The STPM estimates annual transition probabilities from current smoker
to former smoker using a closed-form demographic accounting formula.
The formula adjusts for differential mortality by smoking status, immigration/emigration survivorship,
initiation, and relapse:
where a = age, y = year,
s = sex, d = IMD quintile,
π = smoothed HSE proportions (nnet::multinom),
l(x) = birth cohort survivorship (HMD + ONS),
μs = smoking-status-specific mortality (52 disease RRs from tobalcepi),
prelapse = Hawkins 2010 + Jackson 2019 estimates by years since quit.
Calibration targets average these single-year-of-age probabilities into strata:
Table
Stratification
Years
Purpose
3
Sex × Age (25–44, 45–64, 65–74)
2011–2016
Calibration
4
IMD quintile × 3-year period
2011–2016
Calibration
5
Sex × Age
2017–2019
Validation
6
IMD quintile
2017–2019
Validation
Typical range: 6–12% annual quit probability. Uncertainty: Beta(n=20) assumption with 0.9 correlation
between samples (100 draws).
In STPM, a "quit" means transitioning from current smoker to
former smoker within one year. There is no quit tunnel in STPM.
In the ABM, the verification metric matches this by counting anyone who was a
SMOKER in January and is in any quit state at the December snapshot:
The ABM has a 12-month quit tunnel (NEWQUITTER → ONGOINGQUITTER1–11)
before reaching EXSMOKER. STPM has no tunnel: anyone who quits is
immediately a former smoker. This means STPM's "former smoker" maps
to ABM's tunnel occupants + EXSMOKER.
2b. Smoker demographics
2c. IMD × COM-B variable correlations at baseline
These plots show how the COM-B input variables correlate with IMD quintile at baseline.
Q1 = least deprived, Q5 = most deprived. Click to open full-size lightbox.
Maintenance COM-B variables by IMD
Attempt COM-B variables by IMD
3. ABM Output vs Targets (fake-beta-2)
Run config: attempt bias = −4.0 (recalibrated from SEM −2.169),
maintenance bias = −0.767 (original SEM intercept, already ~monthly per Harry).
cCigConsumptionPrequit frozen at quit start.
mNonSmokerSelfIdentity fake beta (0.001) for maintenance.
Exemplar agents stratified by IMD × sex (10 agents across 5 IMD quintiles × 2 sexes).
STPM quit rate — IMD facets
STPM quit rate — Age×Sex facets
STS attempt rate — Age×Sex
STS attempt rate — IMD
4. Quit Tunnel Survival — Cohort Analysis
Track all agents who were SMOKER in the 2011 December snapshot (n=2,119) across 29 years.
Result: 0 agents reach EXSMOKER in 29 years of simulation.
1,622 of 2,119 entered the tunnel at least once.
Deepest state observed: OQ9 (month 9).
Cohort state over time
Maximum tunnel depth ever reached (December snapshots)
Note: the cohort is defined as SMOKER at the 2011 December snapshot (tick 12), not at baseline
(tick 0). The Dec 2011 snapshot has 2,119 smokers vs 2,000 at tick 0. The difference
(+119 agents) reflects new 16-year-olds who entered during 2011 and baseline
quitters who relapsed back to SMOKER by December.
4b. Agent Journeys
Exemplar agent journeys (click image to open full-size lightbox)
Each panel tracks one COM-B variable across all maintenance ticks for each exemplar agent.
Only variables that change over time are shown — this reveals whether endogenous variables
(addiction decay, cessation aids, non-smoker identity) and exogenous variables (regional prevalence,
age transitions) are working as expected. The first panel shows the resulting P(maintenance).
Exemplar Agent Selection Bias
The 10 exemplar agents were selected to be stratified by IMD × sex (one per IMD quintile per sex).
Their month-0 P(maintenance) values are compared to the full population below.
