Defining Accrual Time and Accrual Intensity with rpact

Utilities
Survival
This document provides a technical overview on the different alternatives to define accrual time and accrual intensity with rpact.
Author

Friedrich Pahlke Gernot Wassmer

Published

February 18, 2025

Load the rpact package

library(rpact)
packageVersion("rpact") # version should be version 3.0 or later
[1] '4.1.1.9280'

Case 1

End of accrual, absolute accrual intensity and maxNumberOfSubjects are given, followUpTime shall be calculated. From 0 time units (which is always the start of accrual) to 6 time units, 22 subjects are recruited per time unit and from 6 to 30 time units, 33 subjects are recruited per time unit, yielding 924 total subjects.

Example: vector-based definition

accrualTime <- getAccrualTime(
    accrualTime = c(0, 6, 30),
    accrualIntensity = c(22, 33), 
    maxNumberOfSubjects = 924
)
accrualTime

Accrual time and intensity

  • 0 - < 6: 22
  • 6 - <=30: 33

Formula

  • maxNumberOfSubjects = 924 = 6 * 22 + 24 * 33

Case (#1)

  • End of accrual, absolute accrual intensity and ‘maxNumberOfSubjects’ are given, ‘followUpTime’** shall be calculated.
  • Example: getAccrualTime(accrualTime = c(0, 6, 30), accrualIntensity = c(22, 33), maxNumberOfSubjects = 924)
  • (*) Can be calculated directly.
  • (**) Cannot be calculated directly but with ‘getSampleSizeSurvival()’ or ‘getPowerSurvival()’.

Details

User defined parameters

  • Accrual time: 0.00, 6.00, 30.00
  • Accrual intensity: 22.0, 33.0
  • Maximum number of subjects: 924

Generated parameters

  • End of accrual is user defined: TRUE
  • Follow-up time must be user defined: FALSE
  • Max number of subjects is user defined: TRUE
  • Max number of subjects can be calculated directly: TRUE
  • Absolute accrual intensity is enabled: TRUE

Example: list-based definition

accrualTime <- getAccrualTime(
    list(
        "0 - <6" = 22,
        "6 - <= 30" = 33
    ),
    maxNumberOfSubjects = 924
)
accrualTime

Accrual time and intensity

  • 0 - < 6: 22
  • 6 - <=30: 33

Formula

  • maxNumberOfSubjects = 924 = 6 * 22 + 24 * 33

Case (#1)

  • End of accrual, absolute accrual intensity and ‘maxNumberOfSubjects’ are given, ‘followUpTime’** shall be calculated.
  • Example: getAccrualTime(accrualTime = c(0, 6, 30), accrualIntensity = c(22, 33), maxNumberOfSubjects = 924)
  • (*) Can be calculated directly.
  • (**) Cannot be calculated directly but with ‘getSampleSizeSurvival()’ or ‘getPowerSurvival()’.

Details

User defined parameters

  • Accrual time: 0.00, 6.00, 30.00
  • Accrual intensity: 22.0, 33.0
  • Maximum number of subjects: 924

Generated parameters

  • End of accrual is user defined: TRUE
  • Follow-up time must be user defined: FALSE
  • Max number of subjects is user defined: TRUE
  • Max number of subjects can be calculated directly: TRUE
  • Absolute accrual intensity is enabled: TRUE

Example: how to use accrual time object

getSampleSizeSurvival(
  accrualTime = accrualTime, 
  pi1 = 0.23, 
  pi2 = 0.3
)

Design plan parameters and output for survival data

Design parameters

  • Critical values: 1.960
  • Significance level: 0.0250
  • Type II error rate: 0.2000
  • Test: one-sided

User defined parameters

  • Assumed treatment rate: 0.230
  • Assumed control rate: 0.300
  • Maximum number of subjects: 924
  • Accrual time: 6.00, 30.00
  • Accrual intensity: 22.0, 33.0

Default parameters

  • Theta H0: 1
  • Type of computation: Schoenfeld
  • Planned allocation ratio: 1
  • Event time: 12
  • kappa: 1
  • Drop-out rate (1): 0.000
  • Drop-out rate (2): 0.000
  • Drop-out time: 12.00

