compute_design_performance: Compute Design Performance
In interAdapt: interAdapt
Description
Usage
Arguments
Details
Value
References
Examples
Description
Generates decision rules for group
sequential trial designs with adaptive enrollment criteria. Tables are
also generated which compare the performance of these designs to the
performance of standard group sequential designs. We use the notation AD to refer to the design with adaptive enrollment, SC to refer to a standard group sequential design enrolling from the combined population, and SS to refer to a standard group sequential design enrolling from only the subpopulation where there is greater prior evidence of a positive treatment effect. Further details are provided in (Fisher et al. 2014).
Usage
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compute_design_performance(p_1 = 0.33, p_10 = 0.25, p_20 = 0.2,
p_11 = p_10 + 0.125, per_stage_sample_size_combined_AD = 280,
per_stage_sample_size_subpop_1_AD = 148, FWER = 0.025,
FWER_H0C_proportion = 0.09, Delta = -0.5, iter = 10000,
time_limit = 45, total_number_stages = 5,
last_stage_subpop_2_enrolled_AD = 3,
enrollment_rate_combined_population = 420,
per_stage_sample_size_combined_SC = 106, per_stage_sample_size_SS = 100,
subpop_2_stop_boundary_constant_AD = 0,
H01_futility_boundary_constant_AD = 0,
H0C_futility_boundary_constant_SC = -0.1,
H01_futility_boundary_constant_SS = -0.1,
lower_bound_treatment_effect_subpop_2 = -0.2,
upper_bound_treatment_effect_subpop_2 = 0.2, CSV)
Arguments
p_1
The proportion of the population in subpopulation 1,
which is the subpopulation having stronger prior evidence of a positive treatment effect.
p_10
The probability of a successful outcome for subpopulation 1 under assignment
to the control arm. This is used in estimating power and expected sample size.
p_20
The probability of a successful outcome for subpopulation 2 under assignment
to the control arm. This is used in estimating power and expected sample size.
p_11
The probability of a successful outcome for subpopulation 1 under assignment
to the treatment arm. Note that the user does not specify the probability of success under treatment for subpopulation 2 (p_2t).
Instead, compute_design_performance considers a range of possible values of p_2t (see the lower_bound_treatment_effect_subpop_2 and upper_bound_treatment_effect_subpop_2 arguments).
per_stage_sample_size_combined_AD
The
number of participants enrolled per stage in the adaptive design while
both subpopulations are being enrolled.
per_stage_sample_size_subpop_1_AD
The number of participants required for each stage
in the adaptive design after enrollment for subpopulation 2 has been
stopped.
FWER
The familywise Type I error rate (α) for all designs (see Fisher et al. 2014).
FWER_H0C_proportion
Proportion of α allocated to H_{0C} for the adaptive design. Here, H_{0C} refers to the null hypothesis of no treatment effect in the combined population.
Delta
Used as the exponent in defining the efficacy and
futility boundaries, as described (Fisher et al. 2014).
iter
The number of simulated trials used to
estimate the power, expected sample size, and expected trial duration.
time_limit
Time limit for simulation in seconds. If the simulation
exceeds the time limit, calculations will stop and the user will get an
error message ("reached CPU time limit"). See setTimeLimit.
To avoid this, the number of iterations (iter) can be reduced or
the time limit can be increased.
total_number_stages
Total number of stages
used in each design (K). The maximum allowable number of stages is 20.
last_stage_subpop_2_enrolled_AD
The last stage subpopulation 2 is enrolled, under the adaptive design. We refer to this stage number as k*.
enrollment_rate_combined_population
The assumed
enrollment rate per year for the combined population. This impacts the
expected duration of each trial design. Active enrollments from
the two subpopulations are assumed to be independent. The enrollment rates
for subpopulations 1 and 2 are assumed proportional, based on p_1.
