Modelling continuous abstinence rates over time from clinical trials of pharmacological interventions for smoking cessation.

BACKGROUND AND AIM: It is useful, for theoretical and practical reasons, to be able to specify functions for continuous abstinence over time in smoking cessation attempts. This study aimed to find the best-fitting models of mean proportion abstinent with different smoking cessation pharmacotherapies up to 52 weeks from the quit date. METHODS: We searched the Cochrane Database of Systematic Reviews to identify randomized controlled trials (RCTs) of pharmacological treatments to aid smoking cessation. For comparability, we selected trials that provided 12 weeks of treatment. Continuous abstinence rates for each treatment at each follow-up point in trials were extracted along with methodological details of the trial. Data points for each pharmacotherapy at each follow-up point were aggregated where the total across contributing studies included at least 1000 participants per data point. Continuous abstinence curves were modelled using a range of different functions from the quit date to 52-week follow-up. Models were compared for fit using R2 and Bayesian information criterion (BIC). RESULTS: Studies meeting our selection criteria covered three pharmacotherapies [varenicline, nicotine replacement therapy (NRT) and bupropion] and placebo. Power functions provided the best fit (R2  > 0.99, BIC < 17.0) to continuous abstinence curves from the target quit date in all cases except for varenicline, where a logarithmic function described the curve best (R2  = 0.99, BIC = 21.2). At 52 weeks, abstinence rates were 22.5% (23.0% modelled) for varenicline, 16.7% (16.0% modelled) for bupropion, 13.0% (12.4% modelled) for NRT and 8.3% (8.9% modelled) for placebo. For varenicline, bupropion, NRT and placebo, respectively, 55.9, 65.0, 62.3 and 56.5% of participants who were abstinent at the end of treatment were still abstinent at 52 weeks. CONCLUSIONS: Mean continuous abstinence rates up to 52 weeks from initiation of smoking cessation attempts in clinical trials can be modelled using simple power functions for placebo, nicotine replacement therapy and bupropion and a logarithmic function for varenicline. This allows accurate prediction of abstinence rates from any time point to any other time point up to 52 weeks.

Continuous time Markov chain approaches for analyzing transtheoretical models of health behavioral change: A case study and comparison of model estimations.

Continuous time Markov chain models are frequently employed in medical research to study the disease progression but are rarely applied to the transtheoretical model, a psychosocial model widely used in the studies of health-related outcomes. The transtheoretical model often includes more than three states and conceptually allows for all possible instantaneous transitions (referred to as general continuous time Markov chain). This complicates the likelihood function because it involves calculating a matrix exponential that may not be simplified for general continuous time Markov chain models. We undertook a Bayesian approach wherein we numerically evaluated the likelihood using ordinary differential equation solvers available from the gnu scientific library. We compared our Bayesian approach with the maximum likelihood method implemented with the R package MSM. Our simulation study showed that the Bayesian approach provided more accurate point and interval estimates than the maximum likelihood method, especially in complex continuous time Markov chain models with five states. When applied to data from a four-state transtheoretical model collected from a nutrition intervention study in the next step trial, we observed results consistent with the results of the simulation study. Specifically, the two approaches provided comparable point estimates and standard errors for most parameters, but the maximum likelihood offered substantially smaller standard errors for some parameters. Comparable estimates of the standard errors are obtainable from package MSM, which works only when the model estimation algorithm converges.