Sample size and output

  • Direction upper: FALSE
  • median(1): 31.8
  • median(2): 23.3
  • lambda(1): 0.0218
  • lambda(2): 0.0297
  • Hazard ratio: 0.733
  • Number of events: 324.8
  • Total accrual time: 30.00
  • Follow up time: 3.66
  • Number of events fixed: 324.8
  • Number of subjects fixed: 924
  • Number of subjects fixed (1): 462
  • Number of subjects fixed (2): 462
  • Analysis time: 33.66
  • Study duration: 33.66
  • Critical values (treatment effect scale): 0.805

Legend

  • (i): values of treatment arm i

Case 2

End of accrual, relative accrual intensity and maxNumberOfSubjects are given, absolute accrual intensity and followUpTime shall be calculated. The use of relative accrual intensities is indicated by all entries of the vector accrualIntensity being smaller than 1. In this example, the accrual intensity from 6 to 30 time units should be 50% greater than the intensity from 0 to 6 time units given a maximum number of subjects of 1000.

Example: vector-based definition

accrualTime <- getAccrualTime(
    accrualTime = c(0, 6, 30),
    accrualIntensity = c(0.22, 0.33), 
    maxNumberOfSubjects = 1000
)
accrualTime

Accrual time and intensity

  • 0 - < 6: 23.80952
  • 6 - <=30: 35.71429

Formula

  • maxNumberOfSubjects = 1000 = 6 * 23.8095 + 24 * 35.7143

Case (#2)

  • End of accrual, relative accrual intensity and ‘maxNumberOfSubjects’ are given, absolute accrual intensity* and ‘followUpTime’** shall be calculated.
  • Example: getAccrualTime(accrualTime = c(0, 6, 30), accrualIntensity = c(0.22, 0.33), maxNumberOfSubjects = 1000)
  • (*) Can be calculated directly.
  • (**) Cannot be calculated directly but with ‘getSampleSizeSurvival()’ or ‘getPowerSurvival()’.

Details

User defined parameters

  • Accrual time: 0.00, 6.00, 30.00
  • Accrual intensity (relative): 0.22, 0.33
  • Maximum number of subjects: 1000

Generated parameters

  • End of accrual is user defined: TRUE
  • Follow-up time must be user defined: FALSE
  • Max number of subjects is user defined: TRUE
  • Max number of subjects can be calculated directly: TRUE
  • Absolute accrual intensity is enabled: FALSE
  • Accrual intensity: 23.8, 35.7
  • Remaining time: 24.00

Example: list-based definition

accrualTime <- getAccrualTime(
    list(
        "0 - <6" = 0.22,
        "6 - <= 30" = 0.33
    ),
    maxNumberOfSubjects = 1000
)
accrualTime

Accrual time and intensity

  • 0 - < 6: 23.80952
  • 6 - <=30: 35.71429

Formula

  • maxNumberOfSubjects = 1000 = 6 * 23.8095 + 24 * 35.7143

Case (#2)

  • End of accrual, relative accrual intensity and ‘maxNumberOfSubjects’ are given, absolute accrual intensity* and ‘followUpTime’** shall be calculated.
  • Example: getAccrualTime(accrualTime = c(0, 6, 30), accrualIntensity = c(0.22, 0.33), maxNumberOfSubjects = 1000)
  • (*) Can be calculated directly.
  • (**) Cannot be calculated directly but with ‘getSampleSizeSurvival()’ or ‘getPowerSurvival()’.

Details

User defined parameters

  • Accrual time: 0.00, 6.00, 30.00
  • Accrual intensity (relative): 0.22, 0.33
  • Maximum number of subjects: 1000

Generated parameters

  • End of accrual is user defined: TRUE
  • Follow-up time must be user defined: FALSE
  • Max number of subjects is user defined: TRUE
  • Max number of subjects can be calculated directly: TRUE
  • Absolute accrual intensity is enabled: FALSE
  • Accrual intensity: 23.8, 35.7
  • Remaining time: 24.00

Example: how to use accrual time object

getSampleSizeSurvival(
  accrualTime = accrualTime, 
  pi1 = 0.23, 
  pi2 = 0.3
)

Design plan parameters and output for survival data

Design parameters

  • Critical values: 1.960
  • Significance level: 0.0250
  • Type II error rate: 0.2000
  • Test: one-sided

User defined parameters

  • Assumed treatment rate: 0.230
  • Assumed control rate: 0.300
  • Maximum number of subjects: 1000
  • Accrual time: 6.00, 30.00

Default parameters

  • Theta H0: 1
  • Type of computation: Schoenfeld
  • Planned allocation ratio: 1
  • Event time: 12
  • kappa: 1
  • Drop-out rate (1): 0.000
  • Drop-out rate (2): 0.000
  • Drop-out time: 12.00

