ldPower | R Documentation |

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

```
ldPower(t, za=NULL, zb=NULL, t2=t, pow=NULL, drift=NULL,
conf=NULL, method=NULL, pvaltime=NULL,
zval=zb[length(zb)])
```

`t` |
a vector of analysis times or an 'ldBounds' object (from either the 'ldBounds' or 'commonbounds' function). If a vector of analysis times, must be increasing and in (0,1]. |

`za` |
the vector of lower boundaries. If not specified, made
symmetric to |

`zb` |
the vector of upper boundaries. |

`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. |

`drift` |
the true drift (i.e. treatment effect when t=1). Default
is 0 when |

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

`method` |
the type of adjusted p-value desired. Possible values are 'SW' (stage-wise) and 'LR' (likelihood ratio). |

`pvaltime` |
the analysis time at which the final Z-statistic was observed and an adjusted p-value is desired. |

`zval` |
the final observed Z-statistic (i.e. when trial is stopped). Used for confidence interval or ajusted p-value. Default is final upper boundary value. |

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`

, `drift`

,
`conf`

, or `pval`

is to be specified and `zval`

is only
used in the latter two
cases.

If `t`

is an 'ldBounds' object, `za`

, `zb`

, `t`

, and
`t2`

are already defined and should not be specified.

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

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

`type` |
Type of computation performed: 1 is drift given power, 2 is exit probabilities given drift, 3 is confidence interval for drift given final Z-statistic, and 4 is adjusted p-value 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 |

`p.ordering` |
the ordering specified for p-value calculation (if given). |

`p.value` |
the adjusted p-value if |

Charlie Casper charlie.casper@hsc.utah.edu, Thomas Cook cook@biostat.wisc.edu, and Oscar A. Perez

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.

Generic functions `summary.ldPower`

and
`plot.ldPower`

.

`ldBounds`

for computation of boundaries using alpha
spending function method.

`commonbounds`

for boundaries that do not use alpha spending.

```
## 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)
bound.pr <- ldPower(t,zb=upper,drift=3.242)
summary(bound.pr)
t <- c(0.2292,0.3333,0.4375,0.5833,0.7083,0.8333)
power.fam <- ldBounds(t,iuse=3,alpha=0.05)
bound.ci <- ldPower(power.fam,conf=0.95,zval=2.82)
bound.p <- ldPower(power.fam,method="LR",pvaltime=5,zval=2.82)
summary(bound.ci)
summary(bound.p)
plot(bound.ci)
obf.bd <- ldBounds(5)
obf.dr <- ldPower(obf.bd,pow=0.9)
summary(obf.dr)
```

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