Course Notes - Department of Mathematics and Statistics

So in our swimming example:• Odds in ≥ 6 hrs group = 32118• Odds in < 6 hrs group = 17127• Odds Ratio = 32/11817/127 = 32×12717×118 = 2.026Why use the Odds Ratio?• Consider the situation when we select less controlsErosion of EnamelSwim Time Per Week Yes (Cases) No (Controls) Total≥ 6 hrs 32 24 56< 6 hours 17 25 4249 49 98• The new Odds Ratio = 32/2417/25 = 32×2517×24 = 2.0• Which is pretty similar to the previous result.If we had used relative risk:‘Risk’ ‘RR’Study 1 ≥ 6 hrs 32/150< 6 hrs 17/144 1.75Study 2 ≥ 6 hrs 32/56< 6 hrs 17/42 1.43• Notice the disagreement. The consequence is that the relative riskcan be made to take any value by choice of numbers of cases andcontrols.If we have a rare disease:Exposed 1 Disease (Case) No Disease (Control) TotalYes w x r 1 = w + xNo y z r 2 = y + zc 1 = w + y c 2 = x + z n = w + x + y + z• For rare diseases w and y are quite small145