7Methodological reconciliation and Ottawa benchmarking
The landmark Ottawa Model for Smoking Cessation study (Mullen et al. 2016) demonstrated the immense potential of hospital-initiated tobacco dependency treatment, achieving an absolute risk reduction (ARR) of 11.6% in 2-year all-cause readmissions. This outcome was driven by a 35.2% quit rate in the intervention arm—which represented a 14.8% incremental improvement over the 20.4% background quit rate in the control arm. Historically, business cases for English hospital services have frequently attempted to model local savings by applying this 11.6% ARR directly to their local treated headcount, often erroneously assuming the full ~35% absolute quit rate was the incremental effect of the service.
While the Ottawa findings provide robust evidence of efficacy, translating effect sizes from a specific, highly severe Canadian clinical cohort into a generalised biological model for English acute Trusts requires careful epidemiological translation. Applying static, unadjusted effect sizes to local populations can mask critical baseline differences and mathematically overestimate the volume of prevented admissions.
To provide complete transparency to stakeholders, validate historical assumptions, and demonstrate the robust nature of the new Lexis simulation, the build_ottawa_reconciliation.R script is engineered to bridge the methodological gap between historical business cases and the dynamic Hospital-TTD-Mod.
7.0.1 The four principles of epidemiological translation
For an analyst to correctly apply the findings of the Ottawa study to a local UK hospital Trust without inflating expectations, four non-negotiable mathematical rules must be observed. The reconciliation script applies these sequentially:
1. The Denominator Rule (excluding the index admission) An intervention delivered during an admission cannot retroactively prevent that exact admission. Therefore, effect sizes cannot be applied to the raw headcount of treated patients. The mathematical denominator must explicitly isolate expected subsequent readmissions over the follow-up period.
2. The Baseline Rule (local risk vs. Ottawa risk) The Ottawa cohort possessed a specific, high baseline rate of readmissions. Absolute Risk Reduction (ARR) is not a directly portable metric across different populations. If a local UK Trust has a lower underlying readmission rate, subtracting an absolute 11.6% per patient mathematically overstates the benefit. Analysts must establish the local Trust’s actual baseline readmission rate as the starting point.
3. The Effect Rule (relative hazard vs. all-cause ARR) Because baseline risks vary across hospital populations, adjustments must utilise the Relative Risk Reduction (or Hazard Ratio) rather than the ARR. The scientifically robust relative comparator for 2-year readmissions reported by Mullen et al. is the adjusted Hazard Ratio (HR = 0.79). This represents a 21% relative reduction in the hazard of readmission, which must be applied to the local baseline established in Rule 2.
4. The Pro-Rata Rule (incremental vs. absolute quits) Health benefits are biologically tied to the cessation of smoking. The Ottawa intervention achieved its relative health benefits by securing a 14.8% incremental quit rate (a 35.2% quit rate in the intervention group against a 20.4% background quit rate in the control group). Historically, models have erroneously used the 35% absolute figure as the incremental effect, effectively ignoring the control group and doubling the expected benefit. Any applied relative risk reduction must be pro-rated (scaled) strictly against the local service’s actual incremental (net) quit rate compared to the 14.8% Ottawa benchmark.
7.0.2 The reconciliation steps
The build_ottawa_reconciliation.R module calculates 2-year hospital savings across a four-step methodological staircase, allowing stakeholders to trace exactly how and why historical estimates differ from the new biological model:
Step 1. Historical expectation (unadjusted ARR): Replicates historical business cases by applying the Ottawa 11.6% all-cause ARR strictly to the treated headcount.
Step 2. Pro-rata adjusted ARR: Scales the historical expectation down to reflect clinical reality, driven by the ratio of the local simulated incremental quit rate to the true Ottawa 14.8% incremental benchmark.
Step 3. Local baseline adjusted (epidemiological gold standard): Corrects the denominator fallacy. Applies the Ottawa adjusted HR (0.79)—scaled by the local incremental quit rate—to the Trust’s true expected baseline of readmissions, excluding the index admission.
Step 4. Dynamic model (Hospital-TTD-Mod): The final model output. Replaces flat readmission subtractions with dynamic Potential Impact Fractions (PIF), driven by disease-specific Relative Risks, risk decay curves, and comorbid disease mapping.
