We want to examine the relationship between smoking and breast cancer. Since smoking has a misclassification, it should be adjusted to find an unbiased relationship. Some methods are presented by Gustafson et al to solve this problem. Some researcher have mentioned that alcohol can also confound this relationship and to find an unbiased relationship; the confounding effect of alcohol should be adjusted too. But the alcohol itself also has misclassification and to controlling total confounding effect of alcohol; this misclassification should be adjusted too. Some methods also exist to solve this problem.
About mentioned scenario; I have a question: so can it be assumed that misclassification alcohol and smoking are independent?
As far as I am concerned misclassification is a kind of information bias (refers to bias arising from measurement error). When you define different categories for each aforementioned variable I think you can deal with it as categorical variables.
Dear Reza Pakzad, these links may be helpful
http://www.medscape.com/viewarticle/704006
http://www.independent.co.uk/life-style/health-and-families/health-news/glass-of-wine-smoking-cigarette-prevent-damage-viktoria-schwarz-a7419301.html
https://www.ncbi.nlm.nih.gov/pubmed/28727853
https://oup.silverchair-cdn.com/oup/backfile/Content_public/Journal/annonc/22/12/10.1093/annonc/mdr027/2/mdr027.pdf?Expires=1502443542&Signature=FRwHP1lfAfUP~hDaICzdgWmz403N6urUU0lIumDbnDQEK-MgT8y44Gt1DubF9GmwKltSKEp8zHQ7MPXx6B8~Z8nM5mn-fbucIx6fm2i2FMl5KiYQ0RnIGNEfnLUc8ZeHKb7WJcZggprA81VGgXUhDfQEHIdqiKu9WmVI5B~NkGut2qZhEJM91seBXNXY0sNxXsmhQqfFuZetegluj9SmZiH7-mL5e6vG0mWbvg2~ZPxGln2KiPh1-NJE0lcrnVwB6EBNY725ofkG-FqraczKCkdYKqi8w8ExxbXfADizsTA2dFKMgor8FMpXofS35~X1Uk7IuP~SKiv5T2Fn4N9-FQ__&Key-Pair-Id=APKAIUCZBIA4LVPAVW3Q
http://cancerres.aacrjournals.org/content/canres/49/14/4024.full.pdf
http://www.breastcancer.org/risk/factors/smoking
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