This implies that each stage of the adaptive design up to and including stage k* takes the same amount of time to complete, regardless of whether or not enrollment stops for subpopulation 2. Each stage after k* will also take the same amount of time to complete.
per_stage_sample_size_combined_SC
The number of participants enrolled in each stage of the standard group sequential design enrolling the
combined population (SC).
per_stage_sample_size_SS
The number of participants enrolled in each stage for standard group sequential design enrolling only
subpopulation 1 (SS).
subpop_2_stop_boundary_constant_AD
Stopping boundary proportionality constant for subpopulation 2 enrollment
in the adaptive design.
H01_futility_boundary_constant_AD
Futility boundary proportionality constant for H_{01} in the adaptive design. This is used to calculate the futility boundaries
(l_{1,k}) for the z-statistics calculated in subpopulation 1
(Z_{1,k}) as defined in (Fisher et al. 2014).
H0C_futility_boundary_constant_SC
Futility boundary proportionality constant for H_{0C} in the standard design always enrolling from the combined population.
H01_futility_boundary_constant_SS
Futility boundary proportionality constant for H_{01} in the standard design only enrolling from subpopulation 1.
lower_bound_treatment_effect_subpop_2
Simulations
are performed under a range of treatment effect sizes for
subpopulation 2 (i.e. p_{2t}-p_{2c}). This parameter sets the lower bound for this range.
This effectively sets the lower bound for the probability of success under treatment for subpopulation 2 (p_21), since p_20 is set
by the user.
upper_bound_treatment_effect_subpop_2
Simulations
are performed under a range of treatment effect sizes for
subpopulation 2 (i.e. p_{2t}-p_{2c}). This parameter sets the upper bound for this range.
CSV
Rather than manually entering the arguments above, this allows for the arguments to be entered via a tabular csv file. The CSV argument should contain a character vector or list of csv filenames. The
table must minimally include the columns "inputId" and "value" (as in the
default_parameter_table).
Details
This function is meant to be applied when there is prior
evidence that a treatment might work better in a one subpopulation
than in another. In this context, a trial with an adaptive enrollment
criteria would determine whether or not to continue enrolling patients
from each subpopulation based on interim analyses of whether each
subpopulation is benefiting. In order for the type I error and the
power of the trial to be calculable, the decision rules for changing
enrollment must be set before the trial starts. This function generates
decision rules for group sequential trial designs with adaptive
enrollment criteria, and compares the performance of these designs
against standard group sequential designs with fixed enrollment criteria. Performance is compared in
terms of power, expected sample size, and expected trial duration.
Value
A list with 5 elements:
performance_comparison
A table comparing the performance of the three trials, in terms of power, expected sample size, and expected duration. See examples.
AD_design
Efficacy and futility boundaries for the group sequential design with adaptive enrollment
SC_design
Efficacy and futility boundaries for the standard group sequential design enrolling from the combined population
SS_design
Efficacy and futility boundaries for the standard group sequential design enrolling subpopulation 1 only
input_parameters
List of input argument values
References
Aaron Fisher, Harris Jaffee, and Michael Rosenblum. interAdapt – An
Interactive Tool for Designing and Evaluating Randomized Trials with
Adaptive Enrollment Criteria. Working Paper, 2014.
