# ldBounds: Group Sequential Boundaries Using Spending Functions In ldbounds: Lan-DeMets Method for Group Sequential Boundaries

 ldBounds R Documentation

## Group Sequential Boundaries Using Spending Functions

### Description

'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.

### Usage

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


### Arguments

 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 t or the analysis times corresponding to t looks. iuse the type of alpha spending function(s) to use for bounds. If two-sided bounds are calculated and iuse is a single value, the same type will be used for each of the two boundaries. If a vector of length two is given, the two values will be used for lower and upper bounds, respectively. Details of specification are given below. asf a list of one or two functions to be used as alpha spending function(s). Used with iuse=5 (See below). 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 iuse=5, any alpha specified is ignored (see details). phi a vector of values used when iuse=3 or 4 (See below). 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.

### 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 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)\leq1 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.

### Value

'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 iuse 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.

### Author(s)

Charlie Casper charlie.casper@hsc.utah.edu, Thomas Cook cook@biostat.wisc.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.

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.

### Examples

   ## 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)



ldbounds documentation built on June 22, 2024, 6:53 p.m.