ldBounds | R Documentation |

'ldBounds' determines group sequential boundaries for interim analyses of accumulating data in clinical trials using the Lan-DeMets alpha spending function method. These can be used as guidelines for early stopping of the trial.

```
ldBounds(t, t2, iuse=1, asf=NULL, alpha=0.05, phi=rep(1,length(alpha)),
sides=2, ztrun=rep(Inf,length(alpha)))
```

`t` |
a vector of analysis times or a number of analysis times. If the number of analyses is specified, they are assumed to be equally spaced. Analysis times must be increasing and in (0,1]. |

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

`iuse` |
the type of alpha spending function(s) to use for bounds.
If two-sided bounds are calculated and |

`asf` |
a list of one or two functions to be used as alpha spending
function(s). Used with |

`alpha` |
Type I error(s). In two-sided situations, alpha can be a
single value, indicating symmetric type I error control (half of
alpha for each boundary). If a vector of length two is given,
this corresponds to the amount allocated to the lower and upper
boundaries, respectively. The total alpha must be greater than 0
and less than or equal to 1. When |

`phi` |
a vector of values used when |

`sides` |
Designates one- or two-sided bounds. |

`ztrun` |
a vector of values specifying where to truncate lower and upper boundaries, respectively. Default is no truncation. |

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 and the ability to specify any valid spending function without changing the program.

`iuse`

values of 1 and 2 correspond to alpha spending functions
which give O'Brien Fleming and Pocock type boundaries, respectively.
A value of 3 is the power family. Here, the spending function is
`\alpha t^{\phi}`

, where `\phi`

must be greater than 0. A value of 4 is the
Hwang-Shih-DeCani family, with spending function
`\alpha (1-e^{-\phi t})/(1-e^{-\phi})`

, where `\phi`

cannot be 0.

With `iuse`

=5, the user will specify any alpha spending function
as `asf`

. Such a function asf() must be of class 'function',
satisfy asf(t)`\leq`

1 for t in (0,1), and be strictly increasing. Alpha
will be derived as asf(1). If two spending functions are specified,
they represent the lower and upper boundary spending functions,
respectively, with the values at time 1 designating the lower and
upper alphas, respectively.
Currently, this option cannot be used for one side of the boundary
with one of the other options for the other side. In other words, the
user may define one spending function for a one-sided boundary or two
for a two-sided boundary, symmetric or asymmetric, but cannot define
one spending function and select the other from `iuse`

1 through
4.

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

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

`bounds.type` |
the type of bounds: 1 is 'one-sided', 2 is 'two-sided symmetric', and 3 is 'two-sided asymmetric'. For non-alpha-spending function boundaries (see 'commonbounds' function) 4, 5, and 6 correspond, respectively, to types 1 through 3 above. |

`spending.type` |
the type(s) of spending function. A descriptive
version of the value(s) used for |

`time` |
the original time scale. |

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

`alpha` |
the alpha(s) used. |

`overall.alpha` |
if two-sided, the sum of the two alphas. If one-sided, just alpha. |

`lower.bounds` |
the vector of lower boundaries calculated. Should be ignored if one-sided. |

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

`exit.pr` |
the vector of cumulative exit probabilities at each analysis. |

`diff.pr` |
the vector of exit probabilities accumulated at each analysis. |

`nom.alpha` |
the nominal alpha level to be used at each analysis (i.e., bound has been crossed if the p-value at that time is less than this value). Not given for two-sided asymmetric boundaries. |

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.ldBounds`

and
`plot.ldPower`

.

`ldPower`

for exit probabilities given boundaries OR drift
(effect) given power OR confidence interval OR adjusted p-value.

`commonbounds`

for some commonly used boundaries that do not use alpha spending.

```
## From Reboussin, et al. (2000)
#t <- seq(0.2,1,length=5)
#obf.bd <- ldBounds(t)
#summary(obf.bd)
#plot(obf.bd)
# Equivalent bounds to above
obf.bd2 <- ldBounds(5)
t <- c(0.2292,0.3333,0.4375,0.5833,0.7083,0.8333)
t2 <- c(56,77,126,177,247,318)
power.fam <- ldBounds(t,t2,iuse=3,alpha=0.05)
summary(power.fam)
```

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