getCP: Conditional Power Allowing for Varying Parameter Values
In lrstat: Power and Sample Size Calculation for Non-Proportional Hazards and Beyond
getCP R Documentation
Conditional Power Allowing for Varying Parameter Values
Description
Obtains the conditional power for specified incremental
information given the interim results, parameter values, and
data-dependent changes in the error spending function, as well as the
number and spacing of interim looks.
Usage
getCP(
INew = NA_real_,
L = NA_integer_,
zL = NA_real_,
theta = NA_real_,
IMax = NA_real_,
kMax = NA_integer_,
informationRates = NA_real_,
efficacyStopping = NA_integer_,
futilityStopping = NA_integer_,
criticalValues = NA_real_,
alpha = 0.025,
typeAlphaSpending = "sfOF",
parameterAlphaSpending = NA_real_,
userAlphaSpending = NA_real_,
futilityBounds = NA_real_,
typeBetaSpending = "none",
parameterBetaSpending = NA_real_,
spendingTime = NA_real_,
MullerSchafer = 0L,
kNew = NA_integer_,
informationRatesNew = NA_real_,
efficacyStoppingNew = NA_integer_,
futilityStoppingNew = NA_integer_,
typeAlphaSpendingNew = "sfOF",
parameterAlphaSpendingNew = NA_real_,
typeBetaSpendingNew = "none",
parameterBetaSpendingNew = NA_real_,
spendingTimeNew = NA_real_,
varianceRatio = 1
)
Arguments
INew
The maximum information of the secondary trial.
L
The interim adaptation look of the primary trial.
zL
The z-test statistic at the interim adaptation look of
the primary trial.
theta
A scalar or a vector of parameter values of
length kMax + kMax - L if MullerSchafer = FALSE or
length kMax + kNew if MullerSchafer = TRUE.
IMax
The maximum information of the primary trial.
kMax
The maximum number of stages of the primary trial.
informationRates
The information rates of the primary trial.
efficacyStopping
Indicators of whether efficacy stopping is
allowed at each stage of the primary trial. Defaults to true
if left unspecified.
futilityStopping
Indicators of whether futility stopping is
allowed at each stage of the primary trial. Defaults to true
if left unspecified.
criticalValues
The upper boundaries on the z-test statistic scale
for efficacy stopping for the primary trial.
alpha
The significance level of the primary trial.
Defaults to 0.025.
typeAlphaSpending
The type of alpha spending for the primary
trial. One of the following:
"OF" for O'Brien-Fleming boundaries,
"P" for Pocock boundaries,
"WT" for Wang & Tsiatis boundaries,
"sfOF" for O'Brien-Fleming type spending function,
"sfP" for Pocock type spending function,
"sfKD" for Kim & DeMets spending function,
"sfHSD" for Hwang, Shi & DeCani spending function,
"user" for user defined spending, and
"none" for no early efficacy stopping.
Defaults to "sfOF".
parameterAlphaSpending
The parameter value of alpha spending
for the primary trial. Corresponds to Delta for "WT", rho for "sfKD",
and gamma for "sfHSD".
userAlphaSpending
The user defined alpha spending for the primary
trial. Cumulative alpha spent up to each stage.
futilityBounds
The lower boundaries on the z-test statistic scale
for futility stopping for the primary trial. Defaults to
rep(-6, kMax-1) if left unspecified.
typeBetaSpending
The type of beta spending for the primary trial.
One of the following:
"sfOF" for O'Brien-Fleming type spending function,
"sfP" for Pocock type spending function,
"sfKD" for Kim & DeMets spending function,
"sfHSD" for Hwang, Shi & DeCani spending function, and
"none" for no early futility stopping.
Defaults to "none".
parameterBetaSpending
The parameter value of beta spending
for the primary trial. Corresponds to rho for "sfKD",
and gamma for "sfHSD".
spendingTime
The error spending time of the primary trial.
Defaults to missing, in which case, it is the same as
informationRates.
