobacco control policies shows a
failure to achieve a smoking prevalence of <5% until after 2050.”
Following this, the methodology was utilized in a knowledge exchange project with the Office for Health Improvement and Disparities (OHID). The understanding produced by this collaboration later supported the government’s internal modelling for the SmokeFree Generation policy.
When the Tobacco and Vapes Bill was introduced to
Parliament, smktrans estimates were used by the government
modelling team for the final Impact Assessment.
* See page 34 of the Tobacco
and Vapes Bill Impact Assessment.
2. Scotland: Minimum Pricing for Tobacco
Funded by the SPECTRUM
Consortium, we extended the methodology to Scotland. These
estimates informed a report commissioned by Public Health
Scotland on the potential effects of minimum pricing for
tobacco.
* Read the report: Model-based
appraisal of the potential effects of minimum pricing for tobacco in
Scotland.
* Read the peer-reviewed publication: Gillespie et al. (2025) in Tobacco
Control.
3. Wales: Knowledge Exchange
Work is currently ongoing to use these estimates for Wales, supported
by a commissioned knowledge exchange project with Public Health
Wales. We have begun to work with their data science team to
integrate smktrans methodology into their internal analytic
workflows.
4. Academic Credibility & External Validation
The credibility of smktrans estimates extends beyond the
University of Sheffield research team. They have been independently
adopted by other academic groups to inform peer-reviewed simulation
studies.
Most notably, Davies et al. (2026) utilized our
estimates to model the potential inequality impacts of the SmokeFree
Generation policy in England.
* Read the publication: Davies N, Murray R, Morling JR, et
al. (2026). Impact of the UK’s smokefree generation policy on
tobacco-related equity in England: a simulation study. Tobacco
Control.
Future Directions
The smktrans estimates continue to evolve. They
currently form the backbone of our tobacco pricing modelling using
TAX-sim (developed under the NIHR SYNTAX
project). They have recently informed modelling of the effects of
changes to tobacco tax in England: Read the peer-reviewed
publication: Chen et al. (2026) in Tobacco
Control.
Furthermore, we are now using these quitting probability estimates as calibration targets for a new Agent-Based Models (ABM) designed to understand the behavioural mechanisms underlying quit attempts and maintenance. Read the peer-reviewed publication: Tian et al. (2026) in Winter Simulation Conference.
References
- Davies, N., et al. (2026). Impact of the UK’s smokefree generation policy on tobacco-related equity in England: a simulation study. Tobacco Control. DOI: 10.1136/tc-2025-059669
- Gillespie, D. & Brennan, A. (Year). The Sheffield Tobacco Policy Model (STPM): full technical documentation. University of Sheffield. DOI: 10.17605/OSF.IO/FR7WN
- Hawkins, J., Hollingworth, W., & Campbell, R. (2010). Long-Term Smoking Relapse: A Study Using the British Household Panel Survey. Nicotine & Tobacco Research. DOI: 10.1093/ntr/ntq175
- Holford, T. R., et al. (2014). Patterns of Birth Cohort–Specific Smoking Histories, 1965–2009. American Journal of Preventive Medicine. DOI: 10.1016/j.amepre.2013.10.022
- Jackson, S. E., et al. (2019). Modelling continuous abstinence rates over time from clinical trials of pharmacological interventions for smoking cessation. Addiction. DOI: 10.1111/add.14549