5  The epidemiological model

The epidemiological model (02_epi_engine.R, called from 04_master_loop.R) turns the quits produced in each service year into admissions avoided over the following five years.

5.1 Service years and cohorts

The master loop steps through each calendar year from 2019. In each year it runs the clinical pathway twice on that year’s patients: once with the service (the treatment arm) and once without it (the control arm). The patients treated in a year form a cohort, and each cohort is followed for five years after its service year. The effect of the service is the difference between the arms.

5.1.1 Earlier quitters in later years

Each year’s patients are the hospital population in the HES inputs, taken as the population of 2026 and grown or shrunk to the year for admissions growth and with smoking prevalence reduced by the background decline. The net quitters from earlier years (treatment minus control, at 12 months, less relapse each year) are then taken off current smoking in the same patient group, in both arms. This stops a person who has quit being counted as a smoker again, and treated and quit again, in a later year.

It assumes that every earlier quitter is among the following years’ patients, in the same patient group and age band, and that they leave only by relapsing. That is the most the adjustment could be, so it is conservative: it never double counts, and it understates the smokers available to treat in later years. Its size grows over the projection as quitters accumulate, so it matters more for the later years than for the first few. Re-admissions within the same year are handled separately, in the clinical pathway (chapter 4).

Each scenario’s control arm carries that scenario’s own earlier quitters, so scenarios are compared through the differences between their arms.

5.1.2 Age

Age is fixed at the index admission. A cohort stays in its age band over its five follow-up years: no ageing is applied to its relative risks, admissions or mortality. Over five years and the model’s wide age bands this matters most at the top of each band, and it is a stated limitation.

5.2 Comorbidity expansion

Patients are grouped by the main condition of their first admission of the year (e.g., a hip fracture), and may have other tobacco-related conditions (e.g., COPD or ischaemic heart disease) whose future admissions also fall when they stop smoking.

To capture this, the model joins each patient group to the pre-calculated comorbidity_matrix, which gives the proportion of the group’s patients with each smoking-related condition. This expands each group into one row for each condition in its patients’ profiles, including the group’s main condition, whose proportion is 1.

5.3 Disease mapping and baseline relative risks

Each condition is defined by ICD-10 codes in HES and has a relative risk for current smokers against never smokers. Some of them:

Condition ICD-10 Lookups Disease Group (Lag Curve) Baseline RR (Current Smoker)
Lung Cancer C33, C34 Cancer 10.92
Larynx Cancer C32 Cancer 7.01
Chronic Obstructive Pulmonary Disease (COPD) J40, J41, J42, J43, J44, J47 Respiratory 4.01
Ischaemic Heart Disease I20, I21, I22, I23, I24, I25 CVD 3.18 (Male 35-64) / 3.93 (Female 35-64)
Ischaemic Stroke I63, I64, I65, I66, I67 CVD 1.57 (Male) / 1.83 (Female)
Asthma J45, J46 Respiratory 1.61
Type 2 Diabetes E11 CVD 1.37

The full list of conditions is in disease_mapping_dictionary.csv, and their relative risks in relative_risks_expanded.csv.

5.4 Dynamic relative risks and disease-specific decay curves

The benefits of stopping smoking build up over time. For a person who has quit for \(t\) months, the relative risk of each condition is

\[RR_{quit}(t) = 1 + (RR_{current} - 1) \times E(t),\]

where \(E(t)\) is the proportion of the excess risk of a current smoker that remains \(t\) months after quitting. \(E(t)\) comes from one of three recovery curves, for cardiovascular disease, COPD and cancers, estimated by Kontis et al. (Kontis et al. 2014) from a re-analysis of the American Cancer Society’s Cancer Prevention Study II (Oza et al. 2011). 00_construct_lags.R turns the published points into a curve for each month to 120 months with a monotone spline (monoH.FC), so that the remaining risk never rises. The relative risks by month are built for each scenario in run_multi_year_service(), because the sensitivity analyses below change the curves.

Every outcome condition must have a relative risk and a recovery curve. If one is missing, the run stops.

The relative risks for men aged 50 to 64 over 10 years after quitting, from the model’s inputs, for ischaemic heart disease and lung cancer:

Relative risk after quitting against never smokers, men aged 50 to 64

5.4.1 Which curve each condition uses

As published, the conditions are assigned to the three curves as below. The table of effects (“Effects of quitting in people who already have a disease” below) sets each condition’s curve, the same for admissions and deaths. It puts the 12 conditions on the cancer curve that are not cancers on the CVD curve instead, as the review that preceded this model did (Gillespie 2024). Every curve is used as published.