Population (n=2000)
Exemplar (n=6)
Median monthly P(maint)
0.213
0.234
Mean monthly P(maint)
0.224
0.218
Logged mean (simulation)
—
0.254
The logged simulation mean (0.254) differs from the static calculation
(0.218) because: (1) regional prevalence is set dynamically at runtime
(~0.17–0.24 depending on region and year), (2) cessation aids (NRT, varenicline, etc.) are allocated
stochastically when an agent enters NEWQUITTER, and (3) addiction decays
during the tunnel, increasing P(maint) in later months. The static calculation uses month-0 values only.
5. Population-Level Maintenance Probability
5a. The COM-B maintenance formula
Implemented in comb_theory.py, class QuitMaintenanceTheory.
P(maint) = σ(η) = 1 / (1 + e−η)
η = C + O + M + b₀
where:
C = Σj βj · xj for j ∈ {capability predictors}
O = Σj βj · xj for j ∈ {opportunity predictors}
M = 0.001 · mNonSmokerSelfIdentity
Current intercept: b₀ = -0.7672137.
Source: data/intermediate_data/com_b/maintenance_SEM_coefficients_202509019_v2.csv.
Per Harry's email, this intercept represents the log-odds of still being abstinent roughly one month
after a quit attempt (reference category: "more than a week and up to a month" since quit).
It is already approximately a monthly probability — no 6-month conversion needed.
5b. Addiction decay during the tunnel
ak+1 = ak · e−λΔt where λ = 0.0368, Δt = 4.33 weeks
On relapse, cCigAddictStrength resets to its pre-quit value.
5c. Distribution across 2,000 baseline smokers
Each agent's maintenance probability is computed from their syn pop attributes. Two scenarios:
Baseline scenario
Best-case scenario
Cessation aids
None (all OFF)
All ON (e-cig, NRT, varenicline, behavioural support, cytisine)
Regional prevalence
0.20 (static)
0.20 (static)
Smoking neighbours
1 (static)
1 (static)
Combined logit boost from aids
0
+2.43
What these numbers mean for the 12-month tunnel
An agent must survive 12 consecutive monthly maintenance checks to reach
EXSMOKER. The 12-month survival probability is the product of
12 monthly probabilities (with addiction decay applied each month):
P(survive 12 months) = ∏k=0..11 P(maint at month k)
Quick conversion guide — if monthly P(maint) were constant:
Monthly P(maint)
Annual survival P12
Interpretation
0.30
0.000005 (0.0005%)
Virtually impossible
0.50
0.000244 (0.02%)
~1 in 4,000
0.70
0.0138 (1.4%)
~1 in 72
0.80
0.0687 (6.9%)
~1 in 15
0.90
0.282 (28%)
~1 in 4
0.95
0.540 (54%)
Majority survive
Baseline (no aids)
Best case (all aids ON)
Per month
Over 12 months
Per month
Over 12 months
Median
0.213
5.98e-08
0.739
4.73e-02
Mean
0.224
8.66e-06
0.729
6.46e-02
Max
0.615
0.004545
0.914
0.341137
Is this an intercept problem or a beta problem?
The predictor sum (C + O + M, excluding intercept) averages -0.537
across all baseline smokers. Even with b₀ = 0, the mean logit would be -0.537,
giving P(maint) ≈ 0.369 and P(12mo) ≈ 6.34e-06.
Largest negative contributors to the logit (mean β·x across baseline smokers):
Variable
β
SE
mean(x)
mean(β·x)
Prevalence
cCigAddictStrength
−0.195
0.051
2.03
−0.396
91% have urge > 0
cCigConsumptionPrequit
−0.029
0.008
12.3
−0.357
All smokers
oSocialHousing
−0.391
0.169
0.48
−0.188
48% in social housing
oEducationalLevelBelowDegree
−0.175
0.160
0.58
−0.102
58% below degree
Meanwhile, the largest positive contributors (cessation aids: e-cigarette β=+0.45, varenicline β=+0.72,
cytisine β=+0.79) contribute almost nothing at baseline because <10% of smokers use them.
They only activate when an agent enters the quit tunnel and is stochastically allocated aids.
