rpact (version 2.0.6)

getSampleSizeSurvival: Get Sample Size Survival

Description

Returns the sample size for testing the hazard ratio in a two treatment groups survival design.

Usage

getSampleSizeSurvival(
  design = NULL,
  ...,
  typeOfComputation = c("Schoenfeld", "Freedman", "HsiehFreedman"),
  thetaH0 = C_THETA_H0_SURVIVAL_DEFAULT,
  pi1 = NA_real_,
  pi2 = NA_real_,
  lambda1 = NA_real_,
  lambda2 = NA_real_,
  median1 = NA_real_,
  median2 = NA_real_,
  kappa = 1,
  hazardRatio = NA_real_,
  piecewiseSurvivalTime = NA_real_,
  allocationRatioPlanned = NA_real_,
  accountForObservationTimes = TRUE,
  eventTime = C_EVENT_TIME_DEFAULT,
  accrualTime = C_ACCRUAL_TIME_DEFAULT,
  accrualIntensity = C_ACCRUAL_INTENSITY_DEFAULT,
  followUpTime = NA_real_,
  maxNumberOfSubjects = NA_real_,
  dropoutRate1 = C_DROP_OUT_RATE_1_DEFAULT,
  dropoutRate2 = C_DROP_OUT_RATE_2_DEFAULT,
  dropoutTime = C_DROP_OUT_TIME_DEFAULT
)

Arguments

design

The trial design. If no trial design is specified, a fixed sample size design is used. In this case, alpha, beta, twoSidedPower, and sided can be directly entered as argument.

...

Ensures that all arguments are be named and that a warning will be displayed if unknown arguments are passed.

typeOfComputation

Three options are available: "Schoenfeld", "Freedman", "HsiehFreedman", the default is "Schoenfeld". For details, see Hsieh (Statistics in Medicine, 1992). For non-inferiority testing (i.e., thetaH0 != 1), only Schoenfelds formula can be used

thetaH0

The null hypothesis value. The default value is 1. For one-sided testing, a bound for testing H0: hazard ratio = thetaH0 != 1 can be specified.

pi1

The assumed event rate in the active treatment group, default is seq(0.4,0.6,0.1).

pi2

The assumed event rate in the control group, default is 0.2.

lambda1

The assumed hazard rate in the treatment group, there is no default. lambda1 can also be used to define piecewise exponentially distributed survival times (see details).

lambda2

The assumed hazard rate in the reference group, there is no default. lambda2 can also be used to define piecewise exponentially distributed survival times (see details).

median1

The assumed median survival time in the treatment group, there is no default.

median2

The assumed median survival time in the reference group, there is no default.

kappa

The shape parameter of the Weibull distribution, default is 1. The Weibull distribution cannot be used for the piecewise definition of the survival time distribution. Note that the parameters shape and scale in Weibull are equivalent to kappa and 1 / lambda, respectively, in rpact.

hazardRatio

The vector of hazard ratios under consideration. If the event or hazard rates in both treatment groups are defined, the hazard ratio needs not to be specified as it is calculated.

piecewiseSurvivalTime

A vector that specifies the time intervals for the piecewise definition of the exponential survival time cumulative distribution function (see details).

allocationRatioPlanned

The planned allocation ratio, default is 1. If allocationRatioPlanned = 0 is entered, the optimal allocation ratio yielding the smallest number of subjects is determined.

accountForObservationTimes

If accountForObservationTimes = TRUE, the number of subjects is calculated assuming specific accrual and follow-up time, default is TRUE (see details).

eventTime

The assumed time under which the event rates are calculated, default is 12.

accrualTime

The assumed accrual time intervals for the study, default is c(0,12) (see details).

accrualIntensity

A vector of accrual intensities, default is the relative intensity 0.1 (see details).

followUpTime

The assumed (additional) follow-up time for the study, default is 6. The total study duration is accrualTime + followUpTime.

maxNumberOfSubjects

If maxNumberOfSubjects > 0 is specified, the follow-up time for the required number of events is determined.

dropoutRate1

The assumed drop-out rate in the treatment group, default is 0.

dropoutRate2

The assumed drop-out rate in the control group, default is 0.

dropoutTime

The assumed time for drop-out rates in the control and the treatment group, default is 12.