http://arxiv.org/abs/1404.0734
Examples
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#Store function output
o<-compute_design_performance()
names(o)
#Decision rules for trial designs
print(o$SS[[1]])
print(o$SC[[1]])
print(o$AD[[1]])
#Plot decision rules
par(mfrow=c(1,3))
matplot(t(o$SS[[1]][2:3,]),type='o',
main='Standard trial - subpop 1',
xlab='stage',ylab='Z-statistic',
col='blue',pch=2:3,lty=3)
legend('topright',c('H01 Efficacy','H01 Futility')
,col='blue',pch=2:3,lty=3)
matplot(t(o$SC[[1]][4:5,]),type='o',
main='Standard trial - combined pop',xlab='stage',
ylab='Z-statistic',col='red',pch=0:1,lty=3)
legend('topright',c('H0C Efficacy','H0C Futility'),
col='red',pch=0:1,lty=3)
matplot(t(o$AD[[1]][4:7,]),type='o',
main='Adaptive Enrollment',xlab='stage',
ylab='Z-statistic',col=c('red','red','blue','blue'),
pch=0:3,lty=3)
legend('topright',c('H0C Efficacy','H0C Futility',
'H01 Efficacy','H01 Futility'),col=c('red',
'red','blue','blue'),pch=0:3,lty=3)
#Check performance
o$performance[[1]]
#Plot performance over a range of treatment effects for subpop2
col1<-c('black','black','black','green','blue')
perform_names<-rownames(o$performance[[1]])
#index for parts of the table corresponding to power
p_ind<- grep('Power',perform_names)
#index for parts of the table corresponding to sample size
s_ind<- grep('Sample Size',perform_names)
#index for parts of the table corresponding to trial duration
d_ind<- grep('DUR',perform_names)
par(mfrow=c(1,3))
lty1<-c(2,3,1,4,5)
matplot(x=t(o$performance[[1]][1,]),t(o$performance[[1]][p_ind,]),
type='l',lty=lty1,col=col1[1:5],xlab='Subpop.2 Tx. Effect',
ylab='Power',main='Power')
legend('bottomleft',perform_names[p_ind],col=col1[1:length(p_ind)],
lty=lty1)
matplot(x=t(o$performance[[1]][1,]),t(o$performance[[1]][s_ind,]),
type='l',lty=1:3,col=col1[3:5],xlab='Subpop.2 Tx. Effect',
ylab='Expected Sample Size',main='Expected Sample Size')
legend('topright',substr(perform_names[d_ind],1,2),col=col1[3:5],
lty=1:3)
matplot(x=t(o$performance[[1]][1,]),t(o$performance[[1]][d_ind,]),
type='l',lty=1:3,col=col1[3:5],xlab='Subpop.2 Tx. Effect',
ylab="Expected Duration",main='Expected Duration')
legend('topright',substr(perform_names[d_ind],1,2),col=col1[3:5],
lty=1:3)
Example output
[1] "performance_comparison" "AD_design" "SC_design"
[4] "SS_design" "input_parameters"
1 2
Cumulative Sample Size 100.000000 200.0000000
H01 Efficacy Boundaries for z-statistics Z(1,k) 4.559666 3.2241708
H01 Futility Boundaries for z-statistics Z(1,k) -0.200000 -0.1414214
3 4
Cumulative Sample Size 300.0000000 400.000000
H01 Efficacy Boundaries for z-statistics Z(1,k) 2.6325244 2.279833
H01 Futility Boundaries for z-statistics Z(1,k) -0.1154701 -0.100000
5
Cumulative Sample Size 500.000000
H01 Efficacy Boundaries for z-statistics Z(1,k) 2.039145
H01 Futility Boundaries for z-statistics Z(1,k) 2.039145
1 2
Cumulative Sample Size Subpop. 1 34.980000 69.9600000
Cumulative Sample Size Subpop. 2 71.020000 142.0400000
Cumulative Sample Size Combined Pop. 106.000000 212.0000000
H0C Efficacy Boundaries for z-statistics Z(C,k) 4.559666 3.2241708
H0C Futility Boundaries for z-statistics Z(C,k) -0.200000 -0.1414214
3 4
Cumulative Sample Size Subpop. 1 104.9400000 139.920000
Cumulative Sample Size Subpop. 2 213.0600000 284.080000
Cumulative Sample Size Combined Pop. 318.0000000 424.000000
H0C Efficacy Boundaries for z-statistics Z(C,k) 2.6325244 2.279833
H0C Futility Boundaries for z-statistics Z(C,k) -0.1154701 -0.100000
