Description Usage Arguments Details Value Note Author(s) References See Also Examples
gsDesign()
is used to find boundaries and trial size required for a group sequential design.
1 2 3 4 |
k |
Number of analyses planned, including interim and final. |
test.type |
|
alpha |
Type I error, always one-sided. Default value is 0.025. |
beta |
Type II error, default value is 0.1 (90% power). |
astar |
Normally not specified. If |
delta |
Effect size for theta under alternative hypothesis. This can be set to the standardized effect size to generate a sample size if |
n.fix |
Sample size for fixed design with no interim; used to find maximum group sequential sample size. For a time-to-event outcome, input number of events required for a fixed design rather than sample size
and enter fixed design sample size (optional) in |
timing |
Sets relative timing of interim analyses. Default of 1 produces equally spaced analyses.
Otherwise, this is a vector of length |
sfu |
A spending function or a character string indicating a boundary type (that is, “WT” for Wang-Tsiatis bounds, “OF” for O'Brien-Fleming bounds and “Pocock” for Pocock bounds).
For one-sided and symmetric two-sided testing is used to completely specify spending ( |
sfupar |
Real value, default is -4 which is an O'Brien-Fleming-like conservative bound when used with the default Hwang-Shih-DeCani spending function. This is a real-vector for many spending functions.
The parameter |
sfl |
Specifies the spending function for lower boundary crossing probabilities when asymmetric, two-sided testing is performed ( |
sflpar |
Real value, default is -2, which, with the default Hwang-Shih-DeCani spending function, specifies a less conservative spending rate than the default for the upper bound. |
tol |
Tolerance for error (default is 0.000001). Normally this will not be changed by the user. This does not translate directly to number of digits of accuracy, so use extra decimal places. |
r |
Integer value controlling grid for numerical integration as in Jennison and Turnbull (2000);
default is 18, range is 1 to 80.
Larger values provide larger number of grid points and greater accuracy.
Normally |
n.I |
Used for re-setting bounds when timing of analyses changes from initial design; see examples. |
maxn.IPlan |
Used for re-setting bounds when timing of analyses changes from initial design; see examples. |
nFixSurv |
If a time-to-event variable is used, |
endpoint |
An optional character string that should represent the type of endpoint used for the study. This may be used by output functions. Types most likely to be recognized initially are "TTE" for time-to-event outcomes with fixed design sample size generated by |
delta1 |
|
delta0 |
|
overrun |
Scalar or vector of length |
Many parameters normally take on default values and thus do not require explicit specification.
One- and two-sided designs are supported. Two-sided designs may be symmetric or asymmetric.
Wang-Tsiatis designs, including O'Brien-Fleming and Pocock designs can be generated.
Designs with common spending functions as well as other built-in and user-specified functions for Type I error and
futility are supported.
Type I error computations for asymmetric designs may assume binding or non-binding lower bounds.
The print function has been extended using print.gsDesign()
to print gsDesign
objects; see examples.
The user may ignore the structure of the value returned by gsDesign()
if the standard
printing and plotting suffice; see examples.
delta
and n.fix
are used together to determine what sample size output options the user seeks.
The default, delta=0
and n.fix=1
, results in a ‘generic’ design that may be used with any sampling
situation. Sample size ratios are provided and the user multiplies these times the sample size for a fixed design
to obtain the corresponding group sequential analysis times. If delta>0
, n.fix
is ignored, and
delta
is taken as the standardized effect size - the signal to noise ratio for a single observation;
for example, the mean divided by the standard deviation for a one-sample normal problem.
In this case, the sample size at each analysis is computed.
When delta=0
and n.fix>1
, n.fix
is assumed to be the sample size for a fixed design
with no interim analyses. See examples below.
Following are further comments on the input argument test.type
which is used to control what type of error measurements are used in trial design.
The manual may also be worth some review in order to see actual formulas for boundary crossing probabilities for the various options.
Options 3 and 5 assume the trial stops if the lower bound is crossed for Type I and Type II error computation (binding lower bound).
