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Fixed design under non-proportional hazards

Source: R/fixed_design_ahr.R, R/fixed_design_fh.R, R/fixed_design_lf.R, and 5 more
fixed_design.Rd

Computes fixed design sample size (given power) or power (given sample size) by:

  • fixed_design_ahr() - Average hazard ratio method.

  • fixed_design_fh() - Weighted logrank test with Fleming-Harrington weights (Farrington and Manning, 1990).

  • fixed_design_mb() - Weighted logrank test with Magirr-Burman weights.

  • fixed_design_lf() - Lachin-Foulkes method (Lachin and Foulkes, 1986).

  • fixed_design_maxcombo() - MaxCombo method.

  • fixed_design_rmst() - RMST method.

  • fixed_design_milestone() - Milestone method.

Additionally, fixed_design_rd() provides fixed design for binary endpoint with treatment effect measuring in risk difference.

Usage

fixed_design_ahr(
  enroll_rate,
  fail_rate,
  alpha = 0.025,
  power = NULL,
  ratio = 1,
  study_duration = 36,
  event = NULL
)

fixed_design_fh(
  alpha = 0.025,
  power = NULL,
  ratio = 1,
  study_duration = 36,
  enroll_rate,
  fail_rate,
  rho = 0,
  gamma = 0
)

fixed_design_lf(
  alpha = 0.025,
  power = NULL,
  ratio = 1,
  study_duration = 36,
  enroll_rate,
  fail_rate
)

fixed_design_maxcombo(
  alpha = 0.025,
  power = NULL,
  ratio = 1,
  study_duration = 36,
  enroll_rate,
  fail_rate,
  rho = c(0, 0, 1),
  gamma = c(0, 1, 0),
  tau = rep(-1, 3)
)

fixed_design_mb(
  alpha = 0.025,
  power = NULL,
  ratio = 1,
  study_duration = 36,
  enroll_rate,
  fail_rate,
  tau = 6
)

fixed_design_milestone(
  alpha = 0.025,
  power = NULL,
  ratio = 1,
  enroll_rate,
  fail_rate,
  study_duration = 36,
  tau = NULL
)

fixed_design_rd(
  alpha = 0.025,
  power = NULL,
  ratio = 1,
  p_c,
  p_e,
  rd0 = 0,
  n = NULL
)

fixed_design_rmst(
  alpha = 0.025,
  power = NULL,
  ratio = 1,
  study_duration = 36,
  enroll_rate,
  fail_rate,
  tau = NULL
)

Arguments

enroll_rate

Enrollment rates.

fail_rate

Failure and dropout rates.

alpha

One-sided Type I error (strictly between 0 and 1).

power

Power (NULL to compute power or strictly between 0 and 1 - alpha otherwise).

ratio

Experimental:Control randomization ratio.

study_duration

Study duration.

event

Targeted event at each analysis.

rho

A vector of numbers paring with gamma and tau for MaxCombo test.

gamma

A vector of numbers paring with rho and tau for MaxCombo test.

tau

Test parameter in RMST.

p_c

A numerical value of the control arm rate.

p_e

A numerical value of the experimental arm rate.

rd0

Risk difference under null hypothesis, default is 0.

n

Sample size. If NULL with power input, the sample size will be computed to achieve the targeted power

Value

A list of design characteristic summary.

Examples

# AHR method ----
library(dplyr)

# Example 1: given power and compute sample size
x <- fixed_design_ahr(
  alpha = .025, power = .9,
  enroll_rate = define_enroll_rate(duration = 18, rate = 1),
  fail_rate = define_fail_rate(
    duration = c(4, 100),
    fail_rate = log(2) / 12,
    hr = c(1, .6),
    dropout_rate = .001
  ),
  study_duration = 36
)
x %>% summary()
#> # A tibble: 1 × 7
#>   Design                   N Events  Time Bound alpha Power
#>   <chr>                <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Average hazard ratio  463.   325.    36  1.96 0.025   0.9

# Example 2: given sample size and compute power
x <- fixed_design_ahr(
  alpha = .025,
  enroll_rate = define_enroll_rate(duration = 18, rate = 20),
  fail_rate = define_fail_rate(
    duration = c(4, 100),
    fail_rate = log(2) / 12,
    hr = c(1, .6),
    dropout_rate = .001
  ),
  study_duration = 36
)
x %>% summary()
#> # A tibble: 1 × 7
#>   Design                   N Events  Time Bound alpha Power
#>   <chr>                <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Average hazard ratio   360   252.    36  1.96 0.025 0.816