MullerSchafer
Whether to use the Muller and Schafer (2001) method
for trial adaptation.
kNew
The number of looks of the secondary trial.
informationRatesNew
The spacing of looks of the secondary trial.
efficacyStoppingNew
The indicators of whether efficacy stopping is
allowed at each look of the secondary trial. Defaults to true
if left unspecified.
futilityStoppingNew
The indicators of whether futility stopping is
allowed at each look of the secondary trial. Defaults to true
if left unspecified.
typeAlphaSpendingNew
The type of alpha spending for the secondary
trial. One of the following:
"OF" for O'Brien-Fleming boundaries,
"P" for Pocock boundaries,
"WT" for Wang & Tsiatis boundaries,
"sfOF" for O'Brien-Fleming type spending function,
"sfP" for Pocock type spending function,
"sfKD" for Kim & DeMets spending function,
"sfHSD" for Hwang, Shi & DeCani spending function, and
"none" for no early efficacy stopping.
Defaults to "sfOF".
parameterAlphaSpendingNew
The parameter value of alpha spending
for the secondary trial. Corresponds to Delta for "WT", rho for "sfKD",
and gamma for "sfHSD".
typeBetaSpendingNew
The type of beta spending for the secondary
trial. One of the following:
"sfOF" for O'Brien-Fleming type spending function,
"sfP" for Pocock type spending function,
"sfKD" for Kim & DeMets spending function,
"sfHSD" for Hwang, Shi & DeCani spending function, and
"none" for no early futility stopping.
Defaults to "none".
parameterBetaSpendingNew
The parameter value of beta spending
for the secondary trial. Corresponds to rho for "sfKD",
and gamma for "sfHSD".
spendingTimeNew
The error spending time of the secondary trial.
Defaults to missing, in which case, it is the same as
informationRatesNew.
varianceRatio
The ratio of the variance under H0 to the variance
under H1.
Value
The conditional power given the interim results, parameter
values, and data-dependent design changes.
Author(s)
Kaifeng Lu, kaifenglu@gmail.com
References
Cyrus R. Mehta and Stuart J. Pocock.
Adaptive increase in sample size when interim results are promising:
A practical guide with examples.
Stat Med. 2011;30:3267–3284.
See Also
getDesign
Examples
# Conditional power calculation with delayed treatment effect
# Two interim analyses have occurred with 179 and 266 events,
# respectively. The observed hazard ratio at the second interim
# look is 0.81.
trialsdt = as.Date("2020-03-04") # trial start date
iadt = c(as.Date("2022-02-01"), as.Date("2022-11-01")) # interim dates
mo1 = as.numeric(iadt - trialsdt + 1)/30.4375 # interim months
# Assume a piecewise Poisson enrollment process with a 8-month ramp-up
# and 521 patients were enrolled after 17.94 months
N = 521 # total number of patients
Ta = 17.94 # enrollment duration
Ta1 = 8 # assumed end of enrollment ramp-up
enrate = N / (Ta - Ta1/2) # enrollment rate after ramp-up
# Assume a median survival of 16.7 months for the control group, a
# 5-month delay in treatment effect, and a hazard ratio of 0.7 after
# the delay
lam1 = log(2)/16.7 # control group hazard of exponential distribution
t1 = 5 # months of delay in treatment effect
hr = 0.7 # hazard ratio after delay
lam2 = hr*lam1 # treatment group hazard after delay
# Assume an annual dropout rate of 5%
gam = -log(1-0.05)/12 # hazard for dropout
# The original target number of events was 298 and the new target is 335
mo2 <- caltime(
nevents = c(298, 335),
allocationRatioPlanned = 1,
accrualTime = seq(0, Ta1),
accrualIntensity = enrate*seq(1, Ta1+1)/(Ta1+1),
piecewiseSurvivalTime = c(0, t1),
lambda1 = c(lam1, lam2),
lambda2 = c(lam1, lam1),
gamma1 = gam,
gamma2 = gam,
accrualDuration = Ta,
followupTime = 1000)
# expected number of events and average hazard ratios
(lr1 <- lrstat(
time = c(mo1, mo2),
accrualTime = seq(0, Ta1),
accrualIntensity = enrate*seq(1, Ta1+1)/(Ta1+1),
piecewiseSurvivalTime = c(0, t1),
lambda1 = c(lam1, lam2),
lambda2 = c(lam1, lam1),
gamma1 = gam,
gamma2 = gam,
accrualDuration = Ta,
followupTime = 1000,
predictTarget = 3))
hr2 = 0.81 # observed hazard ratio at interim 2
z2 = (-log(hr2))*sqrt(266/4) # corresponding z-test statistic value
# expected mean of -log(HR) at the original looks and the new final look
theta = -log(lr1$HR[c(1,2,3,4)])
# conditional power with sample size increase
getCP(INew = (335 - 266)/4,
L = 2, zL = z2, theta = theta,
IMax = 298/4, kMax = 3,
informationRates = c(179, 266, 298)/298,
alpha = 0.025, typeAlphaSpending = "sfOF")
lrstat documentation built on Oct. 18, 2024, 9:06 a.m.