Sample size and output

  • Direction upper: FALSE
  • median(1): 31.8
  • median(2): 23.3
  • lambda(1): 0.0218
  • lambda(2): 0.0297
  • Hazard ratio: 0.733
  • Number of events: 324.8
  • Total accrual time: 30.00
  • Accrual intensity: 23.8, 35.7
  • Follow up time: 2.07
  • Number of events fixed: 324.8
  • Number of subjects fixed: 1000
  • Number of subjects fixed (1): 500
  • Number of subjects fixed (2): 500
  • Analysis time: 32.07
  • Study duration: 32.07
  • Critical values (treatment effect scale): 0.805

Legend

  • (i): values of treatment arm i

Case 3

End of accrual and absolute accrual intensity are given, maxNumberOfSubjects and followUpTime shall be calculated. From 0 to 6 time units, 22 subjects are to be recruited per time unit and from 6 to 30 time units, 33 subjects are to be recruited per time unit.

Example: vector-based definition

accrualTime <- getAccrualTime(
  accrualTime = c(0, 6, 30), 
  accrualIntensity = c(22, 33)
)

Example: list-based definition

accrualTime <- getAccrualTime(list(
    "0 - <6" = 22,
    "6 - <= 30" = 33
))
accrualTime

Accrual time and intensity

  • 0 - < 6: 22
  • 6 - <=30: 33

Formula

  • maxNumberOfSubjects = 924 = 6 * 22 + 24 * 33

Case (#3)

  • End of accrual and absolute accrual intensity are given, ‘maxNumberOfSubjects’* and ‘followUpTime’** shall be calculated.
  • Example: getAccrualTime(accrualTime = c(0, 6, 30), accrualIntensity = c(22, 33))
  • (*) Can be calculated directly.
  • (**) Cannot be calculated directly but with ‘getSampleSizeSurvival()’ or ‘getPowerSurvival()’.

Details

User defined parameters

  • Accrual time: 0.00, 6.00, 30.00
  • Accrual intensity: 22.0, 33.0

Generated parameters

  • End of accrual is user defined: TRUE
  • Follow-up time must be user defined: FALSE
  • Max number of subjects is user defined: FALSE
  • Max number of subjects can be calculated directly: TRUE
  • Absolute accrual intensity is enabled: TRUE
  • Maximum number of subjects: 924
  • Remaining time: 24.00

Example: how to use accrual time object

getSampleSizeSurvival(
  accrualTime = accrualTime, 
  pi1 = 0.23, 
  pi2 = 0.3
)

Design plan parameters and output for survival data

Design parameters

  • Critical values: 1.960
  • Significance level: 0.0250
  • Type II error rate: 0.2000
  • Test: one-sided

User defined parameters

  • Assumed treatment rate: 0.230
  • Assumed control rate: 0.300
  • Accrual time: 6.00, 30.00
  • Accrual intensity: 22.0, 33.0

Default parameters

  • Theta H0: 1
  • Type of computation: Schoenfeld
  • Planned allocation ratio: 1
  • Event time: 12
  • kappa: 1
  • Drop-out rate (1): 0.000
  • Drop-out rate (2): 0.000
  • Drop-out time: 12.00

Sample size and output

  • Direction upper: FALSE
  • median(1): 31.8
  • median(2): 23.3
  • lambda(1): 0.0218
  • lambda(2): 0.0297
  • Hazard ratio: 0.733
  • Maximum number of subjects: 924
  • Number of events: 324.8
  • Total accrual time: 30.00
  • Follow up time: 3.66
  • Number of events fixed: 324.8
  • Number of subjects fixed: 924
  • Number of subjects fixed (1): 462
  • Number of subjects fixed (2): 462
  • Analysis time: 33.66
  • Study duration: 33.66
  • Critical values (treatment effect scale): 0.805

Legend

  • (i): values of treatment arm i

Case 4

End of accrual, relative accrual intensity and followUpTime are given, absolute accrual intensity and maxNumberOfSubjects shall be calculated. As for case 2, the accrual intensity from 6 to 30 time units shall be 50% greater than the accrual intensity from time units 0 to 6, but now, no maximum number of subjects is provided. Note that followUpTime is not provided to the accrual time object, but is specified when calling getSampleSizeSurvival().

