A compartmental model for smoking dynamics in Italy: a pipeline for inference, validation, and forecasting under hypothetical scenarios

Abstract

We propose a compartmental model for investigating smoking dynamics in an Italian region (Tuscany). Calibrating the model on local data from 1993 to 2019, we estimate the probabilities of starting and quitting smoking and the probability of smoking relapse. Then, we forecast the evolution of smoking prevalence until 2043 and assess the impact on mortality in terms of attributable deaths. We introduce elements of novelty with respect to previous studies in this field, including a formal definition of the equations governing the model dynamics and a flexible modelling of smoking probabilities based on cubic regression splines. We estimate model parameters by defining a two-step procedure and quantify the sampling variability via a parametric bootstrap. We propose the implementation of cross-validation on a rolling basis and variance-based Global Sensitivity Analysis to check the robustness of the results and support our findings. Our results suggest a decrease in smoking prevalence among males and stability among females, over the next two decades. We estimate that, in 2023, 18% of deaths among males and 8% among females are due to smoking. We test the use of the model in assessing the impact on smoking prevalence and mortality of different tobacco control policies, including the tobacco-free generation ban recently introduced in New Zealand.

Keywords: Calibration; Compartmental models; Cross validation; Forecasting; Global sensitivity analysis; Parametric bootstrap; Regression splines; Smoking attributable deaths; Smoking dynamics; Tobacco control policies.

Fig. 1

Smoking Habits Compartmental model in its simplest form

Fig. 2

Results of the two-step estimation procedure for males in blue and females in red, with their bootstrap $90\%$ confidence intervals: parameters tuning the probabilities of starting ($\mathit{\psi }$) and stopping smoking ($\mathit{\varphi }$), and the probability of smoking relapse ($\mathit{\omega }$) (a), age-specific mortality for never smokers and for the general population (b), probabilities of starting ($\gamma (a)$), and stopping smoking ( $ϵ(a)$) and probability of smoking relapse ($\eta (c)$) (c), observed and predicted prevalence for never (N), current (C) and former (F) smokers (d), Population Attributable Fraction (PAF) and Smoking Attributable Deaths (SAD) for people over the age of 35 (e) and 65 (f)

Fig. 3

Results of the two-step estimation procedure for males in blue and females in red, by period of calibration (from 1993 to 2004 in a light colour and from 2005 to 2019 in a dark colour): probabilities of starting ($\gamma (a)$) and stopping smoking ($ϵ(a)$), and probability of smoking relapse ($\eta (c)$), with 90% confidence bands, (a) and (c); prevalence of never (N), current (C) and former (F) smokers, with 90% confidence bands, (b) and (d)

Fig. 4

Estimated prevalence of never (N), current (C) and former (F) smokers under different tobacco control policies (TCP) with $90\%$ confidence bands, for males (a) and females (b)