5
Cumulative Sample Size Subpop. 1 174.900000
Cumulative Sample Size Subpop. 2 355.100000
Cumulative Sample Size Combined Pop. 530.000000
H0C Efficacy Boundaries for z-statistics Z(C,k) 2.039145
H0C Futility Boundaries for z-statistics Z(C,k) 2.039145
1 2
Cumulative Sample Size Subpop. 1 92.400000 184.800000
Cumulative Sample Size Subpop. 2 187.600000 375.200000
Cumulative Sample Size Combined Pop. 280.000000 560.000000
H0C Efficacy Boundaries u(C,k) for z-statistics Z(C,k) 4.956000 3.504421
Boundaries l(2,k) for Z(2,k) to Stop Subpop. 2 Enrollment 0.000000 0.000000
H01 Efficacy Boundaries u(1,k) for Z(1,k) 5.101976 3.607642
Boundaries l(1,k) for Z(1,k) to Stop All Enrollment 0.000000 0.000000
3 4
Cumulative Sample Size Subpop. 1 277.200000 425.200000
Cumulative Sample Size Subpop. 2 562.800000 562.800000
Cumulative Sample Size Combined Pop. 840.000000 988.000000
H0C Efficacy Boundaries u(C,k) for z-statistics Z(C,k) 2.861348 NA
Boundaries l(2,k) for Z(2,k) to Stop Subpop. 2 Enrollment Inf NA
H01 Efficacy Boundaries u(1,k) for Z(1,k) 2.945628 2.378361
Boundaries l(1,k) for Z(1,k) to Stop All Enrollment 0.000000 0.000000
5
Cumulative Sample Size Subpop. 1 573.200000
Cumulative Sample Size Subpop. 2 562.800000
Cumulative Sample Size Combined Pop. 1136.000000
H0C Efficacy Boundaries u(C,k) for z-statistics Z(C,k) NA
Boundaries l(2,k) for Z(2,k) to Stop Subpop. 2 Enrollment NA
H01 Efficacy Boundaries u(1,k) for Z(1,k) 2.048431
Boundaries l(1,k) for Z(1,k) to Stop All Enrollment 2.048431
X1 X2 X3 X4
Subpop.2 Tx. Effect -0.2000000 -0.1555556 -0.1111111 -0.06666667
AD:Sample Size 573.9080000 578.3858800 577.8755600 598.50564000
AD:DUR 2.7872150 2.8192522 2.7956733 2.80145079
AD:Power H0C 0.0000000 0.0000000 0.0000000 0.04000000
AD:Power H01 81.5800000 82.2600000 81.4700000 82.39000000
AD:Power H0C or H01 81.5800000 82.2600000 81.4700000 82.39000000
SC:Sample Size 123.6384000 149.5024000 203.7214000 282.57480000
SC:DUR 0.2943771 0.3559581 0.4850510 0.67279714
SC:Power H0C 0.0000000 0.0300000 0.2000000 1.84000000
SS:Sample Size 358.7300000 357.0100000 358.0500000 356.70000000
SS:DUR 2.5882395 2.5758297 2.5833333 2.57359307
SS:Power H01 82.0700000 81.8400000 81.6700000 80.82000000
X5 X6 X7 X8
Subpop.2 Tx. Effect -0.02222222 0.02222222 0.06666667 0.1111111
AD:Sample Size 666.04960000 760.70988000 778.39300000 703.1972000
AD:DUR 2.79216883 2.71581010 2.36965657 1.8502638
AD:Power H0C 1.52000000 13.61000000 43.45000000 73.8000000
AD:Power H01 81.13000000 75.30000000 52.97000000 23.9300000
AD:Power H0C or H01 81.49000000 82.15000000 83.65000000 86.1700000
SC:Sample Size 351.88820000 401.36900000 408.54520000 381.9922000
SC:DUR 0.83782905 0.95564048 0.97272667 0.9095052
SC:Power H0C 10.03000000 30.00000000 57.14000000 80.3700000
SS:Sample Size 359.11000000 359.36000000 356.60000000 358.5700000
SS:DUR 2.59098124 2.59278499 2.57287157 2.5870851
SS:Power H01 81.74000000 80.99000000 81.26000000 81.9300000
X9 X10
Subpop.2 Tx. Effect 0.1555556 0.2000000
AD:Sample Size 613.1808000 548.5851200
AD:DUR 1.4905867 1.3082294
AD:Power H0C 87.0900000 89.7500000
AD:Power H01 8.8200000 4.1600000
AD:Power H0C or H01 89.0500000 89.8500000
SC:Sample Size 340.7900000 303.8172000
SC:DUR 0.8114048 0.7233743
SC:Power H0C 93.2800000 98.2300000
SS:Sample Size 356.9500000 358.5400000
SS:DUR 2.5753968 2.5868687
SS:Power H01 82.1300000 81.0000000
interAdapt documentation built on May 2, 2019, 7:31 a.m.
