Sample Size Calculator:Matched Case-Control

Hypothesis: Two-Sided Equality

Data Input: (Help) (Example)

Input

 

Results

α

 

Npairs

β

 

PA

 

 

PD

 

 

Note:

Variables

Descriptions

£\

Probability of type I error

£]

Probability of type II error

PA

Proportion of discordant pairs of type A among discordant pairs

PD

Proportion of discordant pairs among all pairs

Npairs

Sample size pair for case-control study

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Application: This section illistrates how to determine the minimum sample size pair for a matched case-control study based on McNemar's test.

Procedure:

  1. Enter

a)    Value of £\, the two-sided confidence level

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

c)    Proportion of discordant pairs of type A among discordant pairs

d)    Proportion of discordant pairs among all pairs

  1. Click the button ¡§Calculate¡¨ to obtain

a)    The required sample size pair

  1. 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.

PA            Proportion of discordant pairs of type A among discordant pairs

PD            Proportion of discordant pairs among all pairs

Npairs       Required sample size pair

Example

Suppose we want to compare two different regimens of chemotherapy (A,B) for treatment of breast cancer where the outcome measure is recurrence of breast cancer or death over a 5-year period. A matched-pair design is used, in which patients are matched on age and clinical stage of disease, with one patient in a matched pair assigned to treatment A and the other to treatment B. Based on previous work, it is estimated that patients in a matched pair will respond similarly to the treatments in 85% of matched pairs (i.e., both will either die or have a recurrence over 5 years). Furthermore, for matched pairs in which there is a difference in response, it is estimated that in two-thirds of the pairs the treatment A patient will either die or have a recurrence, and the treatment B patient will not; in one-third of the pairs the treatment B patient will die or have a recurrence, and the treatment A patient will not. How many matched pairs need to be enrolled in the study to have a 90% chance of finding a significant difference using a two-sided test with type I error = 0.05?

£\ = 0.05

£] = 0.1

PA = 2/3

PD=1-0.85=0.15

Npairs = [1.960 + 2*1.282*sqrt((2/3)*(1/3))]2/[4*(2/3-0.5)2*0.15] = 603

Therefore, 1206 women in 603 pairs must be enrolled. This will yield approximately 0.15 * 603 = 90 discordant pairs

Reference: Rosner, B. Fundamentals of Biostatistics 7th ed. Boston: Cengage Learning, 2010. Print.

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