Question

THEN

A study of Navajos residing in the United States formed matched pairs of individuals. In each pair, one member had experienced acute my- ocardial infarction (MI) and the other member was free of heart discase. This rulicd in a toa AA pairs displayd in he able below. No MI MI Diabetes No Diabetes Total Diabetes No Diabetes Total 9 16 25 37 82 119 46 98 144 Calculate a point estimate for the odds ratio, that is, for the odds of having a pair with one member MI+Diabetes and the other No MI No Diabetes, divided by the odds of having a pair with one member MI+No Diabetes and the other No MI+Diabetes. Calculate a 95% confidence interval for the odds ratio just calcu- laicd.

Answer 1

Odds ratio =

$\frac{9/16}{37/82}=1.24662$

The formula for the 95% Confidence Interval for the odds ratio is as follows:

Дод(OR) t [1 .96xSE( log(OR))] )

The standard error for log(OR) is computed using the following equation:

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Calculate the natural log of the risk ratio.

$log_e(1.24662)=0.22043$

Calculate the standard error of the log(OR)

$\\SE(log_e(OR)=\sqrt{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{c}}\\ =\sqrt{\frac{1}{9}+\frac{1}{16}+\frac{1}{37}+\frac{1}{82}}\\=0.4613385$

Calculate the lower and upper confidence bounds on the natural log scale

95% conf. İnt.-log (OR)士1.9бы SE(log (OR) )

$\\log(95\% conf. int.)=\\=0.2204371897\pm1.96*0.4613385\\=(-0.6837862703,1.12466065)$

Convert the log limits back to a normal scale for odds ratios by taking the antilog.

$\\e^{-0.6837862703}=0.5047\\ e^{1.12466065}=3.0792\\95\%\ conf.\ int.=(0.5047,3.0792)$