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| getCP | R Documentation |
Conditional Power Allowing for Varying Parameter Values
Description
Obtains the conditional power for specified incremental information given the interim results, parameter values, and data-dependent changes in the error spending function, as well as the number and spacing of interim looks.
Usage
getCP(
INew = NA_real_,
L = NA_integer_,
zL = NA_real_,
theta = NA_real_,
IMax = NA_real_,
kMax = NA_integer_,
informationRates = NA_real_,
efficacyStopping = NA_integer_,
futilityStopping = NA_integer_,
criticalValues = NA_real_,
alpha = 0.025,
typeAlphaSpending = "sfOF",
parameterAlphaSpending = NA_real_,
userAlphaSpending = NA_real_,
futilityBounds = NA_real_,
typeBetaSpending = "none",
parameterBetaSpending = NA_real_,
spendingTime = NA_real_,
MullerSchafer = 0L,
kNew = NA_integer_,
informationRatesNew = NA_real_,
efficacyStoppingNew = NA_integer_,
futilityStoppingNew = NA_integer_,
typeAlphaSpendingNew = "sfOF",
parameterAlphaSpendingNew = NA_real_,
typeBetaSpendingNew = "none",
parameterBetaSpendingNew = NA_real_,
spendingTimeNew = NA_real_,
varianceRatio = 1
)
Arguments
INew |
The maximum information of the secondary trial. |
L |
The interim adaptation look of the primary trial. |
zL |
The z-test statistic at the interim adaptation look of the primary trial. |
theta |
A scalar or a vector of parameter values of
length |
IMax |
The maximum information of the primary trial. |
kMax |
The maximum number of stages of the primary trial. |
informationRates |
The information rates of the primary trial. |
efficacyStopping |
Indicators of whether efficacy stopping is allowed at each stage of the primary trial. Defaults to true if left unspecified. |
futilityStopping |
Indicators of whether futility stopping is allowed at each stage of the primary trial. Defaults to true if left unspecified. |
criticalValues |
The upper boundaries on the z-test statistic scale for efficacy stopping for the primary trial. |
alpha |
The significance level of the primary trial. Defaults to 0.025. |
typeAlphaSpending |
The type of alpha spending for the primary trial. One of the following: "OF" for O'Brien-Fleming boundaries, "P" for Pocock boundaries, "WT" for Wang & Tsiatis boundaries, "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, "user" for user defined spending, and "none" for no early efficacy stopping. Defaults to "sfOF". |
parameterAlphaSpending |
The parameter value of alpha spending for the primary trial. Corresponds to Delta for "WT", rho for "sfKD", and gamma for "sfHSD". |
userAlphaSpending |
The user defined alpha spending for the primary trial. Cumulative alpha spent up to each stage. |
futilityBounds |
The lower boundaries on the z-test statistic scale
for futility stopping for the primary trial. Defaults to
|
typeBetaSpending |
The type of beta spending for the primary trial. One of the following: "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, and "none" for no early futility stopping. Defaults to "none". |
parameterBetaSpending |
The parameter value of beta spending for the primary trial. Corresponds to rho for "sfKD", and gamma for "sfHSD". |
spendingTime |
The error spending time of the primary trial.