# WLR test with FH weights ----
library(dplyr)

# Example 1: given power and compute sample size
x <- fixed_design_fh(
  alpha = .025, power = .9,
  enroll_rate = define_enroll_rate(duration = 18, rate = 1),
  fail_rate = define_fail_rate(
    duration = c(4, 100),
    fail_rate = log(2) / 12,
    hr = c(1, .6),
    dropout_rate = .001
  ),
  study_duration = 36,
  rho = 1, gamma = 1
)
x %>% summary()
#> # A tibble: 1 × 7
#>   Design                          N Events  Time Bound alpha Power
#>   <chr>                       <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Fleming-Harrington FH(1, 1)  352.   247.    36  1.96 0.025   0.9

# Example 2: given sample size and compute power
x <- fixed_design_fh(
  alpha = .025,
  enroll_rate = define_enroll_rate(duration = 18, rate = 20),
  fail_rate = define_fail_rate(
    duration = c(4, 100),
    fail_rate = log(2) / 12,
    hr = c(1, .6),
    dropout_rate = .001
  ),
  study_duration = 36,
  rho = 1, gamma = 1
)
x %>% summary()
#> # A tibble: 1 × 7
#>   Design                          N Events  Time Bound alpha Power
#>   <chr>                       <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Fleming-Harrington FH(1, 1)   360   252.    36  1.96 0.025 0.906

# LF method ----
library(dplyr)

# Example 1: given power and compute sample size
x <- fixed_design_lf(
  alpha = .025, power = .9,
  enroll_rate = define_enroll_rate(duration = 18, rate = 1),
  fail_rate = define_fail_rate(
    duration = 100,
    fail_rate = log(2) / 12,
    hr = .7,
    dropout_rate = .001
  ),
  study_duration = 36
)
x %>% summary()
#> # A tibble: 1 × 7
#>   Design                 N Events  Time Bound alpha Power
#>   <chr>              <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Lachin and Foulkes  463.   329.    36  1.96 0.025   0.9

# Example 2: given sample size and compute power
x <- fixed_design_fh(
  alpha = .025,
  enroll_rate = define_enroll_rate(duration = 18, rate = 20),
  fail_rate = define_fail_rate(
    duration = 100,
    fail_rate = log(2) / 12,
    hr = .7,
    dropout_rate = .001
  ),
  study_duration = 36
)
x %>% summary()
#> # A tibble: 1 × 7
#>   Design                                    N Events  Time Bound alpha Power
#>   <chr>                                 <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Fleming-Harrington FH(0, 0) (logrank)   360   256.    36  1.96 0.025 0.819

# MaxCombo test ----
library(dplyr)

# Example 1: given power and compute sample size
x <- fixed_design_maxcombo(
  alpha = .025, power = .9,
  enroll_rate = define_enroll_rate(duration = 18, rate = 1),
  fail_rate = define_fail_rate(
    duration = c(4, 100),
    fail_rate = log(2) / 12,
    hr = c(1, .6),
    dropout_rate = .001
  ),
  study_duration = 36,
  rho = c(0, 0.5), gamma = c(0, 0), tau = c(-1, -1)
)
x %>% summary()
#> # A tibble: 1 × 7
#>   Design                            N Events  Time Bound alpha Power
#>   <chr>                         <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 MaxCombo: logrank, FH(0.5, 0)  465.   326.    36  1.96 0.025 0.900

# Example 2: given sample size and compute power
x <- fixed_design_maxcombo(
  alpha = .025,
  enroll_rate = define_enroll_rate(duration = 18, rate = 20),
  fail_rate = define_fail_rate(
    duration = c(4, 100),
    fail_rate = log(2) / 12,
    hr = c(1, .6),
    dropout_rate = .001
  ),
  study_duration = 36,
  rho = c(0, 0.5), gamma = c(0, 0), tau = c(-1, -1)
)
x %>% summary()
#> # A tibble: 1 × 7
#>   Design                            N Events  Time Bound alpha Power
#>   <chr>                         <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 MaxCombo: logrank, FH(0.5, 0)  360.   252.    36  1.96 0.025 0.814

