Estimating the distribution of lag in the effect of short-term exposures and interventions: adaptation of a non-parametric regression spline model.

Information on the distribution of lag duration between exposure or intervention and the subsequent changes in risk can help in assessing the impact of exposure, predicting cost-effectiveness of intervention, and understanding the underlying biological mechanisms. Previous approaches focused more on optimizing the strength of the exposure-disease association than on directly estimating lag duration. We propose an alternative approach applicable to the analysis of the lagged effects of binary exposure variables. The density function of the distribution of lags is estimated based on flexible modelling of changes in hazard ratio of exposed versus unexposed subjects. The methodology is evaluated in a simulation study and is applied to the Framingham data to investigate the lagged effect of smoking cessation on coronary heart disease risk. Copyright 2003 John Wiley & Sons, Ltd.