How to find sample size for Case-control study?

How to find Sample size for Case-control study when Exposure variable of study measured on Nominal scale.

The sample size is calculated using following Formula

Source: Lwanga SK, Lame shaw S. Sample size determination in health studies. WHO, Geneva, 1991.
Where:

n	Sample size.
Z1	Value for the selected alpha level (1.96 at 95% confidence level).
Z2	Value associated with selected Power (1.28 at 90% power of test).
P1	Probability of exposure in cases.
P2	Probability of exposure in control.
P	Average of P1 and P2.

If in a case –control study if you want to study an association between smoking and lung cancer. The Prevalence of smokers in lung cancer patient was 0.30 and prevalence of smoking in controls was 0.10. 

These prevalence are obtained from pilot study or literature. Here we considered 95% confidence level and 90% power of test. What will be the minimum sample size in case and control group.

P1	Probability of exposure in cases.	0.30
P2	Probability of exposure in control.	0.10
P	Average of P1 and P2 (0.30+0.10=0.40/2).	0.20
Z1	Value for 95% confidence level.	1.96
Z2	Value for 90% power of test.	1.28

Required sample size for study is 42 subjects in each group.
So we will enroll 42 subjects in Case group and Control Group for 1: 1 subject in Case group and Control Group.

If you want to enroll subject in Case group and Control Group as 1: 2 then you can enroll 42 subjects in case group and 84 patients in Control group.

Note: Sample size can be decrease by decreasing Poser of a study. Power of stud can be consider minimum up to 80%.

read more Sample Size for Two Independent Samples Groups