Flexible modelling of the cumulative effect of smoking on lung cancer

INTRODUCTION: the risk of lung cancer due to tobacco smoking is the results of exposures sustained in previous years and possibly decades. The effect has been modelled using several time-varying factors, such as intensity, duration, time since first exposure and/or cessation. Here we propose an alternative model providing a flexible, easy-to-interpret yet sophisticated approach.

METHODS: the modelling framework is based on the combination of two functions describing the potentially non-linear dose-response, and the weights of contributions from past exposures, defined here as lag-response. The model can systematically describe complex associations changing dynamically in time, easily allowing for instance for a delay in the increase in risk after smoking initiation and a decrease after cessation. The method is implemented in the freely available package dlnm within R. The framework is applied to pooled data from three case-control studies with complete exposure histories for 1,479 cases and 1,918 controls.

RESULTS: the logistic model using spline functions to describe the exposure and lag-responses indicates a sub-linear exposure-response, with lung cancer risk flattening out at high tobacco consumption. Smoking 20 cigarettes/day in a given year produces a risk peaking after 8 years, with an odds ratio (OR) of 1.12 (95%CI:1.09-1.15), then decreasing to 1.05 (1.03-1.07) after 25 years, and disappearing only after 50 years. After 20 years of smoking 20 cigarettes/day the cumulative OR is 4.68 (3.82-5.74), and if then smoking ceases it decreases to 3.56 (2.66-4.78) after 10 more years.

CONCLUSIONS: the proposed method offers a flexible alternative to models including several time-varying variables for describing the complex temporal dependency between smoking and lung cancer. The framework can be used to produce dynamic predictions of risk based on specific exposure histories, and it can be extended to any association where the risk is assumed to depend on the cumulative effect of time-varying exposures.