Example: vector-based definition

accrualTime <- getAccrualTime(
  accrualTime = c(0, 6, 30), 
  accrualIntensity = c(0.22, 0.33)
)
accrualTime

Accrual time and intensity

  • 0 - < 6: 0.22
  • 6 - <=30: 0.33

Formula

  • maxNumberOfSubjects = 6 * 0.22 * c + 24 * 0.33 * c , where ‘c’ is a constant factor

Case (#4)

  • End of accrual, relative accrual intensity and ‘followUpTime’ are given, absolute accrual intensity** and ‘maxNumberOfSubjects’** shall be calculated.
  • Example: getAccrualTime(accrualTime = c(0, 6, 30), accrualIntensity = c(0.22, 0.33))
  • (*) Can be calculated directly.
  • (**) Cannot be calculated directly but with ‘getSampleSizeSurvival()’ or ‘getPowerSurvival()’.

Details

User defined parameters

  • Accrual time: 0.00, 6.00, 30.00
  • Accrual intensity: 0.22, 0.33

Generated parameters

  • End of accrual is user defined: TRUE
  • Follow-up time must be user defined: FALSE
  • Max number of subjects is user defined: FALSE
  • Max number of subjects can be calculated directly: FALSE
  • Absolute accrual intensity is enabled: FALSE

Example: list-based definition

accrualTime <- getAccrualTime(list(
    "0 - <6" = 0.22,
    "6 - <= 30" = 0.33
))
accrualTime

Accrual time and intensity

  • 0 - < 6: 0.22
  • 6 - <=30: 0.33

Formula

  • maxNumberOfSubjects = 6 * 0.22 * c + 24 * 0.33 * c , where ‘c’ is a constant factor

Case (#4)

  • End of accrual, relative accrual intensity and ‘followUpTime’ are given, absolute accrual intensity** and ‘maxNumberOfSubjects’** shall be calculated.
  • Example: getAccrualTime(accrualTime = c(0, 6, 30), accrualIntensity = c(0.22, 0.33))
  • (*) Can be calculated directly.
  • (**) Cannot be calculated directly but with ‘getSampleSizeSurvival()’ or ‘getPowerSurvival()’.

Details

User defined parameters

  • Accrual time: 0.00, 6.00, 30.00
  • Accrual intensity: 0.22, 0.33

Generated parameters

  • End of accrual is user defined: TRUE
  • Follow-up time must be user defined: FALSE
  • Max number of subjects is user defined: FALSE
  • Max number of subjects can be calculated directly: FALSE
  • Absolute accrual intensity is enabled: FALSE

Example: how to use accrual time object

getSampleSizeSurvival(
  accrualTime = accrualTime, 
  pi1 = 0.23, 
  pi2 = 0.3, 
  followUpTime = 6
)

Design plan parameters and output for survival data

Design parameters

  • Critical values: 1.960
  • Significance level: 0.0250
  • Type II error rate: 0.2000
  • Test: one-sided

User defined parameters

  • Assumed treatment rate: 0.230
  • Assumed control rate: 0.300
  • Accrual time: 6.00, 30.00
  • Accrual intensity (relative): 0.22, 0.33

Default parameters

  • Theta H0: 1
  • Type of computation: Schoenfeld
  • Planned allocation ratio: 1
  • Event time: 12
  • kappa: 1
  • Follow up time: 6.00
  • Drop-out rate (1): 0.000
  • Drop-out rate (2): 0.000
  • Drop-out time: 12.00

Sample size and output

  • Direction upper: FALSE
  • median(1): 31.8
  • median(2): 23.3
  • lambda(1): 0.0218
  • lambda(2): 0.0297
  • Hazard ratio: 0.733
  • Number of events: 324.8
  • Total accrual time: 30.00
  • Accrual intensity: 19.9, 29.8
  • Number of events fixed: 324.8
  • Number of subjects fixed: 834.7
  • Number of subjects fixed (1): 417.4
  • Number of subjects fixed (2): 417.4
  • Analysis time: 36.00
  • Study duration: 36.00
  • Critical values (treatment effect scale): 0.805

Legend

  • (i): values of treatment arm i

Case 5

maxNumberOfSubjects and absolute accrual intensity are given, end of accrual and followUpTime shall be calculated. The calculation of the end of accrual is performed whenever the vectors accrualTime and (absolute) accrualIntensity are of the same length, i.e., the end point of the final accrual interval is not specified. The end of accrual is calculated such that maxNumberOfSubjects is achieved.

