Sample Size Calculator: Simple Logistic Regression

Hypothesis: Two-Sided Equality for binary covariate



Data Input: (Help) (Example)

Input

 

Results

α

 

 

£]

 

P1

 

N

P2

 

 

B

 

 

 

Note:

Variables

Descriptions

£\

Probability of type I error

£]

Probability of type II error

P1

Event rate at X = 0

P2

Event rate at X = 1

B

Proportion of the sample with X = 1

N

Sample size

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Application: This section illistrates how to determine the minimum sample size for simple logistic regression with a binary covariate.

Procedure:

  1. Enter

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

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

c)    Various proportions

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

a)    The required sample size.

  1. Click the button ¡§Reset¡¨ for a new calculation

Formulae:

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Example

Example 1: Given a balanced design with high event rates P1=0.4, P2=0.5 and B = 0.5, what is the required sample size for a simple logistic regression? (Assume both Type I and Type II error to be 0.05).

z£\/2=1.960

z1-£]=1.645

V0=4

V(£]*)=3.33333

R = 1.2

£]*=0.40547

£_=1.09545

N = 1368

Therefore, 1368 participant is required.


Example 2: Given a low prevalence rate P1=0.05, P2=0.1 and B = 0.2, what is the required sample size for a simple logistic regression? (Assume both Type I and Type II error to be 0.05).

N = 2613

Therefore, 2613 participant is required.

Reference: F.Hsieh, D.Bloch and M.Larsen. A Simple Method of Sample Size Calculation for Linear and Logistic Regression. Stanford, 1998. Print.

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