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Description Usage Arguments Details Value References Examples
Description
Generates decision rules for group
sequential trial designs with adaptive enrollment criteria. Tables are
also generated which compare the performance of these designs to the
performance of standard group sequential designs. We use the notation AD to refer to the design with adaptive enrollment, SC to refer to a standard group sequential design enrolling from the combined population, and SS to refer to a standard group sequential design enrolling from only the subpopulation where there is greater prior evidence of a positive treatment effect. Further details are provided in (Fisher et al. 2014).
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | compute_design_performance(p_1 = 0.33, p_10 = 0.25, p_20 = 0.2,
p_11 = p_10 + 0.125, per_stage_sample_size_combined_AD = 280,
per_stage_sample_size_subpop_1_AD = 148, FWER = 0.025,
FWER_H0C_proportion = 0.09, Delta = -0.5, iter = 10000,
time_limit = 45, total_number_stages = 5,
last_stage_subpop_2_enrolled_AD = 3,
enrollment_rate_combined_population = 420,
per_stage_sample_size_combined_SC = 106, per_stage_sample_size_SS = 100,
subpop_2_stop_boundary_constant_AD = 0,
H01_futility_boundary_constant_AD = 0,
H0C_futility_boundary_constant_SC = -0.1,
H01_futility_boundary_constant_SS = -0.1,
lower_bound_treatment_effect_subpop_2 = -0.2,
upper_bound_treatment_effect_subpop_2 = 0.2, CSV)
|
Arguments
p_1 |
The proportion of the population in subpopulation 1, which is the subpopulation having stronger prior evidence of a positive treatment effect. |
p_10 |
The probability of a successful outcome for subpopulation 1 under assignment to the control arm. This is used in estimating power and expected sample size. |
p_20 |
The probability of a successful outcome for subpopulation 2 under assignment to the control arm. This is used in estimating power and expected sample size. |
p_11 |
The probability of a successful outcome for subpopulation 1 under assignment
to the treatment arm. Note that the user does not specify the probability of success under treatment for subpopulation 2 (p_2t).
Instead, |
per_stage_sample_size_combined_AD |
The number of participants enrolled per stage in the adaptive design while both subpopulations are being enrolled. |
per_stage_sample_size_subpop_1_AD |
The number of participants required for each stage in the adaptive design after enrollment for subpopulation 2 has been stopped. |
FWER |
The familywise Type I error rate (α) for all designs (see Fisher et al. 2014). |
FWER_H0C_proportion |
Proportion of α allocated to H_{0C} for the adaptive design. Here, H_{0C} refers to the null hypothesis of no treatment effect in the combined population. |
Delta |
Used as the exponent in defining the efficacy and futility boundaries, as described (Fisher et al. 2014). |
iter |
The number of simulated trials used to estimate the power, expected sample size, and expected trial duration. |
time_limit |
Time limit for simulation in seconds. If the simulation
exceeds the time limit, calculations will stop and the user will get an
error message ("reached CPU time limit"). See |
total_number_stages |
Total number of stages used in each design (K). The maximum allowable number of stages is 20. |
last_stage_subpop_2_enrolled_AD |
The last stage subpopulation 2 is enrolled, under the adaptive design. We refer to this stage number as k*. |
