epi.sssupb: Sample size for a parallel superiority trial, binary outcome

In epiR: Tools for the Analysis of Epidemiological Data

Sample size for a parallel superiority trial, binary outcome

Description

Sample size for a parallel superiority trial, binary outcome.

Usage

epi.sssupb(treat, control, delta, n, power, r = 1, sided.test, 
   nfractional = FALSE, alpha = 0.05)

Arguments

treat	the expected proportion of successes in the treatment group.
control	the expected proportion of successes in the control group.
delta	the equivalence limit, expressed as the absolute change in the outcome of interest that represents a clinically meaningful difference. For a superiority trial the value entered for delta must be greater than or equal to zero.
n	scalar, the total number of study subjects in the trial.
power	scalar, the required study power.
r	scalar, the number in the treatment group divided by the number in the control group.
sided.test	scalar, use a one- or two-sided test?
nfractional	logical, return fractional sample size.
alpha	scalar, defining the desired alpha level.

Value

A list containing the following:

n.total	the total number of study subjects required.
n.treat	the required number of study subject in the treatment group.
n.control	the required number of study subject in the control group.
delta	the equivalence limit, as entered by the user.
power	the specified or calculated study power.

Note

Consider a clinical trial comparing two groups, a standard treatment (s) and a new treatment (n). A proportion of subjects in the standard treatment group experience the outcome of interest P_{s} and a proportion of subjects in the new treatment group experience the outcome of interest P_{n}.

For a superiority trial the null hypothesis is:

H_{0}: P_{n} - P_{s} \leq \delta

and the alternative hypothesis is:

H_{1}: P_{n} - P_{s} > \delta

If the alternative hypothesis is accepted we conclude that P_{n} does not equal P_{s}. Regulatory agencies and most clinical trial guidelines recommend two-sided tests for superiority trials.

When calculating study power the argument n refers to the total study size (that is, the number of subjects in the treatment group plus the number in the control group).

Refer to the documentation for epi.ssequb for a comparison of the key features of superiority, equivalence and non-inferiority trials.

References

Chow S, Shao J, Wang H (2008). Sample Size Calculations in Clinical Research. Chapman & Hall/CRC Biostatistics Series, page 90.

Julious SA (2004). Sample sizes for clinical trials with normal data. Statistics in Medicine 23: 1921 - 1986.

Machin D, Campbell MJ, Tan SB, Tan SH (2009). Sample Size Tables for Clinical Studies. Wiley Blackwell, New York.

Machin D, Campbell MJ, Tan SB, Tan SH (2018). Sample Sizes for Clinical, Laboratory and Epidemiology Studies. Wiley Blackwell, New York.

Pocock SJ (1983). Clinical Trials: A Practical Approach. Wiley, New York.

Wang B, Wang H, Tu X, Feng C (2017). Comparisons of superiority, non-inferiority, and equivalence trials. Shanghai Archives of Psychiatry 29, 385 - 388. DOI: 10.11919/j.issn.1002-0829.217163.

Examples

## EXAMPLE 1 (from Chow S, Shao J, Wang H 2008, p. 91):
## Suppose that a pharmaceutical company is interested in conducting a
## clinical trial to compare the efficacy of two antimicrobial agents 
## when administered orally once daily in the treatment of patients 
## with skin infections. In what follows, we consider the situation 
## where the intended trial is for testing superiority of the 
## test drug over the active control drug. For this purpose, the following 
## assumptions are made. First, sample size calculation will be performed 
## for achieving 80% power at the 5% level of significance.

## Assume the true mean cure rates of the treatment agents and the active 
## control are 85% and 65%, respectively. Assume the superiority
## margin is 5%.

epi.sssupb(treat = 0.85, control = 0.65, delta = 0.05, n = NA, 
   power = 0.80, r = 1, sided.test = 1, nfractional = FALSE, alpha = 0.05)

## A total of 196 subjects need to be enrolled in the trial, 98 in the 
## treatment group and 98 in the control group.

epiR documentation built on Nov. 6, 2025, 1:11 a.m.