Defaults to missing, in which case, it is the same as
|
MullerSchafer |
Whether to use the Muller and Schafer (2001) method for trial adaptation. |
kNew |
The number of looks of the secondary trial. |
informationRatesNew |
The spacing of looks of the secondary trial. |
efficacyStoppingNew |
The indicators of whether efficacy stopping is allowed at each look of the secondary trial. Defaults to true if left unspecified. |
futilityStoppingNew |
The indicators of whether futility stopping is allowed at each look of the secondary trial. Defaults to true if left unspecified. |
typeAlphaSpendingNew |
The type of alpha spending for the secondary trial. One of the following: "OF" for O'Brien-Fleming boundaries, "P" for Pocock boundaries, "WT" for Wang & Tsiatis boundaries, "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, and "none" for no early efficacy stopping. Defaults to "sfOF". |
parameterAlphaSpendingNew |
The parameter value of alpha spending for the secondary trial. Corresponds to Delta for "WT", rho for "sfKD", and gamma for "sfHSD". |
typeBetaSpendingNew |
The type of beta spending for the secondary trial. One of the following: "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, and "none" for no early futility stopping. Defaults to "none". |
parameterBetaSpendingNew |
The parameter value of beta spending for the secondary trial. Corresponds to rho for "sfKD", and gamma for "sfHSD". |
spendingTimeNew |
The error spending time of the secondary trial.
Defaults to missing, in which case, it is the same as
|
varianceRatio |
The ratio of the variance under H0 to the variance under H1. |
Value
The conditional power given the interim results, parameter values, and data-dependent design changes.
Author(s)
Kaifeng Lu, kaifenglu@gmail.com
References
Cyrus R. Mehta and Stuart J. Pocock. Adaptive increase in sample size when interim results are promising: A practical guide with examples. Stat Med. 2011;30:3267–3284.
See Also
getDesign
Examples
# Conditional power calculation with delayed treatment effect
# Two interim analyses have occurred with 179 and 266 events,
# respectively. The observed hazard ratio at the second interim
# look is 0.81.
trialsdt = as.Date("2020-03-04") # trial start date
iadt = c(as.Date("2022-02-01"), as.Date("2022-11-01")) # interim dates
mo1 = as.numeric(iadt - trialsdt + 1)/30.4375 # interim months
# Assume a piecewise Poisson enrollment process with a 8-month ramp-up
# and 521 patients were enrolled after 17.94 months
N = 521 # total number of patients
Ta = 17.94 # enrollment duration
Ta1 = 8 # assumed end of enrollment ramp-up
enrate = N / (Ta - Ta1/2) # enrollment rate after ramp-up
# Assume a median survival of 16.7 months for the control group, a
# 5-month delay in treatment effect, and a hazard ratio of 0.7 after
# the delay
lam1 = log(2)/16.7 # control group hazard of exponential distribution
t1 = 5 # months of delay in treatment effect
hr = 0.7 # hazard ratio after delay
lam2 = hr*lam1 # treatment group hazard after delay
# Assume an annual dropout rate of 5%
gam = -log(1-0.05)/12 # hazard for dropout
# The original target number of events was 298 and the new target is 335
mo2 <- caltime(
nevents = c(298, 335),
allocationRatioPlanned = 1,
accrualTime = seq(0, Ta1),
accrualIntensity = enrate*seq(1, Ta1+1)/(Ta1+1),
piecewiseSurvivalTime = c(0, t1),
lambda1 = c(lam1, lam2),
lambda2 = c(lam1, lam1),
gamma1 = gam,
gamma2 = gam,
accrualDuration = Ta,
followupTime = 1000)
# expected number of events and average hazard ratios
(lr1 <- lrstat(
time = c(mo1, mo2),
accrualTime = seq(0, Ta1),
accrualIntensity = enrate*seq(1, Ta1+1)/(Ta1+1),
piecewiseSurvivalTime = c(0, t1),
lambda1 = c(lam1, lam2),
lambda2 = c(lam1, lam1),
gamma1 = gam,
gamma2 = gam,
accrualDuration = Ta,
followupTime = 1000,
predictTarget = 3))
hr2 = 0.81 # observed hazard ratio at interim 2
z2 = (-log(hr2))*sqrt(266/4) # corresponding z-test statistic value
# expected mean of -log(HR) at the original looks and the new final look
theta = -log(lr1$HR[c(1,2,3,4)])
# conditional power with sample size increase
getCP(INew = (335 - 266)/4,
L = 2, zL = z2, theta = theta,
IMax = 298/4, kMax = 3,
informationRates = c(179, 266, 298)/298,
alpha = 0.025, typeAlphaSpending = "sfOF")
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