Sample Size Calculator:Unmatched Case-Control

Hypothesis: Two-Sided Equality

Data Input: (Help) (Example)

Input	Results
α	P0
β	NKelsey
P1	NFleiss
OR	NFleiss-cc
r

Note:

Variables	Descriptions
α	Probability of type I error
β	Probability of type II error
P0	Proportion for cases
P1	Proportion for controls
OR	Odds Ratio
r	Ratio of case to control (1 case to r control)
NKelsey	Sample size for cases using Kelsey's formula
NFleiss	Sample size for cases using Fleiss's formula
NFleiss-cc	Sample size for cases using Fleiss's formula with continunity correction

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Application: This section illistrates how to determine the minimum sample size for an unmatched case-control study.

Procedure:

1. Enter

a)    Value of α, the two-sided confidence level

b)    Value of β, the type II error (1-power)

c)    Proportion for controls

d)    Odds Ratio

e)    The ratio of case-control

2. Click the button “Calculate” to obtain

a)    The proportion for controls and various sample size

3. Click the button “Reset” for a new calculation

Formulae:

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Variable Notations:

α             The probability of type I error (significance level) is the probability of rejecting the true null hypothesis

β             The probability of type II error (1 - power of the test) is the probability of failing to reject the false null hypothesis.

P₀ The proportion for cases

P₁ The proportion for controls

OR          The calculated odds ratio

r               The ratio of case-control (1 case/r controls)

N_Kelsey Required sample size for cases using Kelsey's formula

N_Fleiss Required sample size for cases using Fleiss's formula

N_Fleiss-cc Required sample size for cases using Fleiss's formula with continunity correction

Examples

Example 1: The efficacy of BCG vaccine in preventing childhood tuberculosis is in doubt and a study is designed to compare the immunization coverage rates in a group of tuberculosis cases compared to a group of controls. Available information indicates that roughly 30% of the controls are not vaccinated, and we wish to have an 80% chance of detecting whether the odds ratio is significantly different from 1 at the 5% level. If an odds ratio of 2 would be considered an important difference between the two groups, how large a sample should be included in each study group?

α = 0.05

β = 0.2

P₁ = 0.30

P₀=0.4615

r=1

OR=2.0

N_Kelsey = [1.960 *sqrt(2*0.38*0.62)+0.842*sqrt(0.4615*0.5385+0.3*0.7)]²/ (0.4615-0.3)²=142

Based on Kelsey's formula, 142 participant is required, which makes a total of 184 participants needed to be recruited.

Example 2: Using the above example with 5 controls per case for the ratio, how large a sample should be included in each study group instead?

α = 0.05

β = 0.2

P₁ = 0.30

P₀=0.4615

r=5

OR=2.0

N_Kelsey = [1.960 *sqrt((5+1)*0.38*0.62)+0.842*sqrt(5*0.4615*0.5385+0.3*0.7)]²/ 5*(0.4615-0.3)²=89

Based on Kelsey's formula, 89 participant is required in the case group while 89*5=445 controls will be included.

References:

Lemeshow, S., Hosmer Jr., D.W., Klar, J.,and Lwanga S.K. Adequacy of Sample Size in Health Studies. WHO, 1990. Print.

Kelsey J.L., Whittemore A.S., Evans A.S.,and Thompson W.D. Methods in Observational Epidemiology. Oxford University Press, 1996. Print.

Fleiss J.L. Statistical Methods for Rates and Proportions. John Wiley & Sons, 1981. Print.

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