phsize {designsize} | R Documentation |

## Sample size determination using proportional hazard assumption

### Description

Determination of sample sizes of the control drug and the test drug intervention for time to event outcome using proportional hazard assumption.

### Usage

```
phsize(type, lambda1, lambda2, delta, prop, d, 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") |

`lambda1` |
Hazard rate of the control group |

`lambda2` |
Hazard rate of the test group |

`delta` |
The inferiority or superiority margin |

`prop` |
The proportion of patients in the control group |

`d` |
The probability of observing an event |

`alpha` |
Level of significance |

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

### Details

The proportional hazards assumption is used for comparing time to event data where, we assume that the hazard function is the product of two components. One component is the non-parametric part which is generally called baseline hazard and another one is the parametric part. The covariates of this regression model are included in the later component. Because of the combination of parametric and non-parametric components, the model is known as semi-parametric model.

### Value

phsize returns a sample size for the control and the test drug intervention.

### Author(s)

Atanu Bhattacharjee, Rajashree Dey ,Soutik Halder and Akash Pawar

### See Also

ABdesign crt.match crt.unmatch precsize prsize crsize

### Examples

```
# (a) Test for equality:
# The phsize function determines the sample size using proportional hazards assumption.
# The type = "equal" denotes the two survival curves are equal under the null hypothesis
# and the hazard rate of the control group is lambda1 = 1 and that of the test group is
# lambda2 = 2. The proportion of patients in the control group is prop = 0.5. The proba-
# bility of observing an event is 0.8. The level of significance is alpha = 0.05 and the
# probability of type-II error is beta = 0.20.
phsize(type = "equal", lambda1 = 1, lambda2 = 2, delta = 0, prop = 0.5,
d = 0.8, alpha = 0.05, beta = 0.20)
# (b) Test for non-inferiority/superiority:
# The phsize function determines the sample size using proportional hazards assumption.
# The type = "noninf.sup" denotes the difference of the two survival curves is less than
# or equal to the marginal value delta = 0.3. The hazard rate of the control group is
# lambda1 = 1 and that of the test group is lambda2 = 2. The proportion of patients in
# the control group is prop = 0.5, the probability of observing a event is 0.8 and level
# of significance is alpha = 0.05 and the probability of type-II error is beta = 0.20.
phsize(type = "noninf.sup", lambda1 = 1, lambda2 = 2, delta = 0.3, prop = 0.5,
d = 0.8, alpha = 0.05, beta = 0.20)
# (c) Test for equivalence:
# The phsize function determines the sample size using proportional hazards assumption.
# The type = "equiv", denotes whether absolute value of the differences between the two
# survival curves is greater than or equal to the marginal value delta = 0.5. The hazard
# rate of the control group is lambda1 = 1 and that of the test group is lambda2 = 2, &
# the proportion of patients in control group is prop = 0.5 and the probability of obs-
# erving a event ais 0.8. The level of significance is alpha = 0.05 and the probability
# of type-II error is beta = 0.20.
phsize(type = "equiv", lambda1 = 1, lambda2 = 1, delta = 0.5, prop = 0.5,
d = 0.8, alpha = 0.05, beta = 0.20)
```

*designsize*version 0.1.0 Index]