Curve Conditions
CVD Ischaemic heart disease, ischaemic and haemorrhagic stroke, abdominal aortic aneurysm, peripheral arterial disease, venous thromboembolism, type 2 diabetes
COPD (respiratory) COPD, asthma, idiopathic pulmonary fibrosis, obstructive sleep apnoea, pneumonia, influenza, tuberculosis
Cancer All cancers, and 12 conditions that are not cancers: chronic kidney disease, end-stage renal disease, hip fracture, rheumatoid arthritis, Crohn’s disease, systemic lupus erythematosus, psoriasis, multiple sclerosis, age-related macular degeneration, senile cataract, hearing loss, low back pain

The share of excess risk remaining at the middle of each follow-up year on the published curves (from monthly_lags.csv):

Months since quitting 6 18 30 42 54
CVD 0.76 0.54 0.42 0.34 0.27
COPD 0.93 0.81 0.71 0.62 0.54
Cancer 0.95 0.87 0.79 0.72 0.66

For a quitter, the fall in risk compared with a continuing smoker is \((RR_{current} - RR_{quit}(t)) / RR_{current}\). For ischaemic heart disease (relative risk 3.18 for men aged 50 to 64) it is 16% in follow-up year 1, 32% in year 2 and 50% in year 5. For COPD (4.01) it is 5%, 14% and 34%; for pneumonia (2.17) 4%, 10% and 25%; and for chronic kidney disease (1.34) 1%, 3% and 9%.

5.4.2 How good is the evidence for the recovery curves?

The recovery curves are among the most uncertain assumptions in the model. The results depend on them through the admissions avoided, and so through the savings to hospitals. The QALYs and lifetime NHS savings do not use them (chapter 6).

What the curves measure. Kontis et al.’s curves describe deaths from new disease in former smokers who were free of the disease when they quit, compared with continuing smokers, in a large US cohort. The model applies them to admissions, mostly readmissions of people who already have the disease. That is a different outcome in a different population, and the evidence on how quickly the risk of exacerbations, complications and readmissions falls after a person with a disease stops smoking is patchy. Three curves also have to stand in for over 40 conditions.

Where the curves are likely to be too slow. Evidence from people who already have a disease suggests some benefits come faster than the curves allow, at least for some conditions:

  • Heart disease. In patients with left ventricular dysfunction, those who had quit for two years or more had risks similar to people who had never smoked (Suskin et al. 2001). A systematic review found a lower risk of death of about a third in patients with coronary heart disease who quit (Critchley and Capewell 2003). The CVD curve takes about two years to remove half of the excess risk.
  • Acute respiratory infections. The airways and immune defences start to recover within weeks to months of stopping smoking (Shahab 2013), but pneumonia and influenza follow the slower COPD curve.
  • Surgery. Complications after surgery fall within weeks of stopping smoking (Mills et al. 2011). The model does not include complications as an outcome.
  • The 12 conditions on the cancer curve that are not cancers. These have little direct evidence either way. The cancer curve is the slowest of the three, and the review that preceded this model put these conditions on the CVD curve (Gillespie 2024).

Where the model may be generous. The relative risks for current smokers come from studies of new disease. For people who already have a disease, the difference in readmission risk between smokers and former smokers is likely to be smaller. For example, the fall in COPD exacerbations after quitting is real but modest, and grows over many years (Au et al. 2009), while the model’s relative risk of 4 for COPD implies a fall of a third by year 5 and more after that. For cancers, quitting after diagnosis improves prognosis (Parsons et al. 2010), but by a different route from the one the incidence-based relative risks describe.

Checks against studies of quitters. In the Ottawa evaluation, patients who had quit at six months had a hazard ratio of 0.78 (95% CI 0.58 to 1.03) for readmission over two years compared with those who carried on smoking (Mullen et al. 2017). In a London service based on the Ottawa Model, patients not smoking at 30 days had an odds ratio of 0.83 (0.51 to 1.35) for readmission between 31 days and a year (Robins et al. 2024). Tab_14e (chapter 7) gives the model’s equivalent for each, for admissions and for deaths. Both studies are observational, and people who manage to quit tend to be healthier in other ways, which makes the benefit of quitting look larger than it is.

Overall. The published curves are probably conservative for the first two years after quitting for heart disease, acute infections and the conditions that are not cancers, and may be generous for COPD and cancers after several years. The direction of the net error is not known. Recovery curves for people who already have a disease, by condition group, would need a structured review of the evidence; a direct estimate from English data, linking the quit status recorded by hospital services to later admissions, would be better still. Until then, the model uses the curves as published and replaces them with studies of people who already have the disease where those exist (“Effects of quitting in people who already have a disease” below).

5.4.3 Why Ottawa’s quitters are a check, not a target

Ottawa’s quitters’ hazard ratio is the only estimate for quitters among hospital inpatients over two years, but the model does not calibrate to it. It compares quitters with continuing smokers in one observational study, so it carries the bias that people who manage to quit are healthier; it is imprecise (95% CI 0.58 to 1.03); and it is for readmissions from all causes. A recovery speed fitted to it would apply to every condition without direct evidence and would carry whatever part of Ottawa’s effect the evidence rows do not, cancers most of all. The cancer curve describes new cancer, with its long latency, not readmissions of people who already have cancer, and no study shows cancer admissions falling quickly after quitting. Fitting the speed would therefore put the largest share of the benefit where the evidence is weakest. Instead, the curves are used as published, the conditions with direct evidence carry it, and Ottawa and London are checks on the result (Tab_14e, chapter 7).