Both the intercept (b₀ = -0.7672137, SE = 0.700) and the predictor betas contribute to the low
P(maintenance). The predictor sum alone averages -0.537 — already
negative before the intercept is added. Is the problem the intercept, the betas, or both?
5c-ii. Sensitivity analysis: which betas and bias matter most?
First, the conversion from monthly P(maintenance) to 12-month tunnel survival.
The curve is P12 — it drops off steeply below ~0.85/month.
Combined variable range tornado: each variable is varied from its minimum to maximum plausible
runtime value (e.g. cessation aids 0→1, addiction 0→5, regional prevalence 0.10→0.30).
The intercept is varied by ±1 SE (0.700). All other terms held at population means.
Three bias scenarios: current (−0.767), moderate uplift (0.0), and strong uplift (+1.0).
At the current intercept, addiction strength barely differentiates agents — all curves collapse
near zero. The intercept dominates. At b₀ = +1.0, the curves separate and addiction strength
starts to matter as intended.
This uses the complementary formula: P(≥1 event in 6 months) is a union of monthly events,
so P(no event in 1 month) = (1 − P6mo)1/6.
6b. Maintenance bias — already monthly
Per Harry's email: the maintenance SEM intercept represents the log-odds of still being abstinent
roughly one month after a quit attempt (reference category: "more than a week and up to a month"
since quit). This is already approximately a monthly probability.
Harry's caveats:
It reflects point prevalence of abstinence at follow-up conditional on having quit 1 week–1 month ago,
not the transition probability P(abstinent at t+1 | abstinent at t).
It probably overestimates early maintenance and underestimates later maintenance (though the negative
cCigAddictStrength coefficient may partially compensate for the latter).
Harry's suggestion: treat the intercept as-is for monthly maintenance, or slightly downscale it
and add uncertainty.
Sweep from b₀ = −1.0 to +1.0. For each bias value, 10 replicate runs of 120 ticks (2011–2020).
The plot shows: (1) number of baseline smokers who reached
EXSMOKER by 2020, (2) number still in the
tunnel at the 2020 snapshot, and (3) the STPM verification quit rate
(right axis, 0–1 scale). The dashed blue line is the mean STPM target.
The STPM quit rate (blue diamonds) is insensitive to the maintenance bias — it stays near the target
across the full sweep because it counts tunnel occupants as quitters.
The actual EXSMOKER count (green bars) is highly sensitive:
~0 at b₀ = −1.0 vs ~151 at b₀ = +1.0.
The STPM verification metric cannot distinguish between agents who survive the tunnel
and agents who merely enter it.
6d. Scenarios for the maintenance bias
Scenario
b₀
Rationale
Expected effect
Current (SEM as-is)
−0.767
Harry says intercept is already monthly
~0 agents reach EXSMOKER. Tunnel is a revolving door.
Moderate uplift
0.0
Remove negative intercept; let predictors drive variation
~8 EXSMOKER per 10 years (sweep data). Still very low.
Strong uplift
+0.5
Compensate for SEM underestimation of transition probability
~40 EXSMOKER per 10 years. Some agents survive.
Calibrate to real-world
TBD
Target ~3–5% of attempters surviving 12 months
Requires b₀ ≈ +0.8 to +1.2 (rough estimate from sweep).
7. Summary & Open Questions
What we know
Zero agents reach EXSMOKER in 29 years of simulation.
The maintenance SEM produces a mean logit of -1.30 (P(maint) ≈ 0.22/month),
giving 12-month survival ≈ 8.7e-06.
This is not purely an intercept problem. The SEM predictor betas themselves sum to a negative mean
(-0.537) for baseline smokers, driven by cCigAddictStrength
(−0.40) and cCigConsumptionPrequit (−0.36).
The STPM verification metric counts tunnel occupants as quitters, so it is insensitive to whether
agents actually survive the 12-month tunnel (slide 6c).
Questions for discussion
How can we further improve the verification here before we move on to calibration — what
reasonable level of betas (including b₀) are we looking for?
How should we verify that the ABM produces a realistic number of long-term ex-smokers, given
that the current STPM metric cannot distinguish tunnel entry from tunnel survival?
