Aim: Sample Size: Hypothesis testing for Relative Risk (RR) in cohort study. Null Hypothesis: RR = 1.
Formula Used: for 2 tailed hypothesis
For 1 tailed hypothesis, please replace α / 2 with α in above formula.
To calculate P1 or P2 or RR, when other two are known
P1 = RR * P2
P2 = RR * P1
RR = P1 / P2
RR = Anticipated Relative Risk
P1 = Anticipated Incidence amongst exposed (out of 1) (e.g. 25% = 0.25)
P2 = Anticipated Incidence amongst non-exposed (out of 1) (e.g. 25% = 0.25)
r= Non-exposed (controls) : Exposed (Cohort) ratio
α = 1 – Confidence level (out of 1) (e.g. 95% confidence level = 0.95, α = 0.05)
Z 1-α/2 = the standard normal deviate corresponding the confidence level
Z 1-β = the standard normal deviate corresponding to power (out of 1)
Example:
A cohort study is planned to test whether attendance in class (risk factor) is a significant risk factor for failure in final examination (outcome). A pilot study has revealed that the incidence of failures amongst less attendees and regular attendees is 30 % and 10 % respectively. How much sample size shall be required to test two tailed null hypothesis of RR =1, at 95% confidence level, power = 80% and Controls: Cohort = 1?
Solution:
Here
P1 = 30%, P2=10%, Confidence level = 95%, power = 80%, tails=2
After putting these values, we get required sample size in each group = 74.
We also get the estimated RR = 3.
Alternate methods:
The formula for sample size in case group, for 2 tailed test, described by Kelsey et al. (For 1 tailed test, please replace α /2 with α.)
Where
The formula for sample size in case group, for 2 tailed test, described by Fleiss et al. without continuity correction. (For 1 tailed test, please replace α /2 with α.)
The formula for sample size in case group, for 2 tailed test, described by Fleiss et al. with continuity correction. (For 1 tailed test, please replace α /2 with α in the formula for Nwithout CC.)
@ Sachin Mumbare