Example: vector-based definition

accrualTime <- getAccrualTime(
    accrualTime = c(0, 6),
    accrualIntensity = c(22, 33), 
    maxNumberOfSubjects = 1000
)
accrualTime

Accrual time and intensity

  • 0.00000 - < 6.00000: 22
  • 6.00000 - <=32.30303: 33

Formula

  • maxNumberOfSubjects = 1000 = 6 * 22 + 26.303 * 33

Case (#5)

  • ‘maxNumberOfSubjects’ and absolute accrual intensity are given, end of accrual* and ‘followUpTime’** shall be calculated
  • Example: getAccrualTime(accrualTime = c(0, 6), accrualIntensity = c(22, 33), maxNumberOfSubjects = 1000)
  • (*) Can be calculated directly.
  • (**) Cannot be calculated directly but with ‘getSampleSizeSurvival()’ or ‘getPowerSurvival()’.

Details

User defined parameters

  • Accrual time: 0.00, 6.00, 32.30
  • Accrual intensity: 22.0, 33.0
  • Maximum number of subjects: 1000

Generated parameters

  • End of accrual is user defined: FALSE
  • Follow-up time must be user defined: FALSE
  • Max number of subjects is user defined: TRUE
  • Max number of subjects can be calculated directly: TRUE
  • Absolute accrual intensity is enabled: TRUE
  • Remaining time: 26.30

Example: list-based definition

accrualTime <- getAccrualTime(
    list(
        "0 - <6" = 22,
        "6" = 33
    ),
    maxNumberOfSubjects = 1000
)
accrualTime

Accrual time and intensity

  • 0.00000 - < 6.00000: 22
  • 6.00000 - <=32.30303: 33

Formula

  • maxNumberOfSubjects = 1000 = 6 * 22 + 26.303 * 33

Case (#5)

  • ‘maxNumberOfSubjects’ and absolute accrual intensity are given, end of accrual* and ‘followUpTime’** shall be calculated
  • Example: getAccrualTime(accrualTime = c(0, 6), accrualIntensity = c(22, 33), maxNumberOfSubjects = 1000)
  • (*) Can be calculated directly.
  • (**) Cannot be calculated directly but with ‘getSampleSizeSurvival()’ or ‘getPowerSurvival()’.

Details

User defined parameters

  • Accrual time: 0.00, 6.00, 32.30
  • Accrual intensity: 22.0, 33.0
  • Maximum number of subjects: 1000

Generated parameters

  • End of accrual is user defined: FALSE
  • Follow-up time must be user defined: FALSE
  • Max number of subjects is user defined: TRUE
  • Max number of subjects can be calculated directly: TRUE
  • Absolute accrual intensity is enabled: TRUE
  • Remaining time: 26.30

Example: how to use accrual time object

getSampleSizeSurvival(
  accrualTime = accrualTime, 
  pi1 = 0.23, 
  pi2 = 0.3
)

Design plan parameters and output for survival data

Design parameters

  • Critical values: 1.960
  • Significance level: 0.0250
  • Type II error rate: 0.2000
  • Test: one-sided

User defined parameters

  • Assumed treatment rate: 0.230
  • Assumed control rate: 0.300
  • Maximum number of subjects: 1000
  • Accrual time: 6.00, 32.30
  • Accrual intensity: 22.0, 33.0

Default parameters

  • Theta H0: 1
  • Type of computation: Schoenfeld
  • Planned allocation ratio: 1
  • Event time: 12
  • kappa: 1
  • Drop-out rate (1): 0.000
  • Drop-out rate (2): 0.000
  • Drop-out time: 12.00

Sample size and output

  • Direction upper: FALSE
  • median(1): 31.8
  • median(2): 23.3
  • lambda(1): 0.0218
  • lambda(2): 0.0297
  • Hazard ratio: 0.733
  • Number of events: 324.8
  • Total accrual time: 32.30
  • Follow up time: 1.08
  • Number of events fixed: 324.8
  • Number of subjects fixed: 1000
  • Number of subjects fixed (1): 500
  • Number of subjects fixed (2): 500
  • Analysis time: 33.38
  • Study duration: 33.38
  • Critical values (treatment effect scale): 0.805

Legend

  • (i): values of treatment arm i

Case 6 (not possible)

maxNumberOfSubjects and relative accrual intensity are given, absolute accrual intensity[x], end of accrual and followUpTime shall be calculated.

