# CVfromCI: CV from a given Confidence interval In PowerTOST: Power and Sample Size for (Bio)Equivalence Studies

## Description

Calculates the CV (coefficient of variation) from a known confidence interval of a BE study.
Useful if no CV but the 90% CI was given in literature.

## Usage

 ```1 2``` ```CVfromCI(pe, lower, upper, n, design = "2x2", alpha = 0.05, robust = FALSE) CI2CV(pe, lower, upper, n, design = "2x2", alpha = 0.05, robust = FALSE) ```

## Arguments

 `pe` Point estimate of the T/R ratio. The `pe` may be missing. In that case it will be calculated as geometric mean of `lower` and `upper`. `lower` Lower confidence limit of the BE ratio. `upper` Upper confidence limit of the BE ratio. `n` Total number of subjects under study if given as scalar. Number of subjects in (sequence) groups if given as vector. `design` Character string describing the study design. See `known.designs()` for designs covered in this package. `alpha` Error probability. Set it to `(1-confidence)/2` (i.e. to 0.05 for the usual 90% confidence intervals). `robust` With `robust=FALSE` (the default) usual degrees of freedom of the designs are used. With `robust=TRUE` the degrees of freedom for the so-called robust evaluation (df2 in known.designs()) will be used. This may be helpful if the CI was evaluated via a mixed model or via intra-subject contrasts (aka Senn’s basic estimator).

## Details

See Helmut Schütz’ presentation for the algebra underlying this function.

## Value

Numeric value of the CV as ratio.

## Note

The calculations are based on the assumption of evaluation via log-transformed values.
The calculations are further based on a common variance of Test and Reference treatments in replicate crossover studies or parallel group study, respectively.

In case of argument `n` given as n(total) and is not divisible by the number of (sequence) groups the total sample size is partitioned to the (sequence) groups to have small imbalance only. A message is given in such cases.
The estimated CV is conservative (i.e., higher than actually observed) in case of unbalancedness.

`CI2CV()` is simply an alias to `CVfromCI()`.

## Author(s)

Original by D. Labes with suggestions by H. Schütz.
Reworked and adapted to unbalanced studies by B. Lang.

## References

Yuan J, Tong T, Tang M-L. Sample Size Calculation for Bioequivalence Studies Assessing Drug Effect and Food Effect at the Same Time With a 3-Treatment Williams Design. Regul Sci. 2013;47(2):242–7. doi: 10.1177/2168479012474273

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```# Given a 90% confidence interval (without point estimate) # from a classical 2x2 crossover with 22 subjects CVfromCI(lower=0.91, upper=1.15, n=22, design="2x2") # will give  0.2279405, i.e a CV ~ 23% # # unbalanced 2x2 crossover study, but not reported as such CI2CV(lower=0.89, upper=1.15, n=24) # will give a CV ~ 26.3% # unbalancedness accounted for CI2CV(lower=0.89, upper=1.15, n=c(16,8)) # should give CV ~ 24.7% ```

### Example output

``` 0.2279405
 0.2629008
 0.2474007
```

PowerTOST documentation built on Jan. 18, 2021, 5:07 p.m.