5.4.4 Range

Scenario Tier C conditions (effect_borrowing) Readmissions after the first year
Basecase Those sharing the mechanism of a condition with evidence borrow its effect (1) Fall to the Ottawa year 2 rate
Sens_Effects_Lower (lower) None borrow: every tier C condition on its default form (0) Fall to the Ottawa year 2 rate
Sens_Effects_Upper Every tier C condition with a related evidence row borrows its effect (2) Fall to the Ottawa year 2 rate
Sens_FollowUp_NoDecline (higher) As the base case Stay at the year 1 rate

The briefings and the report show the central estimate with the lower and higher estimates as its range (SCENARIO_RANGE_LOW and SCENARIO_RANGE_HIGH in 00_config.R); Sens_Effects_Upper is in the report’s sensitivity table. effect_borrowing is described under “The table of effects” below; it applies to admissions and deaths alike.

The effects of quitting also change admissions in the no-service arm, because some patients quit without the service. The scenarios that change the effects of quitting (FOLLOW_UP_OWN_FACTOR_SCENARIOS in 00_config.R: the two effects scenarios and the two death scenarios) therefore get their own follow-up admissions factors, set so that the no-service arm still matches the readmission targets; every other scenario gets the base case’s.

5.5 Effects of quitting in people who already have a disease

Every patient in the model already has a smoking-related condition: the one they were admitted with. The model asks what stopping smoking does for them afterwards. Most evidence on smoking answers a different question: how smoking changes the risk of getting a disease in the first place. This section sets out the difference, what this version does, and how the evidence is held so it can be updated.

5.5.1 Three distinctions

New disease and existing disease. The relative risks in relative_risks_expanded.csv come from studies of new disease. They compare current smokers with never smokers who were free of the disease when followed up. In the potential impact fraction, the most a sustained quitter’s risk can fall, against a continuing smoker’s, is \(1 - 1/RR\). For COPD, with a relative risk of about 4, that is 75%. Studies of people who already have the disease give smaller numbers for some conditions. Ex-smokers with COPD had an 18% lower risk of respiratory admission than current smokers in a Hampshire cohort (Josephs et al. 2017), and the fall in exacerbations after quitting is modest and grows over years (Au et al. 2009). For others the evidence is strong. In people with coronary heart disease who stop smoking, non-fatal heart attacks are 36% lower (HR 0.64) and deaths from all causes 40% lower (HR 0.60) than in those who carry on (Wu et al. 2022).

Illness and death. Quitting can reduce admissions among the patients who survive, and it can reduce deaths. These are separate effects, and the evidence for each is separate, so the table of effects has a row for each (“Effects of quitting on death” below).

Why living longer adds admissions. People kept alive by quitting go on using hospitals. Over the five years this offsets part of the admissions that quitting avoids; over a lifetime, the same effect is why the health care costs of a population of non-smokers end up higher than those of smokers (Barendregt et al. 1997). The model counts it and shows it separately (“Projected admissions” below). How large it is depends on how high death rates after discharge are, which is why they are worked out from each patient group’s conditions rather than taken from the general population.

5.5.2 How quickly the benefits come

The recovery curves (Kontis et al. 2014) describe deaths from new disease in people who were free of it when they quit, so they include the years it takes for disease to develop. In people who already have a disease, part of the benefit comes through processes that reverse quickly. Platelet function returns to normal within days of stopping, and the risks of thrombosis and endothelial dysfunction fall within a short period (Wu et al. 2022). That is one reason the published curves are thought too slow for the first two years for heart disease and acute infections (“How good is the evidence for the recovery curves?” above). The studies of people who quit after a heart attack or stroke report one hazard ratio over several years and say the benefit comes early, so those conditions take their study’s effect from the first month. Conditions that share their mechanism borrow that effect (“Effects of quitting on admissions” below). Cancers, diabetes and the other non-cancer conditions have no such link and keep the published curves, capped by the nearest evidence.

5.5.3 The table of effects

user_inputs/post_diagnosis_effects.csv holds the effect of quitting on each smoking-related condition, one row per condition and outcome (admission and death), and the evidence behind it. R/post_diagnosis_effects.R reads the admission rows and sets each condition’s recovery curve before the relative risks by month are built; build_death_effects() in R/deaths_after_discharge.R reads the death rows. The run prints the number of conditions in each tier, and names any condition the table puts on a different curve from the one its relative risks came with.

Column What it holds
condition, outcome The condition, as in the disease dictionary, and the outcome the row is for: admission or death
tier A: studies of quitting after diagnosis, against continuing to smoke, for the outcome the model uses. B: weaker evidence in people with the disease, such as former against current smokers. C: no direct evidence, so the default form
method How the effect is built. hazard_ratio (tier A rows): a reduction of \(1 - HR\) in every month. incidence_rr: the largest reduction is \(1 - 1/RR\), reached along the recovery curve. borrowed (tier C rows): the reduction of the row named in nearest_evidence
recovery_curve CVD, Respiratory or Cancer, as in monthly_lags.csv; none for a hazard_ratio row. A condition is on the same curve for both outcomes
hazard_ratio, hr_lower, hr_upper Tier A: the study’s hazard ratio and 95% confidence limits. Tier B: the hazard ratio for former against current smokers with the disease, which caps the row’s default form. Blank for tier C
nearest_evidence Tier C only: the tier A or B row of the same outcome that a borrowed row takes its effect from, or whose effect (tier A) or cap (tier B) an incidence_rr row may not exceed; blank for none
source, population, outcome_measured, effect_reported, date_reviewed, notes The evidence: BibTeX key, who was studied, what was measured, what was found, when the row was last checked

R/post_diagnosis_effects.R turns every row, admission or death, into the fall in a quitter’s risk against a continuing smoker’s by month since quitting, in one of three forms:

  • Fall (tier A): \(1 - HR\) in every month.
  • Default (tier B, and tier C incidence_rr): \(1 - RR_q(t)/RR\) from the relative risk and the row’s recovery curve as published, capped at \(1 - HR\) for tier B and at the fall or cap of the nearest_evidence row for tier C.
  • Borrowed (tier C borrowed): the fall of the nearest_evidence row in the same age group, sex and month. For a tier A source that is \(1 - HR\) throughout; for COPD, the tier B source, it is COPD’s own capped default.

