Data were provided by the TDS and the health informatics teams in both organisations.

Covariates

The following covariates were chosen based on the findings of previous research, e.g. [14,15,16, 18].

Patient demographics

Patient demographics were derived from patients’ admission data, specifically the following: sex; self-reported ethnicity, categorised into White, Black, Asian, Mixed, and Other (see Additional file 1: Table S1 for further detail of ethnicity groupings); and age category on admission, categorised into bands 16–24, 25–39, 40–59, and 60 +, representing youth and three stages of adulthood, respectively. Where the patient was resident in England, the Index of Multiple Deprivation (IMD) score associated with their home postcode was used as a measure of relative socio-economic deprivation. Scores were grouped according to national tertile, with lower scores representing greater levels of deprivation [20].

Clinical characteristics of admission Primary diagnosis

Primary diagnoses relating to the presenting problem on admission were grouped according to ICD-10 chapter (A00–B99 infectious and parasitic, C00–D48 neoplasms, E00–E90 endocrine and blood, F00–F99 mental behavioural and neurodevelopmental disorders, G00–G99 nervous system, I00–I99 circulatory, J00–J99 respiratory, K00–K93 digestive, L00–L99 skin and subcutaneous, M00–M99 musculoskeletal, N00–N99 genitourinary, S00–T98 injury poisoning and external causes, and all others) [21]. A binary smoking-related disease variable was created which included any condition from chapters relating to circulatory disease, respiratory disease, or neoplasms.

Intention at first TDS assessment

Patient intention at the first assessment by a TDS was categorised according to whether they declined the offer of support (declined intervention), whether they wished to temporarily abstain with or without the use of smoking cessation aids (withdrawal management), or whether they intended to quit (quit attempt).

Heaviness of Smoking Index (HSI)

Severity of cigarette dependence was measured by the Heaviness of Smoking Index (HSI), a well-validated questionnaire which has been found to be predictive of quit success [22]. The two items of the HSI pertain to the number of cigarettes per day and time to the first cigarette. Respondents are categorised into low (scores 0–1), medium (scores 2–4), or high (scores 5–6) levels of cigarette dependence.

Smoking cessation aids

Licensed smoking cessation aids were available and prescribed to patients during admission, comprising NRT in the form of patches, inhalators, mouth spray, lozenges and gum, and varenicline (see Additional file 1: Tables S2 and S3 for an itemised list of prescribed smoking cessation aids). The number of different types prescribed to a patient during admission were grouped as none, single, or combination.

Clinical characteristics of patients Past diagnoses

Separate binary variables were used to indicate any previously recorded diagnosis of mental and behavioural disorder (excluding those relating to the use of tobacco), cancer, chronic obstructive pulmonary disease (COPD), cardiovascular disease (CVD), or diabetes.

OutcomesOutcome 1: Accepted intervention at TDS assessment

A binary variable was created based on the patient’s intention at first TDS assessment, to indicate whether a patient declined the intervention (opted out) or agreed to the intervention (regardless of whether they intended to quit smoking or simply manage their tobacco withdrawal whilst in hospital).

Outcome 2: Smoking cessation

Smoking status was recorded at the start of admission and at each phone call during the 6-month post-discharge period. As per previous studies, where a TDS was unable to contact the patient, this was assumed to be indicative of the patient having relapsed or continuing to smoke [8, 11]. Three binary variables were used to indicate a patient’s smoking status (non-smoker vs smoker or unknown) at 30, 90, and 180 days post-discharge.

Outcome 3: All-cause death

A binary variable was created to indicate death by any cause, from 31 days to 1 year after discharge. This timespan was chosen as it permits the inclusion of smoking status at up to 30 days post-discharge as an exposure in regression models, and deaths that occur within 30 days are unlikely to have been influenced by the intervention and/or quit success during and immediately after initial admission.

Outcome 4: All-cause readmission

A binary variable was created to indicate readmission for any cause, from 31 days to 1 year after discharge, on the same rationale as outcome 3 (all-cause death) above.

Analysis

All analyses were performed using R version 4.3.0 [23]. Descriptive analyses were conducted using counts and proportions. Quit rates (those defined as non-smokers) at 30, 90, and 180 days were calculated using the numbers seen by TDS as the denominator. Descriptive statistics are reported separately for each hospital site.

Logistic regression models were fit to the data to estimate the association of the covariates described above with each of the outcomes of interest. Adjusted estimates from multivariable models containing all covariates are reported alongside unadjusted estimates. Odds ratios, confidence intervals, and p-values are reported for all covariates, representing the direct effect of each covariate when all others are held constant (in the adjusted model). No set threshold for statistical significance was applied to the primary analysis; odds ratios, confidence intervals, and p-values were all considered in assessing the magnitude and meaning of the results [24, 25].

Patients who died within 180 days of discharge were removed from the models of smoking status outcomes. Patients who lived outside of London were removed for the analysis of all-cause readmission, on the assumption that such patients would be less likely to be readmitted to the index hospital given other hospitals would be closer to home for such patients. The logistic regression models used combined data from both sites to maximise sample size but included the hospital site as a covariate to control for site-specific effects. The full sample frequencies of each covariate stratified by each outcome are available in Additional file 1: Tables S4–S7, and the frequencies as used in the regression models but separated by each hospital site are available in Additional file 1: Tables S8–S11.

Missing data

There were missing data in all variables although the extent of missingness varied greatly, from 0.5% missing sex (n = 10) to 40.4% missing constituent HSI score item time-to-first-cigarette (n = 835). Missing data were imputed using multiple imputation by chained equations, using the mice package in R [26] and following published guidance [27, 28]. All outcomes and covariates from the primary analysis were included in the imputation model in their original form (e.g. component items of the HSI were imputed separately rather than the derived HSI score itself). Where there were auxiliary variables not included in the main analysis but observed in the data provided by both hospitals, these were also included to assist the accuracy of the imputation model. The final imputation model contained 31 variables. Imputed values were generated for all missing data, except for where a smoking status outcome was observed as ‘unknown’ as these were retained as a presumptive indication of smoking, as stated above. Fifty imputed data sets were generated. Variable distributions were compared between observed and imputed data (see Additional file 1: Fig. S1). Results from the analyses were combined using Rubin’s rules [28, 29].

Sensitivity analyses

For smoking status, we also calculated quit rates at 30, 90, and 180 days (i) among those identified as smoking on admission (whether assessed by TDS or not) and (ii) among only those who had complete follow-up data (i.e. where smoking status was not recorded as ‘unknown’).

For the regression results, a range of sensitivity analyses were conducted to test the robustness of the primary analysis. For each outcome, effect estimates from the logistic regression using imputed data (the primary analysis) were compared with effect estimates from (i) a complete case analysis which excluded any cases for which there were missing data in any of the variables included in the primary regression model, (ii) a first-admission-only analysis which excluded any repeat admissions for an individual previously admitted during the study period, (iii) a complete case analysis of the first-admission-only data, and (iv) analysis restricted to patients who were seen by the TDS and accepted the intervention, i.e. excluding any patients where the intervention was declined at first assessment.