For the purpose of computing Type I error, options 4 and 6 assume the trial continues if the lower bound is crossed (non-binding lower bound); that is a Type I error can be made by crossing an upper bound after crossing a previous lower bound.
Beta-spending refers to error spending for the lower bound crossing probabilities
under the alternative hypothesis (options 3 and 4).
In this case, the final analysis lower and upper boundaries are assumed to be the same.
The appropriate total beta spending (power) is determined by adjusting the maximum sample size
through an iterative process for all options.
Since options 3 and 4 must compute boundary crossing probabilities under both the null and alternative hypotheses,
deriving these designs can take longer than other options.
Options 5 and 6 compute lower bound spending under the null hypothesis.
An object of the class gsDesign
. This class has the following elements and upon return from
gsDesign()
contains:
k |
As input. |
test.type |
As input. |
alpha |
As input. |
beta |
As input. |
astar |
As input, except when |
delta |
The standardized effect size for which the design is powered. Will be as input to |
n.fix |
Sample size required to obtain desired power when effect size is |
timing |
A vector of length |
tol |
As input. |
r |
As input. |
n.I |
Vector of length |
maxn.IPlan |
As input. |
nFixSurv |
As input. |
nSurv |
Sample size for Lachin and Foulkes method when |
endpoint |
As input. |
delta1 |
As input. |
delta0 |
As input. |
overrun |
As input. |
upper |
Upper bound spending function, boundary and boundary crossing probabilities under the NULL and alternate hypotheses. See Spending function overview and manual for further details. |
lower |
Lower bound spending function, boundary and boundary crossing probabilities at each analysis.
Lower spending is under alternative hypothesis (beta spending) for |
theta |
Standarized effect size under null (0) and alternate hypothesis. If |
falseprobnb |
For |
en |
Expected sample size accounting for early stopping. For time-to-event outcomes, this would be the expected number of events (although |
The manual is not linked to this help file, but is available in library/gsdesign/doc/gsDesignManual.pdf in the directory where R is installed.
Keaven Anderson keaven\_anderson@merck.
Jennison C and Turnbull BW (2000), Group Sequential Methods with Applications to Clinical Trials. Boca Raton: Chapman and Hall.
gsDesign package overview, gsDesign print, summary and table summary functions, Plots for group sequential designs, gsProbability
,
Spending function overview, Wang-Tsiatis Bounds
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | # symmetric, 2-sided design with O'Brien-Fleming-like boundaries
# lower bound is non-binding (ignored in Type I error computation)
# sample size is computed based on a fixed design requiring n=800
x <- gsDesign(k=5, test.type=2, n.fix=800)
# note that "x" below is equivalent to print(x) and print.gsDesign(x)
x
plot(x)
plot(x, plottype=2)
# Assuming after trial was designed actual analyses occurred after
# 300, 600, and 860 patients, reset bounds
y <- gsDesign(k=3, test.type=2, n.fix=800, n.I=c(300,600,860),
maxn.IPlan=x$n.I[x$k])
y
# asymmetric design with user-specified spending that is non-binding
# sample size is computed relative to a fixed design with n=1000
sfup <- c(.033333, .063367, .1)
sflp <- c(.25, .5, .75)
timing <- c(.1, .4, .7)
x <- gsDesign(k=4, timing=timing, sfu=sfPoints, sfupar=sfup, sfl=sfPoints,
sflpar=sflp,n.fix=1000)
x
plot(x)
plot(x, plottype=2)
# same design, but with relative sample sizes
gsDesign(k=4, timing=timing, sfu=sfPoints, sfupar=sfup, sfl=sfPoints,
sflpar=sflp)
|
Loading required package: xtable
Loading required package: ggplot2
Symmetric two-sided group sequential design with
90 % power and 2.5 % Type I Error.
Spending computations assume trial stops
if a bound is crossed.
