The gs suite

The gs suite provides two commands: gsbounds and gsdesign.

The gsbounds command calculates efficacy and futility bounds based on the number of analyses, also called looks, the desired overall type I error, and the desired power.

You can select from seven boundary-calculation methods:

• Classical O'Brien–Fleming
• Classical Pocock
• Classical Wang–Tsiatis
• Error-spending Pocock style
• Error-spending O'Brien–Fleming style
• Error-spending Kim–DeMets
• Error-spending Hwang–Shih–de Cani

To calculate, for instance, O'Brien–Fleming efficacy and futility bounds for a study with 5 looks, a power of 0.9, and a type I error of 0.05, type

. gsbounds, efficacy(obfleming) futility(obfleming) nlooks(5)
  power(0.9) alpha(0.05)

Want to visualize these boundaries? Add the graphbounds option to the above command.

The gsdesign command computes efficacy and futility boundaries and provides sample sizes at each look for a variety of tests. gsdesign is specified with one of the subcommands listed below, depending on the type of test to be performed for the trial.

Command	Description
gsdesign onemean	GSD for a one-sample mean test
gsdesign twomeans	GSD for a two-sample means test
gsdesign oneproportion	GSD for a one-sample proportion test
gsdesign twoproportions	GSD for a two-sample proportions test
gsdesign logrank	GSD for a log-rank test
gsdesign usermethod	GSD for a user-defined method

Let's see it work

Suppose we are interested in designing a group sequential trial for a new pediatric COVID-19 vaccine (our experimental treatment), which we will compare against the first-generation vaccine (our control treatment). We will measure the log of participants' neutralizing antibody titers and compare the mean log-titer in the experimental group with that of the control group. We can use gsdesign twomeans to calculate stopping boundaries and required sample sizes for such a trial.

Say that we anticipate a mean log-titer of 5.5 with known standard deviation of 2 in the control arm and a mean log-titer of 6.5 with known standard deviation of 3 in the experimental arm. We will compute sample sizes for a one-sided test at the 2.5% level with power of 90% and will allocate twice as many participants to the experimental arm as to the control arm.

We calculate sample sizes for five looks (four interim analyses and a final analysis), scheduled to occur with 50%, 65%, 80%, 90%, and 100% of the data. We calculate efficacy and nonbinding futility boundaries using the error-spending approximation of classical O'Brien–Fleming boundaries.

. gsdesign twomeans 5.5 6.5,  sd1(2) sd2(3) knownsds 
           onesided alpha(0.025) power(0.9) nratio(2) 
           information(50 65 80 90 100)
	   efficacy(errobfleming) futility(errobfleming) graphbounds

Group sequential design for a two-sample means test
z test
H0: m2 = m1 versus Ha: m2 > m1

Efficacy: Error-spending O'Brien–Fleming style
Futility: Error-spending O'Brien–Fleming style, nonbinding

Study parameters:
      alpha = 0.0250  (upper one-sided)
      power = 0.9000
     nratio = 2.0000
      delta = 1.0000
         m1 = 5.5000
         m2 = 6.5000
        sd1 = 2.0000
        sd2 = 3.0000

Expected sample size:
         H0 = 178.59
         Ha = 213.33

Info. ratio = 1.1311
    N fixed =    269
      N max =    305
     N1 max =    102
     N2 max =    203

Fixed-study crit. value = 1.9600

Critical values, p-values, and sample sizes for a group sequential design


      
 
 Info.        Efficacy             Futility      
 
         Sample size        
 Look 
 
 frac.      Upper   p-value      Lower   p-value 
 
       N1        N2         N

    1 
 
  0.50     2.9626    0.0015     0.3842    0.3504 
 
       51       102       153
    2 
 
  0.65     2.5785    0.0050     0.9743    0.1650 
 
       66       132       198
    3 
 
  0.80     2.3086    0.0105     1.4662    0.0713 
 
       81       162       243
    4 
 
  0.90     2.1923    0.0142     1.7330    0.0415 
 
       91       182       273
    5 
 
  1.00     2.0789    0.0188     2.0789    0.0188 
 
      102       203       305

Note: Critical values are for z statistics; otherwise, use p-value boundaries.

If this trial continues to the final analysis, 305 participants will be required. However, the expected sample size is smaller—179 if the null hypothesis is true and 213 if the alternative hypothesis is true. An equivalent fixed study design, which does not have the option to stop early, would require 269 participants.

The table at the bottom of the output presents the stopping boundaries as both critical z-values and p-values, as well as the sample size required at each analysis. The first look occurs once data are collected from 51 participants in the control arm and 102 participants in the experimental arm. If the z statistic is greater than or equal to 2.96, then H₀ is rejected and the trial is stopped. If the z statistic is less than 0.38, then H₀ can be accepted, and the trial can be terminated for futility. However, because the futility boundary is nonbinding, even if the z statistic is less than 0.38, the trial is allowed to continue without overrunning the familywise type I error. If the z statistic at the first look is between 0.38 and 2.96, the trial must continue collecting data until the second look.

The testing procedure at the second, third, and fourth looks is akin to that of the first look; the difference is that the efficacy and futility bounds get progressively closer. At the fifth and final look, which takes place once data have been collected from 102 participants in the control arm and 203 participants in the experimental arm, the efficacy critical value equals the futility critical value, and there is no option to continue. If the z statistic at the final look is greater than or equal to 2.08, then H₀ is rejected; otherwise, H₀ is accepted.

The graph produced when the graphbounds option is specified makes it easy to visualize the stopping boundaries and the required actions to be taken at each look.

When a z statistic falls within the blue rejection region, the trial is stopped for efficacy. When the z statistic falls within the red acceptance region, the trial can be stopped for futility. If the z statistic falls in the green continuation region, the trial continues to the next look.