Contingency analyses

Question 1

What is the relative risk, reduction in absolute risk and reduction in relative risk?

Answer 1

RR= P1/ P2

Relative risk is the probability of success in the treatment group divided by the probability of success in the control group.

Reduction in relative risk shows how much smaller the risk in the treatment group is compared to the control group.

1-RR

Reduction in absolute risk shows the difference between P(success) in control and treatment.

P2 (control) - P1 (treatment)

Question 2

How to calculate an odds ratio

Answer 2

First, You must determine the odds of success in the treatment and then the control group. The odds of success are the probability of success divided by the probability of failure, where “success” refers to the outcome of interest.

O= p/ 1-p

The odds ratio is the ratio between these values.

OR= 1: Odds of success and failure are the same

OR>1: Odds of success are greater in the treatment group than the control group.

P= odds/ 1+ odds

Or odds (x/y) = p (x/x+y)

Question 3

How to use the x2 contingency test to test hypotheses

Answer 3

The χ2 contingency test makes it possible to test the null hypothesis that two categorical variables are independent.

Yout must work out the expected values.

Expected:
Total collum x total row = total

Question 4

How to use Fisher’s exact test

Answer 4

Fisher’s exact test calculates an exact P-value for the test of independence of two variables in a 2×2 table. The test is especially useful when the rules for the χ2 approximation are not met.

Question 5

Odds ratio short cut

Answer 5

OR= (a/c)/ (b/d)

Question 6

Standard error and confidence interval for odds ratio

Answer 6

SE(ln(OR))= sqrt 1/a + 1/b + 1/c + 1/d

ln(OR) - Zx SE(lnOR) < ln(OR)< ln(OR) + Zx SE(lnOR)

Then must do e^x

Z:

1.96= 95%
2.58= 99%