# WLR test with MB weights ----
library(dplyr)

# Example 1: given power and compute sample size
x <- fixed_design_mb(
  alpha = .025, power = .9,
  enroll_rate = define_enroll_rate(duration = 18, rate = 1),
  fail_rate = define_fail_rate(
    duration = c(4, 100),
    fail_rate = log(2) / 12,
    hr = c(1, .6),
    dropout_rate = .001
  ),
  study_duration = 36,
  tau = 4
)
x %>% summary()
#> # A tibble: 1 × 7
#>   Design                            N Events  Time Bound alpha Power
#>   <chr>                         <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Modestly weighted LR: tau = 4  430.   301.    36  1.96 0.025   0.9

# Example 2: given sample size and compute power
x <- fixed_design_mb(
  alpha = .025,
  enroll_rate = define_enroll_rate(duration = 18, rate = 20),
  fail_rate = define_fail_rate(
    duration = c(4, 100),
    fail_rate = log(2) / 12,
    hr = c(1, .6),
    dropout_rate = .001
  ),
  study_duration = 36,
  tau = 4
)
x %>% summary()
#> # A tibble: 1 × 7
#>   Design                            N Events  Time Bound alpha Power
#>   <chr>                         <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Modestly weighted LR: tau = 4   360   252.    36  1.96 0.025 0.844

# Milestone method ----
library(dplyr)

# Example 1: given power and compute sample size
x <- fixed_design_milestone(
  alpha = .025, power = .9,
  enroll_rate = define_enroll_rate(duration = 18, rate = 1),
  fail_rate = define_fail_rate(
    duration = 100,
    fail_rate = log(2) / 12,
    hr = .7,
    dropout_rate = .001
  ),
  study_duration = 36,
  tau = 18
)
x %>% summary()
#> # A tibble: 1 × 7
#>   Design                  N Events  Time Bound alpha Power
#>   <chr>               <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Milestone: tau = 18  606.   431.    36  1.96 0.025   0.9

# Example 2: given sample size and compute power
x <- fixed_design_milestone(
  alpha = .025,
  enroll_rate = define_enroll_rate(duration = 18, rate = 20),
  fail_rate = define_fail_rate(
    duration = 100,
    fail_rate = log(2) / 12,
    hr = .7,
    dropout_rate = .001
  ),
  study_duration = 36,
  tau = 18
)
x %>% summary()
#> # A tibble: 1 × 7
#>   Design                  N Events  Time Bound alpha Power
#>   <chr>               <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Milestone: tau = 18   360   256.    36  1.96 0.025 0.705

# Binary endpoint with risk differences ----
library(dplyr)

# Example 1: given power and compute sample size
x <- fixed_design_rd(
  alpha = 0.025, power = 0.9, p_c = .15, p_e = .1,
  rd0 = 0, ratio = 1
)
x %>% summary()
#> # A tibble: 1 × 5
#>   Design              N Bound alpha Power
#>   <chr>           <dbl> <dbl> <dbl> <dbl>
#> 1 Risk difference 1845.  1.96 0.025   0.9

# Example 2: given sample size and compute power
x <- fixed_design_rd(
  alpha = 0.025, power = NULL, p_c = .15, p_e = .1,
  rd0 = 0, n = 2000, ratio = 1
)
x %>% summary()
#> # A tibble: 1 × 5
#>   Design              N Bound alpha Power
#>   <chr>           <dbl> <dbl> <dbl> <dbl>
#> 1 Risk difference  2000  1.96 0.025 0.923

# RMST method ----
library(dplyr)

# Example 1: given power and compute sample size
x <- fixed_design_rmst(
  alpha = .025, power = .9,
  enroll_rate = define_enroll_rate(duration = 18, rate = 1),
  fail_rate = define_fail_rate(
    duration = 100,
    fail_rate = log(2) / 12,
    hr = .7,
    dropout_rate = .001
  ),
  study_duration = 36,
  tau = 18
)
x %>% summary()
#> # A tibble: 1 × 7
#>   Design             N Events  Time Bound alpha Power
#>   <chr>          <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 RMST: tau = 18  671.   477.    36  1.96 0.025   0.9

# Example 2: given sample size and compute power
x <- fixed_design_rmst(
  alpha = .025,
  enroll_rate = define_enroll_rate(duration = 18, rate = 20),
  fail_rate = define_fail_rate(
    duration = 100,
    fail_rate = log(2) / 12,
    hr = .7,
    dropout_rate = .001
  ),
  study_duration = 36,
  tau = 18
)
x %>% summary()
#> # A tibble: 1 × 7
#>   Design             N Events  Time Bound alpha Power
#>   <chr>          <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 RMST: tau = 18   360   256.    36  1.96 0.025 0.661