Check print.gsProbability vs print.gsDesign

[keaven]

I've a question regarding the output of gsProbability() and gsDesign() in your R package v. 3.2.2.

What is the reason why the output of the two functions differs ? In particular the probabilities of type II error are reported in the "Upper boundary" section in the first case, and in the "Lower boundary" section in the second ? (see highlighted lines below)

>lambda <- -log(1 - 0.145) / 12 
>nSurvival(lambda1 = lambda, lambda2 = lambda * 0.85, Ts = 43, Tr = 22, alpha = 0.025, sided = 1, beta = 1 - 0.97)
>theta1 <- -log(0.85) * sqrt(1) / 2
>gsp <-  gsProbability(k = 4, theta = c(0, theta1), n.I = c(0.33, 0.50, 0.75, 1), a = c(-1.32, 0, 0.5, 1.96), b = c(3.72, 3.09, 3.09, 1.96))
>gsp

               Lower bounds   Upper bounds 
  Analysis N    Z   Nominal p  Z   Nominal p
         1  1 -1.32    0.0934 3.72    0.0001
         2  1  0.00    0.5000 3.09    0.0010
         3  1  0.50    0.6915 3.09    0.0010
         4  1  1.96    0.9750 1.96    0.0250

Boundary crossing probabilities and expected sample size assume
any cross stops the trial

Upper boundary (power or Type I Error)
          Analysis
   Theta     1      2     3      4  Total E{N}
  0.0000 1e-04 0.0009 7e-04 0.0232 0.0250  0.7
  0.0813 1e-04 0.0011 9e-04 0.0279 0.0301  0.7 (THIS LINE WAS HIGHLIGHTED)

Lower boundary (futility or Type II Error)
          Analysis
   Theta      1      2      3      4  Total
  0.0000 0.0934 0.4077 0.2183 0.2556 0.9750
  0.0813 0.0859 0.3924 0.2175 0.2742 0.9699

> sfup <- round(cumsum(gsp$upper$prob[,1]) / 0.025, 3)
> sfup[4] <- 1
> sflp <- round(cumsum(gsp$upper$prob[,2]) / 0.030, 3)
> sflp[4] <- 1

> gsd <- gsDesign(k = 4, test.type = 4, beta = 0.03, delta = theta1, n.fix = 2238, timing = c(0.33, 0.50, 0.75, 1), 
+                    sfu = sfPoints, sfupar = sfup, sfl = sfPoints, sflpar = sflp, nFixSurv = 7034, delta1 = log(0.85))
>gsd

Group sequential design sample size for time-to-event outcome
with sample size 7058. The analysis plan below shows events
at each analysis.
Asymmetric two-sided group sequential design with
97 % power and 2.5 % Type I Error.
Upper bound spending computations assume
trial continues if lower bound is crossed.

                  ----Lower bounds----  ----Upper bounds-----
  Analysis   N    Z   Nominal p Spend+  Z   Nominal p Spend++
         1  741 -1.46    0.0720 0.0001 3.72    0.0001  0.0001
         2 1123 -0.31    0.3781 0.0011 3.09    0.0010  0.0010
         3 1684  0.32    0.6239 0.0009 3.09    0.0010  0.0007
         4 2246  1.97    0.9753 0.0278 1.97    0.0247  0.0232
     Total                      0.0300                 0.0250 
+ lower bound beta spending (under H1):
 User-specified spending function with Points = 0.004 0.042 0.072 1.
++ alpha spending:
 User-specified spending function with Points = 0.004 0.042 0.07 1.

Boundary crossing probabilities and expected sample size
assume any cross stops the trial

Upper boundary (power or Type I Error)
          Analysis
   Theta      1      2      3      4  Total   E{N}
  0.0000 0.0001 0.0010 0.0007 0.0231 0.0249 1641.3
  0.0813 0.0659 0.2935 0.2570 0.3536 0.9700 1670.3

Lower boundary (futility or Type II Error)
          Analysis
   Theta      1      2      3      4  Total
  0.0000 0.0720 0.3081 0.2638 0.3312 0.9751
  0.0813 0.0001 0.0011 0.0009 0.0278 0.0300 (THIS LINE WAS HIGHLIGHTED)

With best regards,

Luca Boni