The scenario setting effect_borrowing decides how tier C rows are read, for admissions and deaths alike: 1 as the table says; 0 every tier C row on its default form (Sens_Effects_Lower); 2 every tier C row that names a nearest_evidence row borrows from it (Sens_Effects_Upper). Cancer admission rows name none, so they keep the published curve in every scenario. For admissions, a quitter’s relative risk is the current smoker’s times one minus the fall (apply_admission_effects()); for deaths, the fall multiplies each condition’s deaths (“Effects of quitting on death” below).

Code 
# Extract from R/post_diagnosis_effects.R, effect_reductions()

out[form_ == "fall", reduction := fall_]
out[form_ == "default" & !is.na(cap_), reduction := pmin(reduction, cap_)]
out[src, source_reduction_ := i.source_reduction_, on = c("source_", strata)]
out[form_ == "borrowed", reduction := source_reduction_]

Every condition is described in the same form, so only the numbers differ between rows, and every row names its source, tier and date reviewed. The input check stops the run if any of these is missing, or if a tier, outcome or method is not one this version knows. It also stops if a tier A row lacks a hazard ratio inside its confidence limits, a tier B row lacks one, a tier C row has one, a borrowed row names no nearest_evidence row, nearest_evidence names anything but a tier A or B row of the same outcome, or a condition’s admission and death rows are on different curves.

5.5.4 Effects of quitting on admissions

Condition Tier Hazard ratio (95% CI) Outcome in the study Source
Ischaemic heart disease A 0.64 (0.58 to 0.72) Non-fatal myocardial infarction, quitters vs continuing smokers (Wu et al. 2022)
Ischaemic stroke A 0.71 (0.51 to 0.97) Recurrent stroke, fatal or non-fatal, quitters vs persistent smokers, first-ever ischaemic stroke, Nanjing registry (Chen et al. 2019)
COPD B 0.82 (0.74 to 0.89) Unplanned respiratory admission, former vs current smokers with COPD, Hampshire (Josephs et al. 2017)

The tier A rows apply from the first follow-up year, as their studies give one hazard ratio over several years. Why each source was chosen, and the other studies read, is under “Choosing the evidence for each row” below. The COPD row caps the default form at an 18% fall; former smokers in that study had mostly quit long before, and in US veterans with COPD the fall in exacerbations was small in the first five years after quitting (Au et al. 2009), so the cap is generous for recent quitters.

Every other admission row is tier C. Where a condition shares the mechanism of a condition with evidence, it borrows that condition’s effect, because evidence from people with a related disease is closer to the question than evidence on new disease:

  • abdominal aortic aneurysm, peripheral arterial disease and venous thromboembolism borrow from ischaemic heart disease (atherosclerotic or thrombotic disease, where the early benefit of quitting comes through platelets and endothelium);
  • haemorrhagic stroke borrows from ischaemic stroke;
  • asthma, idiopathic pulmonary fibrosis, influenza, obstructive sleep apnoea, pneumonia and tuberculosis borrow from COPD, so they recover no faster and by no more than COPD.

Diabetes and the 12 other non-cancer conditions keep the default form, capped by ischaemic heart disease: diabetes is a metabolic disease rather than an atherosclerotic or thrombotic one, and the others have no link to a condition with evidence. Cancers keep the default form with no cap: there is no evidence on admissions after quitting for people with cancer, and their curve describes new cancer, so their early effect is small.

5.5.5 Effects of quitting on death

Quitting lowers a quitter’s death rate from each condition by a fraction \(R_{d,t}\) in follow-up year \(t\), against a continuing smoker’s. It applies to deaths from that condition only (“Deaths after discharge” below), so each death is counted once, under its underlying cause. Four conditions have tier A evidence: studies of people who quit after the diagnosis, against people who carried on smoking. Each gives \(R_d = 1 - HR\) in every follow-up year, because the studies report one hazard ratio over several years and say the benefit comes early.

Condition Hazard ratio (95% CI) Outcome in the study Source
Ischaemic heart disease 0.61 (0.49 to 0.75) Cardiovascular death Cochrane review of cohorts of people with coronary heart disease (Wu et al. 2022)
Ischaemic stroke 0.71 (0.51 to 0.97) Recurrent stroke, fatal or non-fatal People alive and free of recurrence three months after a first-ever ischaemic stroke, Nanjing registry, as for admissions (Chen et al. 2019)
COPD 0.83 (0.69 to 1.00) Death from any cause Men newly diagnosed with COPD in South Korea (Doo et al. 2023)
Lung cancer 0.71 (0.64 to 0.80) Overall survival Meta-analysis of quitting at or around diagnosis (Caini et al. 2022)

For ischaemic stroke the death row uses the same study and hazard ratio as the admission row. Its outcome counts fatal recurrent strokes, which make up much of the deaths from stroke after discharge, so recurrent stroke is the outcome closest to deaths from stroke (“Choosing the evidence for each row” below).