Analysis N Z Nominal p Spend
1 164 3.25 0.0006 0.0006
2 328 2.99 0.0014 0.0013
3 492 2.69 0.0036 0.0028
4 656 2.37 0.0088 0.0063
5 819 2.03 0.0214 0.0140
Total 0.0250
++ alpha spending:
Hwang-Shih-DeCani spending function with gamma = -4.
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 5 Total E{N}
0.0000 0.0006 0.0013 0.0028 0.0063 0.0140 0.025 812.8
0.1146 0.0370 0.1512 0.2647 0.2699 0.1771 0.900 589.3
Lower boundary (futility or Type II Error)
Analysis
Theta 1 2 3 4 5 Total
0.0000 6e-04 0.0013 0.0028 0.0063 0.014 0.025
0.1146 0e+00 0.0000 0.0000 0.0000 0.000 0.000
Symmetric two-sided group sequential design with
90 % power and 2.5 % Type I Error.
Spending computations assume trial stops
if a bound is crossed.
Analysis N Z Nominal p Spend
1 300 2.96 0.0016 0.0016
2 600 2.44 0.0074 0.0067
3 860 2.01 0.0220 0.0167
Total 0.0250
++ alpha spending:
Hwang-Shih-DeCani spending function with gamma = -4.
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 Total E{N}
0.0000 0.0016 0.0067 0.0167 0.0250 854.8
0.1146 0.1655 0.4833 0.2654 0.9142 641.6
Lower boundary (futility or Type II Error)
Analysis
Theta 1 2 3 Total
0.0000 0.0016 0.0067 0.0167 0.025
0.1146 0.0000 0.0000 0.0000 0.000
Asymmetric two-sided group sequential design with
90 % 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++
1 123 -0.83 0.2041 0.025 3.14 0.0008 0.0008
2 489 0.39 0.6513 0.025 3.16 0.0008 0.0008
3 855 1.26 0.8966 0.025 3.06 0.0011 0.0009
4 1222 1.98 0.9761 0.025 1.98 0.0239 0.0225
Total 0.1000 0.0250
+ lower bound beta spending (under H1):
User-specified spending function with Points = 0.25 0.5 0.75 1.
++ alpha spending:
User-specified spending function with Points = 0.033333 0.063367 0.1 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 0.0008 0.0007 0.0009 0.0177 0.0202 564.0
0.1025 0.0222 0.1716 0.2969 0.4094 0.9000 907.4
Lower boundary (futility or Type II Error)
Analysis
Theta 1 2 3 4 Total
0.0000 0.2041 0.4703 0.2361 0.0693 0.9798
0.1025 0.0250 0.0250 0.0250 0.0250 0.1000
Asymmetric two-sided group sequential design with
90 % power and 2.5 % Type I Error.
Upper bound spending computations assume
trial continues if lower bound is crossed.
Sample
Size ----Lower bounds---- ----Upper bounds-----
Analysis Ratio* Z Nominal p Spend+ Z Nominal p Spend++
1 0.122 -0.83 0.2041 0.025 3.14 0.0008 0.0008
2 0.488 0.39 0.6513 0.025 3.16 0.0008 0.0008
3 0.855 1.26 0.8966 0.025 3.06 0.0011 0.0009
4 1.221 1.98 0.9761 0.025 1.98 0.0239 0.0225
Total 0.1000 0.0250
+ lower bound beta spending (under H1):
User-specified spending function with Points = 0.25 0.5 0.75 1.
++ alpha spending:
User-specified spending function with Points = 0.033333 0.063367 0.1 1.
* Sample size ratio compared to fixed design with no interim
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 0.0008 0.0007 0.0009 0.0177 0.0202 0.5640
3.2415 0.0222 0.1716 0.2969 0.4094 0.9000 0.9074
Lower boundary (futility or Type II Error)
Analysis
Theta 1 2 3 4 Total
0.0000 0.2041 0.4703 0.2361 0.0693 0.9798
3.2415 0.0250 0.0250 0.0250 0.0250 0.1000
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