Estimating the decline in excess risk of cerebrovascular disease following quitting smoking - A systematic review based on the negative exponential model

•With the negative exponential model we tried to quantify the decline in stroke risk after quitting.•The model estimates the half-life, H, the time quit when excess risk becomes half that of a smoker.•The method failed if the current smoker RR was <1.40, but H could be derived for 11 datasets.•Overall H was estimated as 4.8 (95%CI 2.2-10.5) years, but large between-study variation existed.•The estimate is similar to that reported for IHD (4.40 years), where heterogeneity was also large.

We attempted to quantify the decline in stroke risk following quitting using the negative exponential model, with methodology previously employed for IHD. We identified 22 blocks of RRs (from 13 studies) comparing current smokers, former smokers (by time quit) and never smokers. Corresponding pseudo-numbers of cases and controls/at risk formed the data for model-fitting. We tried to estimate the half-life (H, time since quit when the excess risk becomes half that for a continuing smoker) for each block. The method failed to converge or produced very variable estimates of H in nine blocks with a current smoker RR <1.40. Rejecting these, and combining blocks by amount smoked in one study where problems arose in model-fitting, the final analyses used 11 blocks. Goodness-of-fit was adequate for each block, the combined estimate of H being 4.78(95%CI 2.17-10.50) years. However, considerable heterogeneity existed, unexplained by any factor studied, with the random-effects estimate 3.08(1.32-7.16). Sensitivity analyses allowing for reverse causation or differing assumed times for the final quitting period gave similar results. The estimates of H are similar for stroke and IHD, and the individual estimates similarly heterogeneous. Fitting the model is harder for stroke, due to its weaker association with smoking.