Applied to deaths from the condition alone, a hazard ratio for death from any cause (COPD, lung cancer) counts for less than in the study; for lung cancer most deaths are from the cancer, so little is lost. The COPD study starts follow-up two years after diagnosis, so it misses early deaths (Doo et al. 2023).

Every other condition is tier C, with the same rule as for admissions. Abdominal aortic aneurysm, peripheral arterial disease and venous thromboembolism borrow the effect for ischaemic heart disease, haemorrhagic stroke borrows the effect for ischaemic stroke, and the respiratory conditions borrow the effect for COPD. The rest are on the default form, \(R_{d,t} = 1 - RR_q(t)/RR\), from the relative risk and recovery curve as published, capped by the tier A row named in nearest_evidence: ischaemic heart disease for diabetes and the other non-cancer conditions, lung cancer for cancers. The curves were estimated from deaths from new disease (Kontis et al. 2014), so for deaths they are on home ground; what is borrowed is that they describe people free of the disease when they quit.

Quitters are counted as for admissions (“Who is quit, and for how long” below). The sensitivity analyses change the effects on deaths and admissions together (“Sensitivity analyses of the effects of quitting” below).

Check. Ottawa’s patients who had quit at six months had a hazard ratio for death over two years of 0.53 (0.32 to 0.83) against continuing smokers (Mullen et al. 2017); in London, patients not smoking at 30 days had an odds ratio for death between 31 days and a year of 1.41 (0.65 to 3.05) (Robins et al. 2024). Tab_14e gives the model’s equivalent beside each: a quitter’s cumulative death rate over a continuing smoker’s in the same patient groups, weighted by the service’s 6-month quitters. Nothing is calibrated to them. A model value above Ottawa’s range would mean the effects on death are smaller than Ottawa saw, which is expected while they apply only to deaths from the model’s conditions; that the two studies disagree shows how imprecise each is.

5.5.6 Choosing the evidence for each row

Each tier A or B row takes its effect from one source, named in the table, and the model does not pool estimates from different studies. A published systematic review with a pooled estimate counts as one source. The other studies read are discussed here, to say why the source was chosen and whether they agree. The register of the numbers taken from each study is model_development/post_diagnosis_evidence.md.

  • Ischaemic heart disease. The Cochrane review of people with coronary heart disease (Wu et al. 2022): non-fatal myocardial infarction for admissions, 0.64 (0.58 to 0.72; 24 studies, little heterogeneity), and cardiovascular death for deaths, 0.61 (0.49 to 0.75; 18 studies, moderate certainty). Its major adverse cardiovascular events (0.57, low certainty, a composite) and death from any cause (0.60, a wider outcome than deaths from heart disease) are not used.
  • Ischaemic stroke. A registry of 3,069 people with a first-ever ischaemic stroke in Nanjing, alive and free of recurrence at three months (Chen et al. 2019): fatal or non-fatal recurrent stroke, quitters against persistent smokers, 0.71 (0.51 to 0.97), for admissions and deaths. It was chosen because it is a registry of first strokes that includes people with diabetes, close to the patients in English hospitals, and it is the most precise of the stroke studies. Three others agree or are consistent with it. In the IRIS trial cohort of people within six months of a stroke or TIA, without diabetes, the hazard ratio for stroke was 0.67 (0.43 to 1.04) (Epstein et al. 2017). In people with coronary heart disease, the hazard ratio for non-fatal stroke was 0.70 (0.53 to 0.90; nine studies, no heterogeneity) (Wu et al. 2022). In the SPS3 trial of lacunar strokes (Anadani et al. 2023), quitters and persistent smokers were each compared with never smokers; the ratio of the two hazard ratios gives about 0.99 for stroke and 0.70 for death from any cause, from 13 strokes and 7 deaths among 162 quitters, so it adds little precision. It is not used because it does not report the comparison itself and covers only lacunar strokes. The IRIS trial’s hazard ratio for death from any cause, 0.49 (0.30 to 0.79), is not used for stroke deaths: it is for every cause of death, and it is larger than the effect on stroke in the same study and than the effect on cardiovascular death in people with coronary heart disease.
  • COPD. No study of quitting after a diagnosis reports admissions, so admissions use a study of former against current smokers with COPD in Hampshire, 0.82 (0.74 to 0.89) (Josephs et al. 2017), as a cap on the default form (tier B). It was chosen over a US study of veterans, 0.84 (0.75 to 0.95) for people with COPD (Au et al. 2009), because it is English; the US study shows the fall growing slowly with years since quitting, which is why the cap applies to the default form rather than from the first month. Deaths use men newly diagnosed with COPD in South Korea who quit within two years, against those who carried on, 0.83 (0.69 to 1.00) for death from any cause (Doo et al. 2023); the same study’s cardiovascular death (0.56) is not used, being one cause among many in COPD.
  • Lung cancer. A meta-analysis of quitting at or around diagnosis, overall survival 0.71 (0.64 to 0.80) (Caini et al. 2022).

