epi.sssupb | R Documentation |

Sample size for a parallel superiority trial, binary outcome.

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

`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 |

`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. |

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. |

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 `\delta`

. 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`

.

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.

```
## 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.
```

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