Example: vector-based definition

accrualTime <- getAccrualTime(
    accrualTime = c(0, 6),
    accrualIntensity = c(0.22, 0.33),
    maxNumberOfSubjects = 1000
)
Warning: The specified accrual time and intensity cannot be supplemented
automatically with the missing information; therefore further calculations are
not possible
accrualTime

Accrual time and intensity

  • 0 - <=6: 0.22

Formula

  • maxNumberOfSubjects = 1000 = 6 * 0.22 * c + (x - 6) * 0.33 * c , where ‘x’ is the unknown last accrual time and ‘c’ a constant factor

Case (#6)

  • ‘maxNumberOfSubjects’ and relative accrual intensity are given, absolute accrual intensity@, end of accrual* and ‘followUpTime’** shall be calculated
  • Example: getAccrualTime(accrualTime = c(0, 6), accrualIntensity = c(0.22, 0.33), maxNumberOfSubjects = 1000)
    1. Cannot be calculated.
  • (*) Can be calculated directly.
  • (**) Cannot be calculated directly but with ‘getSampleSizeSurvival()’ or ‘getPowerSurvival()’.

Details

User defined parameters

  • Accrual time: 0.00, 6.00
  • Accrual intensity: 0.22, 0.33
  • Maximum number of subjects: 1000

Generated parameters

  • End of accrual is user defined: FALSE
  • Follow-up time must be user defined: FALSE
  • Max number of subjects is user defined: TRUE
  • Max number of subjects can be calculated directly: TRUE
  • Absolute accrual intensity is enabled: FALSE

Example: list-based definition

accrualTime <- getAccrualTime(
    list(
        "0 - <6" = 0.22,
        "6" = 0.33
    ),
    maxNumberOfSubjects = 1000
)
accrualTime

Example: how to use accrual time object

Case 6 is not allowed and therefore an error will be shown:

tryCatch(
    {
        getSampleSizeSurvival(accrualTime = accrualTime, pi1 = 0.23, pi2 = 0.3)
    },
    error = function(e) {
        print(e$message)
    }
)
[1] "Illegal argument: the calculation of 'followUpTime' for given 'maxNumberOfSubjects' and relative accrual intensities (< 1) can only be done if end of accrual is defined"

Case 7

followUpTime and absolute accrual intensity are given,
end of accrual and maxNumberOfSubjects shall be calculated. From 0 to 6 time units, 22 subjects are to be recruited per time unit and afterwards, 33 subjects are to be recruited per time unit.

Example: vector-based definition

accrualTime <- getAccrualTime(
  accrualTime = c(0, 6), 
  accrualIntensity = c(22, 33)
)
accrualTime

Accrual time and intensity

  • 0 - <=6: 22
  • 6 - <=[?]: 33

Formula

  • maxNumberOfSubjects = 6 * 22 + (x - 6) * 33, where ‘x’ is the unknown last accrual time

Case (#7)

  • ‘followUpTime’ and absolute accrual intensity are given, end of accrual** and ‘maxNumberOfSubjects’** shall be calculated
  • Example: getAccrualTime(accrualTime = c(0, 6), accrualIntensity = c(22, 33))
  • (*) Can be calculated directly.
  • (**) Cannot be calculated directly but with ‘getSampleSizeSurvival()’ or ‘getPowerSurvival()’.

Details

User defined parameters

  • Accrual time: 0.00, 6.00
  • Accrual intensity: 22.0, 33.0

Generated parameters

  • End of accrual is user defined: FALSE
  • Follow-up time must be user defined: TRUE
  • Max number of subjects is user defined: FALSE
  • Max number of subjects can be calculated directly: FALSE
  • Absolute accrual intensity is enabled: TRUE

Example: list-based definition

accrualTime <- getAccrualTime(list(
    "0 - <6" = 22,
    "6" = 33
))
accrualTime

Accrual time and intensity

  • 0 - <=6: 22
  • 6 - <=[?]: 33

Formula

  • maxNumberOfSubjects = 6 * 22 + (x - 6) * 33, where ‘x’ is the unknown last accrual time

Case (#7)

  • ‘followUpTime’ and absolute accrual intensity are given, end of accrual** and ‘maxNumberOfSubjects’** shall be calculated
  • Example: getAccrualTime(accrualTime = c(0, 6), accrualIntensity = c(22, 33))
  • (*) Can be calculated directly.
  • (**) Cannot be calculated directly but with ‘getSampleSizeSurvival()’ or ‘getPowerSurvival()’.