5.5.7 Sensitivity analyses of the effects of quitting

Four scenario settings in scenarios_control_panel.csv change the effects of quitting, each for admissions and deaths together:

  • effect_borrowing: which tier C rows borrow the effect of their nearest evidence (“The table of effects” above).
  • effect_limit: each tier A and B row’s hazard ratio at its central estimate (0), its 95% confidence limit nearer no effect (1) or the limit further from it (2). Rows that borrow from, or are capped by, a row at its limit follow it.
  • effect_limit_scope: the rows effect_limit applies to, from EFFECT_LIMIT_SCOPES in 00_config.R: every tier A and B row (0) or the ischaemic stroke rows only (1).
  • excess_death_scale: multiplies every condition’s death rate after discharge (“Deaths after discharge” below).
Scenario Setting What it tests
Sens_Effects_Lower (lower estimate) effect_borrowing 0 No condition borrows: the evidence is used only for the conditions it was measured in
Sens_Effects_Upper effect_borrowing 2 Every tier C row with a nearest evidence row borrows it, including diabetes and the 12 other non-cancer conditions (from heart disease) and deaths from other cancers (from lung cancer)
Sens_Evidence_Weaker effect_limit 1 Every study at its confidence limit nearer no effect
Sens_Evidence_Stronger effect_limit 2 Every study at its confidence limit further from no effect
Sens_Stroke_Weaker effect_limit 1, effect_limit_scope 1 The stroke study at its limit nearer no effect (0.97)
Sens_Stroke_Stronger effect_limit 2, effect_limit_scope 1 The stroke study at its limit further from no effect (0.51)
Sens_Death_Rates_Lower excess_death_scale 0.5 Death rates from every condition halved

Ischaemic stroke has its own pair because, of the rows with direct evidence, it carries the largest share of the benefits in the model’s patients and its interval is wide. Halving the death rates is an illustrative bound for the main known bias in them: deaths from a condition among people not admitted with it in the year are counted against those who were (“Deaths after discharge” below). With fewer deaths, fewer are avoided, but more patients stay alive in both arms and go on being admitted. Each of these scenarios has its own follow-up admissions factors (FOLLOW_UP_OWN_FACTOR_SCENARIOS), so the no-service arm still matches the readmission targets.

Tab_25 shows where the benefits for the 2026 cohort come from: admissions prevented, savings and deaths avoided over five years by outcome condition, with the evidence behind each condition’s effects in that run (tier, form, nearest evidence, source and the hazard ratio used). The report groups it by the evidence behind it.

5.5.8 Updating the evidence

To change a row, edit it in the table and fill in the evidence columns, with a key in references.bib for the source. Then run the follow-up calibration, England and the areas (chapter 8, “What to run when”), because the follow-up admissions factors depend on the effects of quitting.

The readmissions without the service that \(k_1\) and \(k_2\) are calibrated to are in user_inputs/readmission_targets.csv: 0.43 smoking-related readmissions per smoker in follow-up year 1 and 0.16 in year 2, from the Ottawa control group (chapter 7). They can be replaced with English figures, with their source and derivation, without changing any code. After changing them, run the follow-up calibration and then the model.

5.5.9 What this version leaves out

  • For admissions, only ischaemic heart disease and stroke have studies of quitting after diagnosis, and COPD a study of former against current smokers. Related conditions borrow their effect; the rest come from studies of new disease, capped where related evidence exists. Cancers are uncapped, on the slow cancer curve.
  • The effects of quitting do not include the parts of a service’s effect that do not run through quitting (chapter 7, the staircase), so the model’s quitters do less well than Ottawa’s.
  • Effects on death apply only to deaths from the model’s conditions; deaths from other causes are the same in both arms.
  • The lifetime QALYs and NHS savings (chapter 6) are valued for people who quit without smoking-related disease, as in NICE’s models. They cover a lifetime that includes the first five years, so the deaths avoided in those years are reported beside them, not added to them.

5.6 Who is quit, and for how long, in each follow-up year

Each follow-up year is valued at its middle, using the quitters still quit and the time since they quit at that point:

Follow-up year Quitters Months since quitting (relative risk read at) Survival
1 6-month quitters 6 \(e^{-0.5 h_1}\)
2 12-month quitters 18 \(e^{-h_1 - 0.5 h_2}\)
3 12-month quitters \(\times (1 - r)\) 30 \(e^{-h_1 - h_2 - 0.5 h_3}\)
4 12-month quitters \(\times (1 - r)^2\) 42 \(e^{-h_1 - h_2 - h_3 - 0.5 h_4}\)
5 12-month quitters \(\times (1 - r)^3\) 54 \(e^{-h_1 - \dots - h_4 - 0.5 h_5}\)

\(r\) is the annual relapse rate among people quit for 12 months or more (Relapse_Rate in macro_trends_panel.csv, for the cohort’s service year), and \(h_t\) is the patient group’s death rate in follow-up year \(t\) (“Deaths after discharge” below). The 6- and 12-month quitters come from the clinical pathway (4-week quitters \(\times\) 0.54 and 0.42).

