All main analysis comparing groups for primary and secondary outcomes, and additional subgroup and adjusted analyses was conducted using Stata version 13 (StataCorp LP, College Station, TX, USA). Baseline characteristics of participants were summarised in terms of the mean, standard deviation (SD), median, minimum, maximum and number of observations and categorical data in terms of frequency counts and percentages. No formal statistical tests were performed.
Comparison of proportions was carried out for binary outcomes between the intervention and the control groups (entry to smoking cessation service, point prevalent and prolonged abstinence, number completing the 6-week SSS course). Univariable logistic regression analysis was carried out to take into account clustering at the SSS level, and multivariable logistic regression was also carried out to take into account any imbalance in important baseline characteristics known to predict smoking cessation outcomes, nominated prior to examination of the trial data, between the groups. Both unadjusted and adjusted estimates are reported. The unadjusted analysis is considered to be the primary analysis. The size of the difference between treatments is expressed as an OR including 95% confidence interval (CI) from logistic regression, with appropriate allowance for clustering.
The therapists were SSS based rather than practice based, and we initially intended that the therapist effect be accounted for by allowing greater variance between SSSs in the intervention group than in the control group, so that the difference in variance would represent the therapist effect. In fact, we discovered that the estimated variance for the primary outcome was slightly lower in the intervention group, rendering it impossible to fit a model including a special clustering effect for participants only assigned to the intervention. Hence, we allowed only for variance between SSSs, assuming it to be the same in the two groups, and thus fitted a random intercepts model.
Self-reported changes in daily cigarette consumption (the difference between cigarette consumption at baseline and at the 6-month follow-up) is a continuous variable and was compared with the two-sample
t-test and with multiple linear regression to account for important baseline characteristics. ORs for the difference in means is quoted together with the 95% CI.
Furthermore, we estimated the ICC for our primary outcome and for the validated 7-day abstinent outcome. The ICC for a binary outcome can be estimated as:
ρ= σ 2 u σ2u+π 2 3 . (1)
The termσ2ucan be interpreted as the component of outcome variance because of differences between
SSSs, the denominator as the total variance andρas the proportion of the total outcome variance that is due to between-cluster variation.57
Loss to follow-up after randomisation is reported. Analysis is based on intention to treat; that is, we assume that all randomised participants received the treatment that they were randomised to, and all those lost to follow-up are assumed to be still smoking.
Levels of significance
During the course of running the trial but prior to locking the database, based on further expert statistical advice, we devised an analysis plan for interpreting significance levels for analysis on multiple outcomes of interest. Hence, the interpretation of the results of the trial for the primary outcome, (1) engagement with SSS, and the main secondary outcome, (2) 7-day point prevalent abstinence, was governed by an alpha spending plan that preserved the study-wise alpha for (1) and (2). We hypothesised that these outcomes fall naturally into a hierarchy with (1) as a step prior to (2). We employed a hierarchical monitoring plan in which alpha was spent first on (1) and the remaining alpha was available for (2). The simple formula below describes alpha allocation in the hierarchy:
α2c = 1 ½(1 α2s)=(1 α2e), (2)
where subscript 2=two sided; s=study-level critical alpha (0.05); e=engagement with SSS; and c=7-day point prevalent abstinence. Thus, if thep-value for attendance at SSS was 0.02, there remains ap-value of 0.031 to spend on the second outcome of 7-day point prevalent abstinence and ap-value for that outcome of<0.031 would be considered significant. If thep-value for the primary outcome (difference in smoking cessation service attendance) was>0.05, then the overall study would be considered neutral and any finding on the second outcome considered exploratory with a nominalp-value.
Likewise, if there was a significant decrease in attendance within the intervention arm over the control arm, the second outcome would be considered exploratory with a nominalp-value.
Subgroup analyses
In order to assess whether or not the intervention was any more effective for any particular subgroup of smokers, we explored interactions between intervention and deprivation (defined in fifths), intervention and gender, and intervention and age (defined by categories 16–39 years, 40–64 years and≥65 years), for the primary outcome (attendance) and 7-day point prevalent abstinence at the 6-month follow-up. We had planned at an early stage to analyse the interaction with deprivation,58and with gender and age
when drawing up our analysis plan,59prior to the end of data collection.
Subsidiary analyses
We also explored any delayed effect of sending repeat reminders to smokers on the uptake of service, and any differences in attendance due to seasonal variations.