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Michael R. Chernick
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Sorry. I am not converting odds ratios to percentages I was talking about the percantage of the variation among the women that is attributable to smoking. The odds ratio is $(p_1/(1-p_1))/(p_2/(1-p_2))$. I guess you are interested in $p_1/(p_1+p_2)$. First remember that you are computing estimates of the parameters and not the parameters themselve. An odds ratio of 1 means $p_1=p_2$ or $p_1/(p_1+p_2)=1/2$. An odds ratio of $1.8$ means $p_1/(1-p_1)= 1.8 p_2/(1-p_2)$ or $p_1(1-p_2)=1.8 p_2(1-p_1)$ or $p_1-p_1 p_2 =1.8 p_2-1.8 p_1 p_2$. This implies $p_1=1.8 p_2-.8 p_1 p_2$ or $p_1= 1.8 p_2(1-.8 p_1)$ or $p_1/(p_1+p_2)=1.8 p_2(1-.8 p_1)/[p_2(2-.8 p_1)]= 1.8 (1-.8 p_1)/(2-.8 p_1)]$ This depends on $p_1$. If $p_1=0$ this is $1.8/2$=0.9 and if $p_1=1$ it is 1.8 $.2/1.2=1.8/6$=0.3. for any $p_1>0$ the ratio ranges from 0.9 to 0.3.

Michael R. Chernick
  • 43.2k
  • 28
  • 85
  • 159