5.7 Admissions a year in follow-up

Without the service, each patient group is assumed to keep being admitted at a multiple of its index-year rate in each follow-up year:

  • for the group’s own condition: \(k \times\) (focal multiplier \(- 1\)). The focal multiplier counts the index admission, which is not repeated, so it is taken off;
  • for each other smoking-related condition: \(k \times\) the comorbid multiplier.

\(k\) is \(k_1\) in follow-up year 1 and \(k_2\) in years 2 to 5 (follow_up_admissions_factor_y1 and follow_up_admissions_factor_y2plus in scenarios_control_panel.csv). They are calibrated on a national run so that, without the service, smoking-related admissions per smoker match the readmissions per smoker in the control group of the Ottawa evaluation (Mullen et al. 2017): about 0.43 in the first year after discharge and 0.16 in the second. Readmissions fall after the first year because many happen soon after discharge. Ottawa followed patients for two years, so years 3 to 5 carry on at the year 2 rate. How the factors are set and checked (Tab_14b) is described in chapter 7. Area runs keep the national factors. The higher estimate of the range, Sens_FollowUp_NoDecline, sets \(k_2\) equal to \(k_1\), so that readmissions don’t fall after the first year.

5.8 The potential impact fraction (PIF) framework

For each patient group and outcome condition, the model calculates the average relative risk before and after the quitters move from current to former smoking. The new quitters carry the relative risk for their time since quitting, at the middle of the follow-up year. Patients who were already former smokers carry the long-term risk of a former smoker, the same recovery curve FORMER_SMOKER_MONTHS_SINCE_QUIT months after quitting (60 in 00_config.R, the approximate average time since quitting used in the spreadsheet model), in both arms and every follow-up year. The PIF (Gunning-Schepers 1989) is the ratio of the two averages:

Code 
# Extract from 02_epi_engine.R, project_follow_up_year()

shares <- quit_shares(joined, fy, relapse_rate)
new_prev_current <- shares$current
new_quitters     <- shares$new_quitters

baseline_avg_rr <- joined$prevalence_current * rr_current + joined$prevalence_former * joined$rr_former + joined$prevalence_never
new_avg_rr      <- new_prev_current * rr_current + new_quitters * rr_quitters +
  joined$prevalence_former * joined$rr_former + joined$prevalence_never
pif <- fifelse(baseline_avg_rr <= 0, 1.0, new_avg_rr / baseline_avg_rr)

Never smokers have a relative risk of 1. Every smoking-related outcome condition must have a relative risk for every age group and sex; the run stops if one is missing.

5.9 Deaths after discharge

People who have died can’t be admitted. Patients admitted with a smoking-related condition die at far higher rates than other people of the same age, and which conditions they have makes most of the difference. So each patient group’s death rate is built from its conditions.

A patient group’s death rate. In follow-up year \(t\),

\[h_t = m_{other} + \sum_d p_d \, x_d \, f_{d,t} \, (1 - q_t R_{d,t})\]

where \(m_{other}\) is the death rate from causes other than the model’s conditions, for the group’s age group, sex and IMD quintile; \(p_d\) is the proportion of the group with condition \(d\) (1 for the group’s own condition); \(x_d\) is the deaths a year from condition \(d\) per patient who has it; \(f_{d,t}\) spreads those deaths over the five years; \(q_t\) is the share of the group who are new quitters in year \(t\), in that arm; and \(R_{d,t}\) is the fall in a quitter’s deaths from \(d\) (“Effects of quitting on death” above). Every patient in a group starts from the same rate, so a quitter’s deaths fall from the group’s average, not from a smoker’s (likely higher) rate. Survival to the middle of year \(t\) is \(e^{-(h_1 + \dots + h_{t-1}) - 0.5 h_t}\), so it differs between the arms by the quits the service adds. The rates are national; each area applies them to its own mix of patients. Tab_23 gives the deaths in each arm for every year’s patients, the deaths avoided (all ages and under 75 at the index admission) and the life-years gained within the five years.

Deaths from each condition per patient. 10_process_cause_deaths.R works out \(x_d\) and \(m_{other}\) for each age group, sex and IMD quintile in four steps:

  1. Each cause’s share of deaths, from ONS deaths in England in 2018 by underlying cause, single year of age (16 to 90; age 90 stands for 90 and over), sex and IMD quintile, with each model condition as a cause. Oesophageal adenocarcinoma and squamous cell carcinoma together make oesophageal cancer (CAUSE_DEATHS_MERGE); every other cause is an other cause.
  2. Deaths from each cause: its share of the model’s ONS deaths for 2023 (ons_mortality_rates.csv). \(m_{other}\) is the other causes’ share of the all-cause rate, so the population’s overall death rate is unchanged.
  3. Deaths in a first admission taken off. The ONS deaths include people who died in their first admission of the year. They are not in the model’s patients, who are only those discharged alive (chapter 3, “Admissions that end in death”), so their deaths must not be counted against the patients who survived. Left in, they would raise death rates after discharge and lower the admissions avoided; 42.8% of deaths in England in 2023 were in hospital (Office for Health Improvement and Disparities 2025). Their number, from HES (hes_index_deaths.csv), as a share of all deaths in the stratum, is taken off every condition’s deaths alike. HES is used rather than the share of deaths in hospital because some deaths in hospital are of patients who survived an earlier admission that year; they are in the model, so their deaths stay.
  4. Per patient: what remains, divided by the patients in HES who had the condition recorded in any admission in the year (hes_condition_patients.csv). Where fewer than 100 patients have a condition in a stratum (EXCESS_MORTALITY_MIN_PATIENTS), deaths and patients are pooled across IMD quintiles, then sexes, then ages.

