Generate Dataset with different treatment effect in subgroup

Create an empty assumtions data.frame for generate_subgroup

Calculate true summary statistics for scenarios with differential treatment effect in subgroup

Calculate hazards in treatment arm in subgroup and compliment

Usage

generate_subgroup(condition, fixed_objects = NULL)

assumptions_subgroup(print = interactive())

true_summary_statistics_subgroup(
  Design,
  cutoff_stats = NULL,
  milestones = NULL,
  fixed_objects = NULL
)

hazard_subgroup_from_PH_effect_size(
  design,
  target_power_ph = NA_real_,
  final_events = NA_real_,
  target_alpha = 0.025
)

cen_rate_from_cen_prop_subgroup(design)

Arguments

condition: condition row of Design dataset
fixed_objects: additional settings, see details
print: print code to generate parameter set?
Design: Design data.frame for subgroup
cutoff_stats: (optionally named) cutoff times, see details
milestones: (optionally named) vector of times at which milestone survival should be calculated
design: design data.frame
target_power_ph: target power under proportional hazards
final_events: target events for inversion of Schönfeld Formula, defaults to condition$final_events
target_alpha: target one-sided alpha level for the power calculation

Value

For generate_subgroup: A dataset with the columns t (time) and trt (1=treatment, 0=control), evt (event, currently TRUE for all observations)

For assumptions_subgroup: a design tibble with default values invisibly

For true_summary_statistics_subgroup: the design data.frame passed as argument with the additional columns

For hazard_subgroup_from_PH_effect_size: the design data.frame passed as argument with the additional columns hazard_trt and hazard_subgroup.

for cen_rate_from_cen_prop_subgroup: design data.frame with the additional column random_withdrawal

Details

Condidtion has to contain the following columns:

n_trt number of paitents in treatment arm
n_ctrl number of patients in control arm
hazard_ctrl hazard in the control arm
hazard_trt hazard in the treatment arm for not cured patients
hazard_subgroup hazard in the subgroup in the treatment arm
prevalence proportion of cured patients

assumptions_subgroup generates a default design data.frame for use with generate_subgroup If print is TRUE code to produce the template is also printed for copying, pasting and editing by the user. (This is the default when run in an interactive session.)

cutoff_stats are the times used to calculate the statistics like average hazard ratios and RMST, that are only calculated up to a certain point.

hazard_subgroup_from_PH_effect_size calculates the hazard rate in the subgroup and the compliment of the subgroup in the treatment arm as follows: First, the hazard ratio needed to archive the desired power under proportional hazards is calculated by inverting Schönfeld's sample size formula. Second the median survival times for both arms under this hazard ratio and proportional hazards are calculated. Finally the hazard rate of the treatment arm in the subgroup and its complement are set such that the median survival time is the same as the one calculated under proportional hazards.

This is a heuristic and to some extent arbitrary approach to calculate hazard ratios that correspond to reasonable and realistic scenarios.

cen_rate_from_cen_prop_subgroup takes the proportion of censored patients from the column censoring_prop. This column describes the proportion of patients who are censored randomly before experiencing an event, without regard to administrative censoring.

Functions

generate_subgroup(): simulates a dataset with a mixture of cured patients
assumptions_subgroup(): generate default assumptions data.frame
true_summary_statistics_subgroup(): calculate true summary statistics for subgroup
hazard_subgroup_from_PH_effect_size(): Calculate hazards in treatement arm
cen_rate_from_cen_prop_subgroup(): calculate censoring rate from censoring proportion