Value

Returns a TrialDesignPlanSurvival object.

Details

At given design the function calculates the number of events and an estimate for the necessary number of subjects for testing the hazard ratio in a survival design. It also calculates the time when the required events are expected under the given assumptions (exponentially, piecewise exponentially, or Weibull distributed survival times and constant or non-constant piecewise accrual). Additionally, an allocation ratio = n1/n2 can be specified where n1 and n2 are the number of subjects in the two treatment groups.

The formula of Kim & Tsiatis (Biometrics, 1990) is used to calculate the expected number of events under the alternative (see also Lakatos & Lan, Statistics in Medicine, 1992). These formulas are generalized to piecewise survival times and non-constant piecewise accrual over time. If accountForObservationTimes = FALSE, only the event rates are used for the calculation of the maximum number of subjects.

piecewiseSurvivalTime The first element of this vector must be equal to 0. piecewiseSurvivalTime can also be a list that combines the definition of the time intervals and hazard rates in the reference group. The definition of the survival time in the treatment group is obtained by the specification of the hazard ratio (see examples for details).

accrualTime can also be used to define a non-constant accrual over time. For this, accrualTime needs to be a vector that defines the accrual intervals and accrualIntensity needs to be specified. The first element of accrualTime must be equal to 0. accrualTime can also be a list that combines the definition of the accrual time and accrual intensity accrualIntensity (see below and examples for details). If the length of accrualTime and the length of accrualIntensity are the same (i.e., the end of accrual is undefined), maxNumberOfSubjects > 0 needs to be specified and the end of accrual is calculated.

accrualIntensity needs to be defined if a vector of accrualTime is specified. If the length of accrualTime and the length of accrualIntensity are the same (i.e., the end of accrual is undefined), maxNumberOfSubjects > 0 needs to be specified and the end of accrual is calculated. In that case, accrualIntensity is given by the number of subjects per time unit. If the length of accrualTime equals the length of accrualIntensity - 1 (i.e., the end of accrual is defined), maxNumberOfSubjects is calculated. If all elements in accrualIntensity are smaller than 1, accrualIntensity defines the *relative* intensity how subjects enter the trial, and maxNumberOfSubjects must be given or can be calculated at given follow-up time. For example, accrualIntensity = c(0.1, 0.2) specifies that in the second accrual interval the intensity is doubled as compared to the first accrual interval. The actual accrual intensity is calculated for the given (or calculated) maxNumberOfSubjects. Note that the default is accrualIntensity = 0.1 meaning that the *absolute* accrual intensity will be calculated.

accountForObservationTime can be selected as FALSE. In this case, the number of subjects is calculated from the event probabilities only. This kind of computation does not account for the specific accrual pattern and survival distribution.

Examples

# NOT RUN {
# Fixed sample size trial with median survival 20 vs. 30 months in treatment and 
# reference group, respectively, alpha = 0.05 (two-sided), and power 1 - beta = 90%.
# 20 subjects will be recruited per month up to 400 subjects, i.e., accrual time is 20 months.  
getSampleSizeSurvival(alpha = 0.05, sided = 2, beta = 0.1, lambda1 = log(2) / 20, 
    lambda2 = log(2) / 30, accrualTime = c(0,20), accrualIntensity = 20)

# }
# NOT RUN {
# Fixed sample size with minimum required definitions, pi1 = c(0.4,0.5,0.6) and 
# pi2 = 0.2 at event time 12, accrual time 12 and follow-up time 6 as default, 
# only alpha = 0.01 is specified  
getSampleSizeSurvival(alpha = 0.01)

# Four stage O'Brien & Fleming group sequential design with minimum required 
# definitions, pi1 = c(0.4,0.5,0.6) and pi2 = 0.2 at event time 12, 
# accrual time 12 and follow-up time 6 as default  
getSampleSizeSurvival(design = getDesignGroupSequential(kMax = 4))

# For fixed sample design, determine necessary accrual time if 200 subjects and 
# 30 subjects per time unit can be recruited 
getSampleSizeSurvival(accrualTime = c(0), accrualIntensity = c(30), 
	   maxNumberOfSubjects = 200)