Both HES files are counts for England over all providers, written by section 3b of 01_process_hes_data.R. Deaths after a hip fracture are coded to the fall, an other cause, so hip fracture has no deaths of its own (CAUSE_DEATHS_NONE).

When the deaths happen. For some conditions deaths are concentrated in the first year. user_inputs/excess_death_timing.csv gives each condition a year1_ratio \(R\): its death rate in year 1 over its average rate in years 2 to 5, \(R = -\ln S_1 \big/ \big((\ln S_1 - \ln S_5)/4\big)\), from one- and five-year survival \(S_1\) and \(S_5\). Year 1 is \(5R/(R+4)\) times \(x_d\) and each later year \(5/(R+4)\) times, so the five years still average to \(x_d\): the timing moves deaths between years without changing how many there are. one_year_mortality_cap, \(1 - S_1\), is the most of a condition’s patients that can die of it in year 1; where \(x_d\) would pass it, \(x_d\) is lowered, and the run says so.

Condition year1_ratio one_year_mortality_cap Source
Lung cancer 2.91 0.55 Almost 45% survive one year and more than 15% five years (Cancer Research UK)
Pancreatic cancer 4.25 0.722 One-year net survival 27.4% (men) and 28.1% (women), five-year 8.4% and 8.2% (NHS Digital, diagnosed 2016 to 2020)
All others 1 none No published figure used; deaths spread evenly

Check. Tab_14d gives the proportion of smokers at the index admission dead by the end of each follow-up year in each arm (national run) next to Ottawa’s control group, 11.4% within one year and 15.1% within two, and its intervention group, 5.4% and 7.9% (Mullen et al. 2017). Nothing is calibrated to it. The no-service arm and Ottawa’s control group should be of a similar size (chapter 7); figures well above Ottawa’s would suggest \(x_d\) is too high. Ottawa’s fall in deaths is far larger than its difference in quit rates could give, so the model’s difference between arms is expected to be much smaller.

What this leaves out. Deaths from a condition in people not admitted with it in the year are counted against those who were, which pushes \(x_d\) up; Sens_Death_Rates_Lower halves \(x_d\) to show what that could mean. Deaths in a first admission are assumed to fall on each cause in the same proportions as all deaths in the stratum. The other-cause rate is the general population’s, lower than hospital patients’. The deaths file and the HES extract are one year each.

Updating. For a newer deaths file in the same layout, set FILE_CAUSE_DEATHS_RAW; for another condition’s survival, add it to excess_death_timing.csv with its source. Then run 10_process_cause_deaths.R (for a new deaths file), the follow-up calibration, England and the areas (chapter 8).

5.10 Projected admissions

Projected admissions for each condition are the patients in the group, times the proportion with the condition, times admissions a year with it in follow-up, times the PIF, times survival:

Code 
# Extract from 02_epi_engine.R

# build_outcome_frame()
frame[, adms_index_year := fifelse(focal_condition == get(TOB_COL_OUTCOME_CONDITION),
                                   get(FOCAL_ADMS_PER_PATIENT) - 1, get(COMORBID_ADMS_PER_PATIENT))]
frame[, adms_per_patient_y1     := k_y1     * adms_index_year]
frame[, adms_per_patient_y2plus := k_y2plus * adms_index_year]

# project_follow_up_year(): survival to the middle of follow-up year fy, in this arm
survival_prob <- joined[[paste0("surv_fy", fy)]]
adms_per_patient <- if (fy == 1) joined$adms_per_patient_y1 else joined$adms_per_patient_y2plus
year_dt[, baseline_adms := joined$unique_individuals * joined$comorbidity_prob * adms_per_patient]
year_dt[, projected_adms := baseline_adms * pif * survival_prob]

The parts of this that don’t change between service years (the comorbidity proportions, admissions a year, unit costs, lengths of stay, the death rates and the relative risks at each follow-up month) are joined once per scenario in build_outcome_frame(), and each service year adds only its patients, prevalence and quits; add_arm_survival() then gives each arm its survival.

The effect on illness and the effect on survival. With \(B\) the admissions without the service before deaths, \(PIF\) the potential impact fraction and \(S\) survival, in the no-service (\(c\)) and service (\(t\)) arms, the admissions avoided are

\[B \, PIF_c \, S_c - B \, PIF_t \, S_t = \underbrace{B \, S_c (PIF_c - PIF_t)}_{\text{less illness}} - \underbrace{B \, PIF_t (S_t - S_c)}_{\text{patients alive because they quit}}\]

The first part is the admissions avoided because patients who quit are less ill; the second is the admissions of patients alive because they quit. Tab_20 gives both, with the savings split the same way, for the patients treated in 2026, and the results report the admissions avoided net of the second part. The comparison with Ottawa’s quitters’ hazard ratio for readmission (chapter 7) uses the first part only, because a hazard ratio compares patients while they are alive.