# epi.sssupb: Sample size for a parallel superiority trial, binary outcome In epiR: Tools for the Analysis of Epidemiological Data

## Description

Sample size for a parallel superiority trial, binary outcome.

## Usage

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

## 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. `r` scalar, the number in the treatment group divided by the number in the control group. `power` scalar, the required study power. `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}. We specify the absolute value of the maximum acceptable difference between P_{n} and P_{s} as δ. For a superiority trial the value entered for `delta` must be greater than or equal to zero.

For a superiority trial the null hypothesis is:

H_{0}: P_{s} - P_{n} = 0

The alternative hypothesis is:

H_{1}: P_{s} - P_{n} != 0

When calculating the power of a study, 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).

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

## 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.

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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```## 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, r = 1, power = 0.80, 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 Oct. 11, 2021, 9:08 a.m.