Aim: Statistical Power Calculation: Hypothesis testing for Relative Risk (RR) in cohort study. Null Hypothesis: RR = 1.

Formula Used: for 2 tailed hypothesis


Formula Used: for 1 tailed hypothesis


To calculate P1 or P2 or RR, when other two are known

P1 = RR * P2

P2 = RR * P1

RR = P1 / P2

RR = Relative Risk

P1 = Incidence amongst exposed(out of 1) (e.g. 25% = 0.25)

P2 = Incidence amongst non-exposed (out of 1) (e.g. 15% = 0.15)

Nexposed = Sample Size in exposed group

r = no-exposed to exposed sample size ratio = Nnon-exposed / Nexposed

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

Φ(x)=P(Z ≤ x). It is the cumulative distribution function (CDF) of normal distribution. Simply, it is the area of the standard normal curve towards left side of x.

Example:

A cohort study is planned to test whether less attendance in class (risk factor) is associated with result in final examination (outcome) with 95% confidence level,. The study was conducted with 50 students with less attendance and 100 students with adequate attendance.  The study revealed that in each group the number of failure students were 20. How much was the statistical power to identify less attendance as a significant risk factor? 

Solution:

Here

P1 = 20 / 50 = 40%, P2=20 / 100 = 20%, Confidence level = 95%, Nexposed = 50, Nnon-exposed = 200, tails=2.

After putting these values, we get power = 74.53%

We also get the RR = 2.

@ Sachin Mumbare