Details

User defined parameters

  • Accrual time: 0.00, 6.00
  • Accrual intensity: 22.0, 33.0

Generated parameters

  • End of accrual is user defined: FALSE
  • Follow-up time must be user defined: TRUE
  • Max number of subjects is user defined: FALSE
  • Max number of subjects can be calculated directly: FALSE
  • Absolute accrual intensity is enabled: TRUE

Example: how to use accrual time object

getSampleSizeSurvival(
    accrualTime = accrualTime,
    pi1 = 0.4, 
    pi2 = 0.2, 
    followUpTime = 6
)

Design plan parameters and output for survival data

Design parameters

  • Critical values: 1.960
  • Significance level: 0.0250
  • Type II error rate: 0.2000
  • Test: one-sided

User defined parameters

  • Assumed treatment rate: 0.400
  • Accrual intensity: 22.0, 33.0
  • Follow up time: 6.00

Default parameters

  • Theta H0: 1
  • Type of computation: Schoenfeld
  • Assumed control rate: 0.200
  • Planned allocation ratio: 1
  • Event time: 12
  • kappa: 1
  • Drop-out rate (1): 0.000
  • Drop-out rate (2): 0.000
  • Drop-out time: 12.00

Sample size and output

  • Direction upper: TRUE
  • median(1): 16.3
  • median(2): 37.3
  • lambda(1): 0.0426
  • lambda(2): 0.0186
  • Hazard ratio: 2.289
  • Maximum number of subjects: 186.1
  • Number of events: 45.8
  • Accrual time: 6.00, 7.64
  • Total accrual time: 7.64
  • Number of events fixed: 45.8
  • Number of subjects fixed: 186.1
  • Number of subjects fixed (1): 93
  • Number of subjects fixed (2): 93
  • Analysis time: 13.64
  • Study duration: 13.64
  • Critical values (treatment effect scale): 1.785

Legend

  • (i): values of treatment arm i

Case 8 (not possible)

followUpTime and relative accrual intensity are given,
absolute accrual intensity[x], end of accrual and maxNumberOfSubjects shall be calculated.

Example: vector-based definition

accrualTime <- getAccrualTime(
  accrualTime = c(0, 6), 
  accrualIntensity = c(0.22, 0.33)
)
Warning: The specified accrual time and intensity cannot be supplemented
automatically with the missing information; therefore further calculations are
not possible
accrualTime

Accrual time and intensity

  • 0 - <=6: 0.22
  • 6 - <=[?]: 0.33

Formula

  • maxNumberOfSubjects = 6 * 0.22 * c + (x - 6) * 0.33 * c , where ‘x’ is the unknown last accrual time and ‘c’ a constant factor

Case (#8)

  • ‘followUpTime’ and relative accrual intensity are given, absolute accrual intensity@, end of accrual and ‘maxNumberOfSubjects’ shall be calculated
  • Example: getAccrualTime(accrualTime = c(0, 6), accrualIntensity = c(0.22, 0.33))
    1. Cannot be calculated.
  • (*) Can be calculated directly.
  • (**) Cannot be calculated directly but with ‘getSampleSizeSurvival()’ or ‘getPowerSurvival()’.

Details

User defined parameters

  • Accrual time: 0.00, 6.00
  • Accrual intensity: 0.22, 0.33

Generated parameters

  • End of accrual is user defined: FALSE
  • Follow-up time must be user defined: TRUE
  • Max number of subjects is user defined: FALSE
  • Max number of subjects can be calculated directly: FALSE
  • Absolute accrual intensity is enabled: FALSE

Example: list-based definition

accrualTime <- getAccrualTime(list(
    "0 - <6" = 0.22,
    "6" = 0.33
))
Warning: The specified accrual time and intensity cannot be supplemented
automatically with the missing information; therefore further calculations are
not possible
accrualTime

Accrual time and intensity

  • 0 - <=6: 0.22
  • 6 - <=[?]: 0.33

Formula

  • maxNumberOfSubjects = 6 * 0.22 * c + (x - 6) * 0.33 * c , where ‘x’ is the unknown last accrual time and ‘c’ a constant factor

Case (#8)

  • ‘followUpTime’ and relative accrual intensity are given, absolute accrual intensity@, end of accrual and ‘maxNumberOfSubjects’ shall be calculated
  • Example: getAccrualTime(accrualTime = c(0, 6), accrualIntensity = c(0.22, 0.33))
    1. Cannot be calculated.
  • (*) Can be calculated directly.
  • (**) Cannot be calculated directly but with ‘getSampleSizeSurvival()’ or ‘getPowerSurvival()’.

