# Conditional Power Calculations

### Description

This package provides several functions for calculating the conditional power for different models in survival time analysis within randomized clinical trials with two different treatments to be compared and survival as an endpoint.

### Details

Package: | CP |

Type: | Package |

Version: | 1.6 |

Date: | 2016-06-28 |

License: | GPL-3 |

This package could be some help when you want to calculate the conditional power at the time of an interim analysis of a randomized clinical trial with survival as an endpoint.

The conditional power is defined as the probability of obtaining a significant result at the end of the trial when the real effect is equal to the expected effect given the data from the interim analysis.

Functions for the model with exponential survival (`ConPwrExp`

)
and the non-mixture models with exponential (`ConPwrNonMixExp`

),
Weibull type (`ConPwrNonMixWei`

)
and Gamma type survival (`ConPwrNonMixGamma`

) are provided.

There is also the function `CompSurvMod`

to compare the four mentioned models.

Additionally, there is also a function for the exponential model
with the original formulae of the Andersen paper
(`ConPwrExpAndersen`

).

Finally, the user is able to generate further data frames
by random via `GenerateDataFrame`

.

### Note

The theoretical results of this implementation
are based on some assumptions.

Non-Mixture-Exponential: *λ[1] = λ[2]*

Non-Mixture-Weibull: *λ[1] = λ[2]* and *k[1] = k[2]*

Non-Mixture-Gamma: *a[1] = a[2]* and *b[1] = b[2]*

In general, such assumptions are not fulfilled when using real data.

Nevertheless, when doing conditional power calculations the situation is that you have no significant difference at the time of interim analysis. In this case, no treatment arm is superior to the other one. Thus, the assumptions named above are approximately satisfied.

In contrast to this, caution should be exercised when calculating the conditional power in the case of significant results at the time of interim analysis.

### Author(s)

Andreas Kuehnapfel

Maintainer: Andreas Kuehnapfel <andreas.kuehnapfel@imise.uni-leipzig.de>

### References

Kuehnapfel, A. (2013). Die bedingte Power in der Ueberlebenszeitanalyse.

Andersen, P. K. (1987). Conditional power calculations as an aid in the decision whether to continue a clinical trial. Controlled Clinical Trials 8, 67-74.

### See Also

`ConPwrExp`

`ConPwrNonMixExp`

`ConPwrNonMixWei`

`ConPwrNonMixGamma`

`CompSurvMod`

`ConPwrExpAndersen`

`GenerateDataFrame`

`test`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | ```
# data frame 'test' generated by 'GenerateDataFrame'
# conditional power calculations
# within the exponential model
ConPwrExp(data = test, cont.time = 12, new.pat = c(2.5, 2.5),
theta.0 = 0.75, alpha = 0.05,
disp.data = TRUE, plot.km = TRUE)
# conditional power calculations
# within the non-mixture model with exponential survival
ConPwrNonMixExp(data = test, cont.time = 12, new.pat = c(2.5, 2.5),
theta.0 = 0.75, alpha = 0.05,
disp.data = TRUE, plot.km = TRUE)
# conditional power calculations
# within the non-mixture model with Weibull type survival
ConPwrNonMixWei(data = test, cont.time = 12, new.pat = c(2.5, 2.5),
theta.0 = 0.75, alpha = 0.05,
disp.data = TRUE, plot.km = TRUE)
# conditional power calculations
# within the non-mixture model with Gamma type survival
ConPwrNonMixGamma(data = test, cont.time = 12, new.pat = c(2.5, 2.5),
theta.0 = 0.75, alpha = 0.05,
disp.data = TRUE, plot.km = TRUE)
# conditional power calculations
# within the four mentioned models
CompSurvMod(data = test, cont.time = 12, new.pat = c(2.5, 2.5),
theta.0 = 0.75, alpha = 0.05,
disp.data = TRUE, plot.km = TRUE)
# conditional power calculations
# within the exponential model
# with the original formulae of the Andersen paper
ConPwrExpAndersen(data = test, cont.time = 12, new.pat = c(2.5, 2.5),
theta.0 = 0.75, alpha = 0.05,
disp.data = TRUE, plot.km = TRUE)
``` |