expsize {designsize} | R Documentation |

## Sample size determination for survival data using exponential assumption

### Description

Sample size determination for control drug and test drug for time to event outcome using exponential assumption

### Usage

```
expsize(type, k, delta, lambda1, lambda2, sigma1, sigma2,
sigma.lambda, alpha, beta)
```

### Arguments

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

`k` |
Ratio of sample sizes |

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

`lambda1` |
Hazard rate of the control drug |

`lambda2` |
Hazard rate of the test drug |

`sigma1` |
Variability in the hazard rate due to using control drug |

`sigma2` |
Variability in the hazard rate due to using test drug |

`sigma.lambda` |
Variability in the hazard rate due to combination of control and test drug |

`alpha` |
Level of significance |

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

### Details

Our aim is to determine the sample size based on the hazard rates for median survival times between control drug and test drug. Since, the hazard function is constant for an exponential distribution, the median survival time is determined by the hazard function. Moreover, comparing the hazard rates between the treatment drugs is our hypothesis of interest.

### Value

expsize returns a sample size for control and test drug intervention.

### Author(s)

Atanu Bhattacharjee, Rajashree Dey ,Soutik Halder and Akash Pawar

### See Also

ABdesign crt.match crt.unmatch phsize precsize prsize crsize

### Examples

```
# (a) Test for equality:
# The exponential assumption is used to determine the sample size with null hypothesis
# that the hazard rates of a test drug and a reference drug are equal i.e.type ="equal".
# The both sample sizes are taken to be equal (k = 1). The hazard rate of control drug
# is lambda1 = 2 and that of test drug is lambda2 = 1. The standard deviation (s.d.) in
# hazard rate due to using control drug & test drug is 0.97 and 3.94 respectively. Their
# combined standard deviation is sigma.lambda = 2.56. The level of significance is alpha
# = 0.05 and the probability of type-II error is beta = 0.20.
expsize(type = "equal", k = 1, delta = 0, lambda1 = 2, lambda2 = 1, sigma1 = 0.97,
sigma2 = 3.94, sigma.lambda = 2.56, alpha = 0.05, beta = 0.20)
# (b) Test for noninferiority/superiority:
# The exponential assumption is used to determine sample size by testing null hypothesis
# (type = "noninf.sup") that the difference between the hazard rates of a test drug and
# the reference drug is less than or equal to a superiority margin delta = 0.2,where k=1
# indicates both the sample sizes are taken to be equal. The hazard rate of the control
# drug is lambda1 = 2 and that of test drug is lambda2 = 1. The standard deviation in
# hazard rate due to using control drug & test drug is 0.97 and 3.94 respectively. Their
# combined standard deviation is sigma, lambda =2.56. The level of significance is alpha
# = 0.05 and the probability of type-II error is beta = 0.20.
expsize(type = "noninf.sup", k = 1, delta = 0.2, lambda1 = 2, lambda2 = 1, sigma1 = 0.97,
sigma2 = 3.94, sigma.lambda = 2.56, alpha = 0.05, beta = 0.20)
# (c) Test for equivalence:
# The exponential assumption is used to determine sample size by testing null hypothesis
# (type = "equiv") that the absolute difference between the hazard rates of a test drug
# and a ref drug is greater than or equal to a superiority margin delta =0.5, where k =1
# indicates both the sample sizes are taken to be equal. The hazard rate of the control
# drug is lambda1 = 2 and that of test drug is lambda2 = 1. The standard deviation in
# the hazard rate due to using control drug and test drug is 0.97 and 3.94 respectively.
# Their combined standard deviation is sigma.lambda = 2.56. The level of significance is
# alpha = 0.05 and the probability of type-IIqerror is beta = 0.20.
expsize(type = "equiv", k = 1, delta = 0.5, lambda1 = 2, lambda2 = 1, sigma1 = 0.97,
sigma2 = 3.94, sigma.lambda = 2.56, alpha = 0.05, beta = 0.20)
```

*designsize*version 0.1.0 Index]