Sample Size Calculator: Unmatched/Independent Cohort

Hypothesis: Two-Sided Equality

or

Data Input: (Help) (Example)

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

Note:

Variables	Descriptions
α	Probability of type I error
β	Probability of type II error
P0	Proportion of the unexposed group
P1	Proportion of the exposed group
RR	Calculated Relative Risk
r	Ratio of unexposed to exposed
NKelsey	Sample size for unexposed group using Kelsey formula
NFleiss	Sample size for unexposed group using Fleiss formula
NFleiss-cc	Sample size for unexposed group using Fleiss with continunity correction formula

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Help Aids Top

Application: This section illistrates how to determine the minimum sample size for an independent cohort 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 the unexposed group

d)    Proportion for the exposed group

e)    The ratio of unexposed to exposed

2. Click the button “Calculate” to obtain

a)    The relative risk 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 of the unexposed group

P₁ The proportion of the exposed group

RR          The calculated relative risk

r               The ratio of unexposed to exposed (1 unexposed to r exposed)

N_Kelsey Required sample size for the unexposed group using Kelsey formula

N_Fleiss Required sample size for the unexposed group using Fleiss formula

N_Fleiss-cc Required sample size for the unexposed group using Fleiss formula with continunity correction

Example

Two competing therapies for a particular cancer are to be evaluated by the cohort study strategy in a multi-center clinical trial. Patients are randomized to either treatment A or B and are followed for recurrence of disease for 5 years following treatment. How many patients should be studied in each of the two arms of the trial in order to be 90% confident of rejecting H₀: RR=1 in favor of the alternative H_a: RR≠1, if the test is to be performed at α=0.05 level and if it is assumed that p₀=0.35 and p₁=0.175.

α = 0.05

β = 0.1

P₀ = 0.35

P₁=0.175

r=1

RR=0.5

N_Kelsey = (1.960+1.282)²*0.2625*0.7375*2 / (0.35-0.175)²= 133

Therefore, using Kelsey's formula 133 per arm of participant is required, which makes a total of 266 participants needed to be recruited.

N_Fleiss = [1.96 sqrt(2*0.2625*0.7375)+1.282*sqrt(0.35*0.65+0.175*0.825)]²/(0.35-0.175)²=131

Therefore, using Fleiss's formula 131 per arm of participant is required, which makes a total of 262 participants needed to be recruited.

Reference:

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 2nd EditionOxford University Press, 1996. Print.

Fleiss, J.L. Statistical Methods for Rates and Proportions. 2nd Ed. NewYork: John Wiley, 1981. Print.

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