Return to Answer

Sorry. I am not converting odds ratios to percentages I was talking about the percentage 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 $1.9$ means $p_1/(1-p_1)= 1.9 p_2/(1-p_2)$ or $p_1(1-p_2)=1.9 p_2(1-p_1)$ or $$p_1-p_1 p_2 =1.9 p_2-1.9 p_1 p_2$$ This implies $p_1=1.9 p_2-.9 p_1 p_2$ or $p_1= 1.9 p_2(1-.9 p_1)$ or $$p_1/(p_1+p_2)=1.9 p_2(1-.9 p_1)/[p_2(2-.9 p_1)]= 1.9 (1-.9 p_1)/(2-.9 p_1)]$$ This depends on $p_1$. If $p_1=0$ this is $1.9/2=0.95$ and if $p_1=1$ it is $1.9 \cdot .1/1.1=0.19/1.1=0.1727$. for any $p_1>0$ the ratio ranges from $0.95$ to $0.173$.

Sorry. I am not converting odds ratios to percentages I was talking about the percentage 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 $1.9$ means $p_1/(1-p_1)= 1.9 p_2/(1-p_2)$ or $p_1(1-p_2)=1.9 p_2(1-p_1)$ or $$p_1-p_1 p_2 =1.9 p_2-1.9 p_1 p_2$$ This implies $p_1=1.9 p_2-.9 p_1 p_2$ or $p_1= 1.9 p_2(1-.9 p_1)$ or $$p_1/(p_1+p_2)=1.9 p_2(1-.9 p_1)/[p_2(2-.9 p_1)]= 1.9 (1-.9 p_1)/(2-.9 p_1)]$$ This depends on $p_1$. If $p_1=0$ this is $1.9/2=0.95$ and if $p_1=1$ it is $1.9 \cdot .1/1.1=0.19/1.1=0.1727$. for any $p_1>0$ the ratio ranges from $0.95$ to $0.173$. However given the complete contingency table you can calculate $p_1$.

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 $1.9$ means $p_1/(1-p_1)= 1.9 p_2/(1-p_2)$ or $p_1(1-p_2)=1.9 p_2(1-p_1)$ or $$p_1-p_1 p_2 =1.9 p_2-1.9 p_1 p_2$$ This implies $p_1=1.9 p_2-.9 p_1 p_2$ or $p_1= 1.9 p_2(1-.9 p_1)$ or $$p_1/(p_1+p_2)=1.9 p_2(1-.9 p_1)/[p_2(2-.9 p_1)]= 1.9 (1-.9 p_1)/(2-.9 p_1)]$$ This depends on $p_1$. If $p_1=0$ this is $1.9/2=0.95$ and if $p_1=1$ it is $1.9 \cdot .1/1.1=0.19/1.1=0.1727$. for any $p_1>0$ the ratio ranges from $0.95$ to $0.173$.

Sorry. I am not converting odds ratios to percentages I was talking about the percentage 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 $1.9$ means $p_1/(1-p_1)= 1.9 p_2/(1-p_2)$ or $p_1(1-p_2)=1.9 p_2(1-p_1)$ or $$p_1-p_1 p_2 =1.9 p_2-1.9 p_1 p_2$$ This implies $p_1=1.9 p_2-.9 p_1 p_2$ or $p_1= 1.9 p_2(1-.9 p_1)$ or $$p_1/(p_1+p_2)=1.9 p_2(1-.9 p_1)/[p_2(2-.9 p_1)]= 1.9 (1-.9 p_1)/(2-.9 p_1)]$$ This depends on $p_1$. If $p_1=0$ this is $1.9/2=0.95$ and if $p_1=1$ it is $1.9 \cdot .1/1.1=0.19/1.1=0.1727$. for any $p_1>0$ the ratio ranges from $0.95$ to $0.173$.

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 $1.8 \cdot .2/1.2=1.8/6=0.3$. for any $p_1>0$ the ratio ranges from $0.9$ to $0.3$.

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 $1.9$ means $p_1/(1-p_1)= 1.9 p_2/(1-p_2)$ or $p_1(1-p_2)=1.9 p_2(1-p_1)$ or $$p_1-p_1 p_2 =1.9 p_2-1.9 p_1 p_2$$ This implies $p_1=1.9 p_2-.9 p_1 p_2$ or $p_1= 1.9 p_2(1-.9 p_1)$ or $$p_1/(p_1+p_2)=1.9 p_2(1-.9 p_1)/[p_2(2-.9 p_1)]= 1.9 (1-.9 p_1)/(2-.9 p_1)]$$ This depends on $p_1$. If $p_1=0$ this is $1.9/2=0.95$ and if $p_1=1$ it is $1.9 \cdot .1/1.1=0.19/1.1=0.1727$. for any $p_1>0$ the ratio ranges from $0.95$ to $0.173$.