enrollment_rate_combined_population |
The assumed
enrollment rate per year for the combined population. This impacts the
expected duration of each trial design. Active enrollments from
the two subpopulations are assumed to be independent. The enrollment rates
for subpopulations 1 and 2 are assumed proportional, based on |
per_stage_sample_size_combined_SC |
The number of participants enrolled in each stage of the standard group sequential design enrolling the
combined population ( |
per_stage_sample_size_SS |
The number of participants enrolled in each stage for standard group sequential design enrolling only
subpopulation 1 ( |
subpop_2_stop_boundary_constant_AD |
Stopping boundary proportionality constant for subpopulation 2 enrollment in the adaptive design. |
H01_futility_boundary_constant_AD |
Futility boundary proportionality constant for H_{01} in the adaptive design. This is used to calculate the futility boundaries (l_{1,k}) for the z-statistics calculated in subpopulation 1 (Z_{1,k}) as defined in (Fisher et al. 2014). |
H0C_futility_boundary_constant_SC |
Futility boundary proportionality constant for H_{0C} in the standard design always enrolling from the combined population. |
H01_futility_boundary_constant_SS |
Futility boundary proportionality constant for H_{01} in the standard design only enrolling from subpopulation 1. |
lower_bound_treatment_effect_subpop_2 |
Simulations
are performed under a range of treatment effect sizes for
subpopulation 2 (i.e. |
upper_bound_treatment_effect_subpop_2 |
Simulations
are performed under a range of treatment effect sizes for
subpopulation 2 (i.e. |
CSV |
Rather than manually entering the arguments above, this allows for the arguments to be entered via a tabular csv file. The |
Details
This function is meant to be applied when there is prior evidence that a treatment might work better in a one subpopulation than in another. In this context, a trial with an adaptive enrollment criteria would determine whether or not to continue enrolling patients from each subpopulation based on interim analyses of whether each subpopulation is benefiting. In order for the type I error and the power of the trial to be calculable, the decision rules for changing enrollment must be set before the trial starts. This function generates decision rules for group sequential trial designs with adaptive enrollment criteria, and compares the performance of these designs against standard group sequential designs with fixed enrollment criteria. Performance is compared in terms of power, expected sample size, and expected trial duration.
Value
A list with 5 elements:
performance_comparison |
A table comparing the performance of the three trials, in terms of power, expected sample size, and expected duration. See examples. |
AD_design |
Efficacy and futility boundaries for the group sequential design with adaptive enrollment |
SC_design |
Efficacy and futility boundaries for the standard group sequential design enrolling from the combined population |
SS_design |
Efficacy and futility boundaries for the standard group sequential design enrolling subpopulation 1 only |
input_parameters |
List of input argument values |
References
Aaron Fisher, Harris Jaffee, and Michael Rosenblum. interAdapt – An Interactive Tool for Designing and Evaluating Randomized Trials with Adaptive Enrollment Criteria. Working Paper, 2014. http://arxiv.org/abs/1404.0734
Examples
