# 'Odd' Odd ratio question

Assuming Intervention group to be mothers having c-section and control group to be mothers having natural birth. Also, the numerical data is as follows:

               Mothers opting for natural    mothers c section    Adjusted OR
n=75057                       n=1515
Death  53                            0                    -


(i) If the intervention group were similar in background factors to the control group, roughly how many adverse events would you expect in the intervention group?

(ii) If the adjusted odds ratio is correct, about how many adverse events would be expected if the 1515 mothers in intervention group had instead were in control group? What, in terms of their background risk, would this say about the those 1515 mothers from intervention group

I am getting (i) 24 by using simple expectations and (ii) 15 by simply multiplying 1.7 by 9.

extremely unsure about my answers and hence turned to you mathmos (cambridge term for mathematicians)

Any help will be appreciated!

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i) I get about 24.52 which rounds to 25, not 24

ii) odds ratio $=\frac{p_1(1-p_2)}{p_2(1-p_1)}$

$p_2=\frac{9}{1515}$

$\frac{1506p_1}{9(1-p_1}=2.7$

$\frac{1-p_1}{p_2}=0.016135$

$1.016135p_1=0.01635$

$p_1=0.01588$

$1515p_1=24.06$ adverse effects

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Thanks Angela! =) Also, the Back ground risk is less when mothers have c-section as compared to natural birth. Can I write that 25-24 = 1 ,i.e., the risk difference suggests background risk is greater? – Hassan Khan Mar 25 '12 at 2:44