prsize {designsize} | R Documentation |

## Sample size determination for parallel study design.

### Description

Determination of sample sizes of two factors of each of the two groups using one of the tests for equality, non-inferiority/superiority or equivalence.

### Usage

```
prsize(type, mu1, mu2, s, alpha, beta, k, r1, r2, del)
```

### Arguments

`type` |
There are three types of test, (1) test of equality, (2) test for non-inferiority/superiority, |

`mu1` |
The mean value of 1st group |

`mu2` |
The mean value of 2nd group |

`s` |
The common standard deviation |

`alpha` |
The level of significance |

`beta` |
The probability of the type II error i.e. 1 - power |

`k` |
The ratio of 1st sample size(n1) and 2nd sample size(n2) i.e k=n1/n2 |

`r1` |
The ratio of n1fac1 (sample size of the 1st factor for 1st group) and n1 i.e r1=n1fac1/n1 |

`r2` |
The ratio of n2fac2 (sample size of the 1st factor for 2nd group) and n2 i.e r2=n2fac1/n2 |

`del` |
The superiority or non-inferiority margin |

### Details

Parallel arm design is the most commonly used study design where subjects are randomized to one or more study arms. Each study arm will be allocated a different intervention. After randomization each subject will stay in their assigned arm during the whole study. The randomized subjects should not inadvertently contaminate with the other group. A major characteristic of a parallel study is randomization, which ensures accuracy of the results and lower risk of being biased.

### Value

prsize returns returns the required sample sizes for each groups and their factors in a 2x2 contingency table.

### Author(s)

Atanu Bhattacharjee, Rajashree Dey ,Soutik Halder and Akash Pawar

### See Also

ABdesign crt.match crt.unmatch phsize precsize crsize

### Examples

```
# (a) Test for equality:
# This is a parallel study design. The type = "equal" tests the equality of mean respon-
# ses of a test drug (mu1 = 12) and a reference drug (mur = 8). The common standard dev-
# iation of the drugs is s = 5. k = 2 indicates the ratio of the sample sizes of the two
# groups. alpha = 0.05 is the level of significance and the probability of type-II error
# is beta = 0.10. The proportion of factor- 1 and factor-2 are taken to be r1 = 0.6 and
# r2 = 0.6 respectively.
prsize(type="equal", mu1=12, mu2=8, s=5, alpha=0.05, beta=0.10, k=2, r1=0.6, r2=0.6)
# (b) Test for superiority/noninferiority:
# This is a Parallel design. The type = "noninf.sup" test whether the difference of mean
# responses of a test drug (mu1 = 12) and a reference drug (mu2 = 8) being greater than
# or equal to the marginal value delta = 0.8. s = 5 is the common standard deviation of
# the drugs. The value k = 2 indicates the ratio of the sample sizes of the two groups.
# alpha = 0.05 is the level of significance and the probability of type-II error is beta
# = 0.10. The proportion of factor-1 and factor-2 are taken to be r1 = 0.6 and r2 = 0.6
# respectively.
prsize(type="noninf.sup", mu1=12, mu2=8, s=5, alpha=0.05, beta=0.10, k=2, r1=0.6,
r2=0.6, del=0.8)
# (c) Test for equivalence:
# This is a Parallel design. The type = "equiv" tests whether the absolute value of the
# difference of mean responses of a test drug (mu1 = 12) and a reference drug (mu2 = 8)
# being less than or equal to the marginal value delta = 0.8. The number of responses
# are m = 4 observed from each subject in each sequence.The s = 5 is the common standard
# deviation of the drugs. The value k = 2 indicates the ratio of the sample sizes of the
# two groups. The alpha = 0.05 is the level of significance and the probability of type
# -II error is beta = 0.10. The proportion of factor-1 (r1) and factor-2 (r2) both are
# taken to be equal to 0.6.
prsize(type="equiv", mu1=12, mu2=8, s=5, alpha=0.05, beta=0.10, k=2, r1=0.6,
r2=0.6, del=0.8)
```

*designsize*version 0.1.0 Index]