crsize {designsize} | R Documentation |

## Sample size determination for crossover study design

### Description

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

### Usage

```
crsize(type, delta, m, k, mur, mut, sigbr, sigbt, rho, sigwr, sigwt,
alpha, beta, r1, r2)
```

### Arguments

`type` |
The three different types of tests are (1) test for equality, (2) test for non-inferiority/ superiority, (3) test for equivalence i.e. type = c("equal", "noninf.sup", "equiv") |

`delta` |
Non-inferiority/Superiority margin |

`m` |
Number of responses observed from each subject in each sequence under a fixed treatment |

`k` |
Ratio of the sample sizes of the two sequences |

`mur` |
Mean value of reference therapy |

`mut` |
Mean value of test therapy |

`sigbr` |
Between standard deviation due to the effect of reference therapy |

`sigbt` |
Between standard deviation due to the effect of test therapy |

`rho` |
Correlation between reference and test therapy |

`sigwr` |
Within standard deviation due to the effect of reference therapy |

`sigwt` |
Within standard deviation due to the effect of test therapy |

`alpha` |
Level of significance |

`beta` |
The probability of type-II error |

`r1` |
Proportion of factor-1 |

`r2` |
Proportion of factor-2 |

### Details

Consider a 2x2m replicated crossover design for comparing mean responses of a test drug and a reference drug. Under both treatments the design consists of two sequences with m subjects each.

### Value

crsize returns the required sample sizes for each sequence 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

### Examples

```
# (a) Test for equality:
# This is a crossover design. The type = "equal" tests the equality of mean responses of
# a test drug (mut = 9) and a reference drug (mur = 8.5) and the number of responses are
# m = 4 observed from each subject in each sequence. k = 1 indicates the ratio of the
# sample sizes of the two sequences are equal. The between standard deviation due to the
# effect of reference therapy is sigbr = 1.5 and that of test therapy is 1.5. The corre-
# lation between reference and test therapy is rho = 0.7. The within standard deviation
# due to the effect of reference therapy is sigwr = 1 as well as test therapy is sigwt =
# 1. The alpha = 0.05 is 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 = 0.5 and
# r2 = 0.5 respectively.
crsize(type= "equal", delta = 0.4, m = 4, k = 1, mur = 8.5, mut = 9, sigbr = 1.5,
sigbt = 1.5, rho = 0.7, sigwr = 1, sigwt = 1, alpha = 0.05, beta = 0.10,
r1 = 0.5, r2 = 0.5)
# (b) Test for non-inferiority/superiority:
# This is a crossover design. The type = "noninf.sup", tests whether the difference of
# mean responses of a test drug (mut = 9) and a reference drug (mur = 8.5) being greater
# than or equal to the marginal value delta = 0.4. The number of responses are m = 4,
# observed from each subject in each sequence. The value of k = 1 indicates the ratio of
# the sample sizes of the two sequences are equal. The between standard deviation due to
# the effect of reference therapy is sigbr = 1.5 and that of test therapy is 1.5. The
# correlation between reference and test therapy is rho = 0.7. The within standard devi-
# ation due to the effect of reference therapy is sigwr = 1, as well as test therapy is
# sigwt = 1. A 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 0.5.
crsize(type = "noninf.sup", delta = 0.4, m = 4, k = 1, mur = 8.5, mut = 9, sigbr = 1.5,
sigbt = 1.5, rho = 0.7, sigwr = 1, sigwt = 1, alpha = 0.05, beta = 0.10,
r1 = 0.5, r2 = 0.5)
#(c) Test for equivalence:
# This is a crossover design. The type = "equiv" tests whether the absolute value of the
# difference of mean responses of a test drug (mut = 9) and a reference drug (mur = 8.5)
# being less than or equal to the marginal value delta = 0.6. The number of responses
# are m = 4 observed from each subject in each sequence. k = 1, indicates that the ratio
# of the sample sizes of the two sequences are equal. The between standard deviation due
# to the effect of reference therapy is sigbr = 1.5 and that of test therapy is 1.5. The
# correlation between reference and test therapy is rho = 0.7. The within standard devi-
# ation due to the effect of reference therapy is sigwr = 1 as well as test therapy is
# sigwt = 1. 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 0.5.
crsize(type = "equiv", delta = 0.6, m = 4, k = 1, mur = 8.5, mut = 9, sigbr = 1.5,
sigbt = 1.5,rho = 0.7, sigwr = 1, sigwt = 1, alpha = 0.05, beta = 0.10,
r1 = 0.5, r2 = 0.5)
```

*designsize*version 0.1.0 Index]