7.0.3 Illustrative worked example
To demonstrate the mathematical impact of these rules, consider a hypothetical local Trust cohort:
Local quit rate: The Trust achieves a 7.4% incremental quit rate (exactly half of the true 14.8% Ottawa benchmark).
Local baseline risk: The Lexis engine projects these 1,000 individuals will generate 300 expected true readmissions over the next 2 years if left untreated.
Tracing this cohort through the reconciliation steps illustrates the necessity of epidemiological adjustment:
Step 1 (historical method): 1,000 patients × 11.6% ARR = 116 readmissions prevented. (Flaw: Assumes a massive 35% net quit rate and applies absolute reductions to headcount).
Step 2 (pro-rata fix): 116 readmissions × 0.5 (quit scalar) = 58 readmissions prevented. (Correction: Acknowledges that the local service is achieving half the incremental quits (7.4%) of the Ottawa benchmark (14.8%). Flaw: Still applies an absolute risk reduction).
Step 3 (epidemiological gold standard): 300 expected readmissions × ((1 - 0.79 HR) × 0.5 quit scalar) = 300 × (0.21 × 0.5) = 300 × 0.105 = 31.5 readmissions prevented. (Correction: Safely anchors the relative benefit to the actual baseline and true incremental quit rates).
Step 4 (Hospital-TTD-Mod output): The dynamic PIF engine maps the cohort’s specific comorbidities and yields ~41 readmissions prevented. (Note on Step 4: You might notice this number is slightly higher than Step 3. This happens because Step 3 applies a general, average benefit across all types of hospital readmissions. Step 4 works differently: it removes any benefit for non-smoking-related readmissions (which lowers the estimate), but applies a much stronger benefit to specific smoking-related diseases like COPD or heart disease (which raises the estimate). Because hospitalized smokers typically have multiple severe smoking-related conditions, focusing purely on these specific diseases often results in a higher overall impact than using a general average).
7.0.4 Code execution
The code isolates these dimensions to ensure mathematical bounds are respected:
Code
# Extract from build_ottawa_reconciliation.R# Note: Benchmark constants (OTTAWA_ARR_2YR, OTTAWA_INC_QUIT_RATE, OTTAWA_HR_2YR) # are securely inherited from the central 00_config.R file.# Step 1: Unadjusted Historical Expectation (Headcount * ARR)total_treated_indiv <-sum(pathway_t$group_seen_indiv, na.rm =TRUE)step1_naive <- total_treated_indiv * OTTAWA_ARR_2YR# Step 2: Pro-Rata Adjustment (Scaling by local quit success)quit_scalar <- english_inc_quit_rate / OTTAWA_INC_QUIT_RATEstep2_prorata <- step1_naive * quit_scalar# Step 3: Local Baseline Adjusted (Epidemiological Gold Standard)# Calculate expected annual admissions for the treated cohort using their actual multiplierscohort_yr1_admissions <-sum(pathway_t$group_seen_indiv * pathway_t[[ADMISSION_MULTIPLIERS]], na.rm =TRUE)# ISOLATE Year 1 true readmissions by subtracting the index headcount firstyr1_readms <-max(0, cohort_yr1_admissions - total_treated_indiv)# Linearly project ONLY the readmissions to 2 yearstrue_expected_readms <- yr1_readms *2# Apply the Ottawa HR to this clean cohort baseline, pro-rated by true quit successrelative_hazard_reduction <-1- OTTAWA_HR_2YRstep3_baseline_fixed <- true_expected_readms * (relative_hazard_reduction * quit_scalar)
7.1 Conclusion of validation
By presenting the Hospital-TTD-Mod outputs (Step 4) alongside the baseline-adjusted Ottawa benchmark (Step 3), analysts can demonstrate that Hospital-TTD-Mod is accurate and methodologically safe.
Because the Lexis model relies on dynamic Potential Impact Fractions (PIFs), it naturally filters out readmissions that have no causal link to tobacco consumption. As a result, the PIF-driven outputs align closely with, but remain slightly more conservative than, the rigorously adjusted Step 3 benchmark. This shows that the new model successfully captures the “Ottawa effect” while providing a more defensible, biologically grounded forecast than previous spreadsheet extrapolations.