# Drift and Probabilities for Group Sequential Boundaries

### Description

'drift' calculates drift (effect), confidence interval for drift, or power and other probabilities given drift for specified group sequential boundaries for interim analyses of accumulating data in clinical trials.

### Usage

1 2 |

### Arguments

`za` |
the vector of lower boundaries. Symmetric to |

`zb` |
the vector of upper boundaries. |

`t` |
the vector of analysis times, which must be increasing and in (0,1]. |

`t2` |
the second time scale, usually in terms of amount of
accumulating information. By default, same as |

`pow` |
the desired power when drift is not specified. |

`drft` |
the true drift (i.e. treatment effect when t=1). |

`conf` |
the confidence level when a confidence interval for drift is wanted. |

`zval` |
the final observed Z statistic (i.e. when trial is stopped). Used for confidence interval. |

### Details

This is based on a Fortran program, 'ld98', by Reboussin, DeMets, Kim,
and Lan. It has some advantages, like making use of probability
distributions in R. Only one of `pow`

, `drft`

, and
`conf`

is to be specified and `zval`

is only used in the last
case.

### Value

'drift' returns an object of 'class' '"drift"'.

An object of class '"drift"' is a list containing the following components:

`type` |
Type of computation performed: 1 is drift given power, 2 is exit probabilities given drift, and 3 is confidence interval for drift given final Z statistic. |

`time` |
the original time scale. |

`time2` |
the second (information) time scale. |

`lower.bounds` |
the vector of lower boundaries given. |

`upper.bounds` |
the vector of upper boundaries given. |

`power` |
the power. If power is given, it is returned here. If drift is given, the resulting power is calculated. |

`drift` |
the drift. If drift is given, it is returned here. If power is given, the drift resulting in given power is calculated. |

`lower.probs` |
the vector of exit probabilities across the lower boundary. Returned if power or drift is given. |

`upper.probs` |
the same for upper boundary. |

`exit.probs` |
the probability at each analysis of crossing the
boundary. The sum of |

`cum.exit` |
the cumulative probability of crossing. |

`conf.level` |
the desired confidence level, if given. |

`final.zvalue` |
the final Z statistic, if given. |

`conf.interval` |
the confidence interval for drift, if |

### Author(s)

Charlie Casper charlie.casper@hsc.utah.edu and Oscar A. Perez

### References

Reboussin, D. M., DeMets, D. L., Kim, K. M., and Lan,
K. K. G. (2000) Computations for group sequential boundaries using the
Lan-DeMets spending function method. *Controlled Clinical Trials*,
21:190-207.

Fortran program 'ld98' by the same authors as above.

DeMets, D. L. and Lan, K. K. G. (1995) *Recent Advances in Clinical
Trial Design and Analysis*, Thall, P. F. (ed.). Boston: Kluwer
Academic Publishers.

Lan, K. K. G. and DeMets, D. L. (1983) Discrete sequential boundaries
for clinical trials. *Biometrika*, 70:659-63.

### See Also

Generic functions `summary.drift`

and
`plot.drift`

.

`bounds`

for computation of boundaries using alpha
spending function method.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
## From Reboussin, et al. (2000)
t <- c(0.13,0.4,0.69,0.9,0.98,1)
upper <- c(5.3666,3.7102,2.9728,2.5365,2.2154,1.9668)
drift.pr <- drift(zb=upper,t=t,drft=3.242)
summary(drift.pr)
t <- c(0.2292,0.3333,0.4375,0.5833,0.7083,0.8333)
upper <- c(2.53,2.61,2.57,2.47,2.43,2.38)
drift.ci <- drift(zb=upper,t=t,conf=0.95,zval=2.82)
summary(drift.ci)
plot(drift.ci)
## Using output from 'bounds'
t <- seq(0.2,1,length=5)
obf.bd <- bounds(t,iuse=c(1,1),alpha=c(0.025,0.025))
drift.dr <- drift(obf.bd$lower.bounds,obf.bd$upper.bounds,t,pow=0.9)
summary(drift.dr)
``` |

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