Ch02-LanDemets: The Lan-Demets method of Boundary Construction
In PwrGSD: Power in a Group Sequential Design

Description Usage Arguments Details Value Note Author(s) References See Also Examples

The function LanDemets is used in calls to the functions GrpSeqBnds and PwrGSD as a possible setting for the arguments EfficacyBoundary and FutilityBoundary, in specification of the method whereby efficacy and or futility boundaries are to be constructed. The Lan-Demets method is one of four currently availiable choices, the others being SC (stochastic curtailment), Haybittle (efficacy only) and user specified.

1 2	LanDemets(alpha, spending, from = NULL, to = NULL)

`alpha`	If `LanDemets` is used to specify the `EfficacyBoundary` then the argument `alpha` is the total probability of type I error. If `LanDemets` is used to specify the `FutilityBoundary` then the argument `alpha` is the total probability of type II error.
`spending`	Specify the alpha spending function. Set this to `ObrienFleming`, `Pow(rho=<x>)`, or `Pocock`. See help files for these spending functions.
`from`	WARNING EXPERIMENTAL: you can actually construct boundaries via a hybrid of the 3 boundary construction methods, `LanDemets`, `SC`, and 'user specified'. When using a hybrid boundry, set the argument `EfficacyBoundary` or `FutilityBoundary` respectively, to a list with components `LanDemets`, `SC`, or user specified numbers. In the former two cases, `from` and `to` are used in `LanDemets` and also in `SC` to stipulate how many interim analyses they are in effect. See the help for `GrpSeqBnds` and `PwrGSD`
`to`	See above.

The cornerstone of the Lan-Demets method is that the amount of alpha (type I or II error probability) that is "spent" at a given interim analysis is determined via a user specified "spending function". A spending function is a monotone increasing mapping on (0,1) with range (0,alpha). The 'alpha' spent at a given analysis is determined by the increment in the values of the spending function at the current and at the most recent information fractions.

An object of class boundary.construction.method which is really a list with the following components. The print method displays the original call.

`type`	Gives the boundary construction method type, which is the character string "LanDemets"
`alpha`	The numeric value passed to the argument 'alpha' which is the total probability of type I (efficacy) or type II (futility) error.
`spending`	The spending function that was passed to the argument 'spending'. Note that this will be of class 'name' for 'ObrienFleming' and 'Pocock', but will be of class 'function' for 'Pow'
`from`	The numeric value passed to the argument 'from'. See above.
`to`	The numeric value passed to the argument 'to'. See above.
`call`	returns the call

The print method returns the call by default

Grant Izmirlian

see references under PwrGSD

SC, ObrienFleming, Pow, Pocock, GrpSeqBnds, and PwrGSD

## example 1: what is the result of calling a Boundary Construction Method function
    ## A call to 'LanDemets' just returns the call
    LanDemets(alpha=0.05, spending=ObrienFleming)
    
    ## It does arguement checking...this results in an error
    ## Not run: 
      LanDemets(alpha=0.05)
    
## End(Not run)
    
    ## but really its value is a list with the a component containing
    ## the boundary method type, "LanDemts", and components for each
    ## of the arguments.
    names(LanDemets(alpha=0.05, spending=ObrienFleming))

    LanDemets(alpha=0.05, spending=ObrienFleming)$type
    LanDemets(alpha=0.05, spending=ObrienFleming)$alpha
    LanDemets(alpha=0.05, spending=ObrienFleming)$spending
    class(LanDemets(alpha=0.05, spending=ObrienFleming)$spending)
    LanDemets(alpha=0.05, spending=Pow(2))$spending
    class(LanDemets(alpha=0.05, spending=Pow(2))$spending)
    LanDemets(alpha=0.05, spending=ObrienFleming)$call

## example 2: ...But the intended purpose of the spending functions is
## in constructing calls to 'GrpSeqBnds' and to 'PwrGSD':
     

    frac <- c(0.07614902,0.1135391,0.168252,0.2336901,0.3186155,
              0.4164776,0.5352199,0.670739,0.8246061,1)
    drift <- c(0.3836636,0.5117394,0.6918584,0.8657705,1.091984,
               1.311094,1.538582,1.818346,2.081775,2.345386)

    test <- GrpSeqBnds(frac=frac, EfficacyBoundary=LanDemets(alpha=0.05, spending=ObrienFleming),
                       FutilityBoundary=LanDemets(alpha=0.10, spending=Pocock),
                       drift=drift)