# Determine necessary accrual time if 200 subjects and if the first 6 time units 
# 20 subjects per time unit can be recruited, then 30 subjects per time unit 
getSampleSizeSurvival(accrualTime = c(0, 6), accrualIntensity = c(20, 30), 
	   maxNumberOfSubjects = 200)

# Determine maximum number of Subjects if the first 6 time units 20 subjects 
# per time unit can be recruited, and after 10 time units 30 subjects per time unit
getSampleSizeSurvival(accrualTime = c(0, 6, 10), accrualIntensity = c(20, 30))

# Specify accrual time as a list
at <- list(
    "0 - <6"  = 20,
    "6 - Inf" = 30)
getSampleSizeSurvival(accrualTime = at, maxNumberOfSubjects = 200)

# Specify accrual time as a list, if maximum number of subjects need to be calculated
at <- list(
    "0 - <6"   = 20,
    "6 - <=10" = 30)
getSampleSizeSurvival(accrualTime = at)

# Specify effect size for a two-stage group design with O'Brien & Fleming boundaries
# Effect size is based on event rates at specified event time 
# needs to be specified because it should be shown that hazard ratio < 1
getSampleSizeSurvival(design = getDesignGroupSequential(kMax = 2), 
	   pi1 = 0.2, pi2 = 0.3, eventTime = 24)

# Effect size is based on event rate at specified event 
# time for the reference group and hazard ratio 
getSampleSizeSurvival(design = getDesignGroupSequential(kMax = 2), 
	   hazardRatio = 0.5, pi2 = 0.3, eventTime = 24)

# Effect size is based on hazard rate for the reference group and hazard ratio
getSampleSizeSurvival(design = getDesignGroupSequential(kMax = 2), 
	   hazardRatio = 0.5, lambda2 = 0.02) 

# Specification of piecewise exponential survival time and hazard ratios  
getSampleSizeSurvival(design = getDesignGroupSequential(kMax = 2), 
	   piecewiseSurvivalTime = c(0, 5, 10), lambda2 = c(0.01, 0.02, 0.04), 
	   hazardRatio = c(1.5, 1.8, 2))

# Specification of piecewise exponential survival time as a list and hazard ratios 
pws <- list(
    "0 - <5"  = 0.01,	
    "5 - <10" = 0.02,	
    ">=10"    = 0.04)
getSampleSizeSurvival(design = getDesignGroupSequential(kMax = 2), 
	   piecewiseSurvivalTime = pws, hazardRatio = c(1.5, 1.8, 2))

# Specification of piecewise exponential survival time for both treatment arms
getSampleSizeSurvival(design = getDesignGroupSequential(kMax = 2), 
	   piecewiseSurvivalTime = c(0, 5, 10), lambda2 = c(0.01, 0.02, 0.04), 
	   lambda1 = c(0.015, 0.03, 0.06))

# Specification of piecewise exponential survival time as a list
pws <- list(
    "0 - <5"  = 0.01,
    "5 - <10" = 0.02,
    ">=10"    = 0.04)
getSampleSizeSurvival(design = getDesignGroupSequential(kMax = 2), 
	   piecewiseSurvivalTime = pws, hazardRatio = c(1.5, 1.8, 2))

# Specify effect size based on median survival times
getSampleSizeSurvival(median1 = 5, median2 = 3)

# Specify effect size based on median survival times of Weibull distribtion with kappa = 2
getSampleSizeSurvival(median1 = 5, median2 = 3, kappa = 2)

# Identify minimal and maximal required subjects to 
# reach the required events in spite of dropouts
getSampleSizeSurvival(accrualTime = c(0, 18), accrualIntensity = c(20, 30), 
    lambda2 = 0.4, lambda1 = 0.3, followUpTime = Inf, dropoutRate1 = 0.001, 
    dropoutRate2 = 0.005)
getSampleSizeSurvival(accrualTime = c(0, 18), accrualIntensity = c(20, 30), 
    lambda2 = 0.4, lambda1 = 0.3, followUpTime = 0, dropoutRate1 = 0.001, 
    dropoutRate2 = 0.005)

# }
# NOT RUN {
# }