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Unfortunately, no.  That is one of the limitations of all cross-sectional studies, which are a snapshot in time.  That is why we are careful to say there is an "association."

The fact that some of the MI's occurrent before e-cigarettes were available, called exposure missclassification, biases the results toward the null, which means that we are almost certainly underestimating  the association between e-cig use and having had an MI.  You can see this issue discussed, including citations to a statistical methods paper that explains why this is the case, in our paper showing that e-cigarette use is associated with less smoking cessation in the EU, which is avaiable here.

Getting information on timing requires longitudinal studies in which people are followed forward in time, often for many years.  These studies take a long time to do (because you have to wait for time to pass) and are much more expensive to do than cross-sectional studies.  That is why the cross-sectional studies are always done first.  Finding associations as we did between daily e-cig use and MI demonstrates the need for longitudinal studies.

While longitudinal studies are better, the fact is that well-done cross sectional studies generally come up with similar risk estimates as longitudinal studies.  This is illustrated by the studies on gateway effects for e-cigs causing kids to take up cigarettes.  The original cross-sectional studies pointed the way for sunsequent longitudinal studies, which nailed down the link.

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