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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 | #Store function output
o<-compute_design_performance()
names(o)
#Decision rules for trial designs
print(o$SS[[1]])
print(o$SC[[1]])
print(o$AD[[1]])
#Plot decision rules
par(mfrow=c(1,3))
matplot(t(o$SS[[1]][2:3,]),type='o',
main='Standard trial - subpop 1',
xlab='stage',ylab='Z-statistic',
col='blue',pch=2:3,lty=3)
legend('topright',c('H01 Efficacy','H01 Futility')
,col='blue',pch=2:3,lty=3)
matplot(t(o$SC[[1]][4:5,]),type='o',
main='Standard trial - combined pop',xlab='stage',
ylab='Z-statistic',col='red',pch=0:1,lty=3)
legend('topright',c('H0C Efficacy','H0C Futility'),
col='red',pch=0:1,lty=3)
matplot(t(o$AD[[1]][4:7,]),type='o',
main='Adaptive Enrollment',xlab='stage',
ylab='Z-statistic',col=c('red','red','blue','blue'),
pch=0:3,lty=3)
legend('topright',c('H0C Efficacy','H0C Futility',
'H01 Efficacy','H01 Futility'),col=c('red',
'red','blue','blue'),pch=0:3,lty=3)
#Check performance
o$performance[[1]]
#Plot performance over a range of treatment effects for subpop2
col1<-c('black','black','black','green','blue')
perform_names<-rownames(o$performance[[1]])
#index for parts of the table corresponding to power
p_ind<- grep('Power',perform_names)
#index for parts of the table corresponding to sample size
s_ind<- grep('Sample Size',perform_names)
#index for parts of the table corresponding to trial duration
d_ind<- grep('DUR',perform_names)
par(mfrow=c(1,3))
lty1<-c(2,3,1,4,5)
matplot(x=t(o$performance[[1]][1,]),t(o$performance[[1]][p_ind,]),
type='l',lty=lty1,col=col1[1:5],xlab='Subpop.2 Tx. Effect',
ylab='Power',main='Power')
legend('bottomleft',perform_names[p_ind],col=col1[1:length(p_ind)],
lty=lty1)
matplot(x=t(o$performance[[1]][1,]),t(o$performance[[1]][s_ind,]),
type='l',lty=1:3,col=col1[3:5],xlab='Subpop.2 Tx. Effect',
ylab='Expected Sample Size',main='Expected Sample Size')
legend('topright',substr(perform_names[d_ind],1,2),col=col1[3:5],
lty=1:3)
matplot(x=t(o$performance[[1]][1,]),t(o$performance[[1]][d_ind,]),
type='l',lty=1:3,col=col1[3:5],xlab='Subpop.2 Tx. Effect',
ylab="Expected Duration",main='Expected Duration')
legend('topright',substr(perform_names[d_ind],1,2),col=col1[3:5],
lty=1:3)
|
Example output
[1] "performance_comparison" "AD_design" "SC_design"
[4] "SS_design" "input_parameters"
1 2
Cumulative Sample Size 100.000000 200.0000000
H01 Efficacy Boundaries for z-statistics Z(1,k) 4.559666 3.2241708
H01 Futility Boundaries for z-statistics Z(1,k) -0.200000 -0.1414214
3 4
Cumulative Sample Size 300.0000000 400.000000
H01 Efficacy Boundaries for z-statistics Z(1,k) 2.6325244 2.279833
H01 Futility Boundaries for z-statistics Z(1,k) -0.1154701 -0.100000
5
Cumulative Sample Size 500.000000
H01 Efficacy Boundaries for z-statistics Z(1,k) 2.039145
H01 Futility Boundaries for z-statistics Z(1,k) 2.039145
1 2
Cumulative Sample Size Subpop. 1 34.980000 69.9600000
Cumulative Sample Size Subpop. 2 71.020000 142.0400000
Cumulative Sample Size Combined Pop. 106.000000 212.0000000
H0C Efficacy Boundaries for z-statistics Z(C,k) 4.559666 3.2241708
H0C Futility Boundaries for z-statistics Z(C,k) -0.200000 -0.1414214
3 4
Cumulative Sample Size Subpop. 1 104.9400000 139.920000
Cumulative Sample Size Subpop. 2 213.0600000 284.080000
Cumulative Sample Size Combined Pop. 318.0000000 424.000000
H0C Efficacy Boundaries for z-statistics Z(C,k) 2.6325244 2.279833