Details

User defined parameters

  • Accrual time: 0.00, 6.00
  • Accrual intensity: 0.22, 0.33

Generated parameters

  • End of accrual is user defined: FALSE
  • Follow-up time must be user defined: TRUE
  • Max number of subjects is user defined: FALSE
  • Max number of subjects can be calculated directly: FALSE
  • Absolute accrual intensity is enabled: FALSE

Example: how to use accrual time object

Case 8 is not allowed and therefore an error will be shown:

tryCatch(
    {
        getSampleSizeSurvival(accrualTime = accrualTime, pi1 = 0.23, pi2 = 0.3, followUpTime = 6)
    },
    error = function(e) {
        print(e$message)
    }
)
[1] "Illegal argument: the calculation of 'maxNumberOfSubjects' for given 'followUpTime' and relative accrual intensities (< 1) can only be done if end of accrual is defined"

How to show accrual time details

You can use a sample size or power object as argument for function getAccrualTime:

sampleSize <- getSampleSizeSurvival(
    accrualTime = c(0, 6), 
    accrualIntensity = c(22, 53),
    lambda2 = 0.05, 
    hazardRatio = 0.8, 
    followUpTime = 6
)
sampleSize

Design plan parameters and output for survival data

Design parameters

  • Critical values: 1.960
  • Significance level: 0.0250
  • Type II error rate: 0.2000
  • Test: one-sided

User defined parameters

  • lambda(2): 0.050
  • Hazard ratio: 0.800
  • Accrual intensity: 22.0, 53.0
  • Follow up time: 6.00

Default parameters

  • Theta H0: 1
  • Type of computation: Schoenfeld
  • Planned allocation ratio: 1
  • kappa: 1
  • Piecewise survival times: 0.00
  • Drop-out rate (1): 0.000
  • Drop-out rate (2): 0.000
  • Drop-out time: 12.00

Sample size and output

  • Direction upper: FALSE
  • median(1): 17.3
  • median(2): 13.9
  • lambda(1): 0.040
  • Maximum number of subjects: 1205.9
  • Number of events: 630.5
  • Accrual time: 6.00, 26.26
  • Total accrual time: 26.26
  • Number of events fixed: 630.5
  • Number of subjects fixed: 1205.9
  • Number of subjects fixed (1): 602.9
  • Number of subjects fixed (2): 602.9
  • Analysis time: 32.26
  • Study duration: 32.26
  • Critical values (treatment effect scale): 0.855

Legend

  • (i): values of treatment arm i
accrualTime <- getAccrualTime(sampleSize)
accrualTime

Accrual time and intensity

  • 0 - <=6: 22
  • 6 - <=[?]: 53

Formula

  • maxNumberOfSubjects = 6 * 22 + (x - 6) * 53, where ‘x’ is the unknown last accrual time

Case (#7)

  • ‘followUpTime’ and absolute accrual intensity are given, end of accrual** and ‘maxNumberOfSubjects’** shall be calculated
  • Example: getAccrualTime(accrualTime = c(0, 6), accrualIntensity = c(22, 33))
  • (*) Can be calculated directly.
  • (**) Cannot be calculated directly but with ‘getSampleSizeSurvival()’ or ‘getPowerSurvival()’.

Details

User defined parameters

  • Accrual time: 0.00, 6.00
  • Accrual intensity: 22.0, 53.0

Generated parameters

  • End of accrual is user defined: FALSE
  • Follow-up time must be user defined: TRUE
  • Max number of subjects is user defined: FALSE
  • Max number of subjects can be calculated directly: FALSE
  • Absolute accrual intensity is enabled: TRUE

System: rpact 4.1.1.9280, R version 4.4.2 (2024-10-31), platform: x86_64-pc-linux-gnu

To cite R in publications use:

R Core Team (2024). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.

To cite package ‘rpact’ in publications use:

Wassmer G, Pahlke F (2025). rpact: Confirmatory Adaptive Clinical Trial Design and Analysis. R package version 4.1.1.9280, commit dd4318fc8bf1b2b9bb09b7830f814871b43bcef8, https://github.com/rpact-com/rpact.