lrstat (version 0.2.13)

getCP: 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
)

Value

The conditional power given the interim results, parameter values, and data-dependent design changes.

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.

Author

Kaifeng Lu,

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")