H0C Futility Boundaries for z-statistics Z(C,k) -0.1154701 -0.100000
5
Cumulative Sample Size Subpop. 1 174.900000
Cumulative Sample Size Subpop. 2 355.100000
Cumulative Sample Size Combined Pop. 530.000000
H0C Efficacy Boundaries for z-statistics Z(C,k) 2.039145
H0C Futility Boundaries for z-statistics Z(C,k) 2.039145
1 2
Cumulative Sample Size Subpop. 1 92.400000 184.800000
Cumulative Sample Size Subpop. 2 187.600000 375.200000
Cumulative Sample Size Combined Pop. 280.000000 560.000000
H0C Efficacy Boundaries u(C,k) for z-statistics Z(C,k) 4.956000 3.504421
Boundaries l(2,k) for Z(2,k) to Stop Subpop. 2 Enrollment 0.000000 0.000000
H01 Efficacy Boundaries u(1,k) for Z(1,k) 5.101976 3.607642
Boundaries l(1,k) for Z(1,k) to Stop All Enrollment 0.000000 0.000000
3 4
Cumulative Sample Size Subpop. 1 277.200000 425.200000
Cumulative Sample Size Subpop. 2 562.800000 562.800000
Cumulative Sample Size Combined Pop. 840.000000 988.000000
H0C Efficacy Boundaries u(C,k) for z-statistics Z(C,k) 2.861348 NA
Boundaries l(2,k) for Z(2,k) to Stop Subpop. 2 Enrollment Inf NA
H01 Efficacy Boundaries u(1,k) for Z(1,k) 2.945628 2.378361
Boundaries l(1,k) for Z(1,k) to Stop All Enrollment 0.000000 0.000000
5
Cumulative Sample Size Subpop. 1 573.200000
Cumulative Sample Size Subpop. 2 562.800000
Cumulative Sample Size Combined Pop. 1136.000000
H0C Efficacy Boundaries u(C,k) for z-statistics Z(C,k) NA
Boundaries l(2,k) for Z(2,k) to Stop Subpop. 2 Enrollment NA
H01 Efficacy Boundaries u(1,k) for Z(1,k) 2.048431
Boundaries l(1,k) for Z(1,k) to Stop All Enrollment 2.048431
X1 X2 X3 X4
Subpop.2 Tx. Effect -0.2000000 -0.1555556 -0.1111111 -0.06666667
AD:Sample Size 573.9080000 578.3858800 577.8755600 598.50564000
AD:DUR 2.7872150 2.8192522 2.7956733 2.80145079
AD:Power H0C 0.0000000 0.0000000 0.0000000 0.04000000
AD:Power H01 81.5800000 82.2600000 81.4700000 82.39000000
AD:Power H0C or H01 81.5800000 82.2600000 81.4700000 82.39000000
SC:Sample Size 123.6384000 149.5024000 203.7214000 282.57480000
SC:DUR 0.2943771 0.3559581 0.4850510 0.67279714
SC:Power H0C 0.0000000 0.0300000 0.2000000 1.84000000
SS:Sample Size 358.7300000 357.0100000 358.0500000 356.70000000
SS:DUR 2.5882395 2.5758297 2.5833333 2.57359307
SS:Power H01 82.0700000 81.8400000 81.6700000 80.82000000
X5 X6 X7 X8
Subpop.2 Tx. Effect -0.02222222 0.02222222 0.06666667 0.1111111
AD:Sample Size 666.04960000 760.70988000 778.39300000 703.1972000
AD:DUR 2.79216883 2.71581010 2.36965657 1.8502638
AD:Power H0C 1.52000000 13.61000000 43.45000000 73.8000000
AD:Power H01 81.13000000 75.30000000 52.97000000 23.9300000
AD:Power H0C or H01 81.49000000 82.15000000 83.65000000 86.1700000
SC:Sample Size 351.88820000 401.36900000 408.54520000 381.9922000
SC:DUR 0.83782905 0.95564048 0.97272667 0.9095052
SC:Power H0C 10.03000000 30.00000000 57.14000000 80.3700000
SS:Sample Size 359.11000000 359.36000000 356.60000000 358.5700000
SS:DUR 2.59098124 2.59278499 2.57287157 2.5870851
SS:Power H01 81.74000000 80.99000000 81.26000000 81.9300000
X9 X10
Subpop.2 Tx. Effect 0.1555556 0.2000000
AD:Sample Size 613.1808000 548.5851200
AD:DUR 1.4905867 1.3082294
AD:Power H0C 87.0900000 89.7500000
AD:Power H01 8.8200000 4.1600000
AD:Power H0C or H01 89.0500000 89.8500000
SC:Sample Size 340.7900000 303.8172000
SC:DUR 0.8114048 0.7233743
SC:Power H0C 93.2800000 98.2300000
SS:Sample Size 356.9500000 358.5400000
SS:DUR 2.5753968 2.5868687
SS:Power H01 82.1300000 81.0000000
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