Solution to question 6.2
I have calculated risks and odds on the basis of unhealthy implants as this made more sense to me. You may have done it the other way and calculated for healthy implants. In this case you answers will be different to mine.
Risk ratio
The risk of a smoker having an unhealthy implant is: 48÷80 = 0·600
48 out of 80 smokers have unhealthy implants.
The risk of a non-smoker having an unhealthy implant is: 7÷17 = 0·412
7 out of 17 non-smokers have unhealthy implants.
The risk ratio for having a healthy implant for smokers compared to non-smokers is 0·600÷0·412= 1·46
Smokers have about one and a half times the risk of having an unhealthy implant compared to non-smokers
Odds ratio
The odds of a smoker having an unhealthy implant are: 48÷32 = 1·5
48 smokers have unhealthy implants, 32 do not.
The odds of a non-smoker having an unhealthy implant are: 7÷10 = 0·7
7 non-smokers have unhealthy implants, 10 do not.
The odds ratio for having a healthy implant for smokers compared to non-smokers is 1·5÷0·7= 2·14
Smokers have about twice the odds of having an unhealthy implant compared to non-smokers
Which to use?
As this is a retrospective study (the subjects were selected on the basis of the outcome - health of implant - rather than exposure - smoking status) we have to use the odds ratio.
The χ2 test
As P > 0·05 the χ2 test failed to show a significant association between smoking and health of implant. This leads us to believe that the odds ratio of 2·14 we calculated would be likely to have a confidence interval that includes 1 (indicating no difference in the odds of an unhealthy implant between the two groups).
