How maximum information is calculated in proc seqdesign

[wikich]

Dear all, When I using proc seqdesign to calculate the sample size in group sequential design, the generation of maximum information is confused me.

let's use the example in sas help to explain,

proc seqdesign altref=0.4
               pss
               stopprob
               errspend
               ;
   TwoSidedPocock:        design nstages=4 method=poc;
   TwoSidedOBrienFleming: design nstages=4 method=obf;
   samplesize model=twosamplemean(stddev=0.8 weight=2);
run;

In the design information, 

Method	Pocock
Boundary Key	Both
Alternative Reference	0.4
Number of Stages	4
Alpha	0.05
Beta	0.1
Power	0.9
Max Information (Percent of Fixed Sample)	118.3143
Max Information	77.69844

In the help document, the I0=(Φ−1(1−α/2)+Φ−1(1−β))20.42=(1.96+1.28155)20.16=65.6728, 

How to calcuate max information Ix = 77.69844?

[StatDave]

See "Specified and Derived Parameters" in the Details section of the PROC SEQDESIGN documentation. As noted there, when the alternative reference (ALTREF=) and the type I and type II error levels (ALPHA=, BETA=) are specified, then the procedure internally derives a drift parameter. GIven the drift and the alternative reference, that documentation section shows how the maximum information is computed. 

[wikich]

Thanks for replay :). I have read this section before, but I still do not understand the generation of the drift parameters. I am really interested in the "procedure internally derives a drift parameter". where could I to read the source code to calculation this procedure? Thanks again for your replay.

[StatDave]

There isn't a simple, closed-form expression for computing the drift parameter. It is derived using an iterative, root-finding algorithm.

[wikich]

I also find other papers to explain the procedure. I use the function uniroot() in R which could repeat the drift parameter generated in SAS. Thanks for your replay 🙂