Examples

one_simulation <- merge(
    assumptions_subgroup(),
    design_fixed_followup(),
    by=NULL
  ) |>
  head(1) |>
  generate_subgroup()
head(one_simulation)
#>      t trt  evt subgroup
#> 1 5389   1 TRUE        0
#> 2 2356   1 TRUE        0
#> 3  445   1 TRUE        0
#> 4 1201   1 TRUE        0
#> 5  429   1 TRUE        0
#> 6 1850   1 TRUE        0
tail(one_simulation)
#>        t trt  evt subgroup
#> 295 1911   0 TRUE        0
#> 296 1649   0 TRUE        0
#> 297 3451   0 TRUE        0
#> 298  805   0 TRUE        0
#> 299 1670   0 TRUE        1
#> 300  621   0 TRUE        0
Design <- assumptions_subgroup()
Design
#>    hazard_ctrl   hazard_trt hazard_subgroup prevalence random_withdrawal
#> 1 0.0009488668 0.0006325779    9.488668e-05        0.2      0.0001897734
#> 2 0.0009488668 0.0006325779    9.488668e-05        0.4      0.0001897734
#> 3 0.0009488668 0.0006325779    9.488668e-05        0.6      0.0001897734
#> 4 0.0009488668 0.0006325779    9.488668e-05        0.8      0.0001897734
my_design <- merge(
    assumptions_subgroup(),
    design_fixed_followup(),
    by=NULL
  )
my_design <- true_summary_statistics_subgroup(my_design)
my_design
#>    hazard_ctrl   hazard_trt hazard_subgroup prevalence random_withdrawal n_trt
#> 1 0.0009488668 0.0006325779    9.488668e-05        0.2      0.0001897734   150
#> 2 0.0009488668 0.0006325779    9.488668e-05        0.4      0.0001897734   150
#> 3 0.0009488668 0.0006325779    9.488668e-05        0.6      0.0001897734   150
#> 4 0.0009488668 0.0006325779    9.488668e-05        0.8      0.0001897734   150
#>   n_ctrl followup recruitment median_survival_trt median_survival_ctrl
#> 1    150    730.5     182.625            1422.745                730.5
#> 2    150    730.5     182.625            2001.270                730.5
#> 3    150    730.5     182.625            3143.728                730.5
#> 4    150    730.5     182.625            5119.929                730.5

my_design <- merge(
  assumptions_subgroup(),
  design_fixed_followup(),
  by=NULL
)

my_design$hazard_trt <- NA
my_design$hazard_subgroup <- NA
my_design$hr_subgroup_relative <- 0.9
my_design$final_events <- ceiling((my_design$n_ctrl + my_design$n_trt) * 0.75)
my_design <- hazard_subgroup_from_PH_effect_size(my_design, target_power_ph=0.9)
my_design
#>    hazard_ctrl   hazard_trt hazard_subgroup prevalence random_withdrawal n_trt
#> 1 0.0009488668 0.0006288263    0.0005659437        0.2      0.0001897734   150
#> 2 0.0009488668 0.0006421335    0.0005779202        0.4      0.0001897734   150
#> 3 0.0009488668 0.0006558156    0.0005902340        0.6      0.0001897734   150
#> 4 0.0009488668 0.0006698768    0.0006028891        0.8      0.0001897734   150
#>   n_ctrl followup recruitment hr_subgroup_relative final_events
#> 1    150    730.5     182.625                  0.9          225
#> 2    150    730.5     182.625                  0.9          225
#> 3    150    730.5     182.625                  0.9          225
#> 4    150    730.5     182.625                  0.9          225
#>   target_median_trt
#> 1          1125.442
#> 2          1125.442
#> 3          1125.442
#> 4          1125.442
design <- expand.grid(
  hazard_ctrl=0.2,                   # hazard under control and before treatment effect
  hazard_trt=0.02,                   # hazard after onset of treatment effect
  hazard_subgroup=0.01,              # hazard in the subgroup in treatment
  prevalence = c(0.2, 0.5),           # subgroup prevalence
  censoring_prop=c(0.1, 0.25, 0.01), # 10%, 25%, 1% random censoring
  followup=100,                      # followup of 100 days
  n_trt=50,                          # 50 patients treatment
  n_ctrl=50                          # 50 patients control
)
cen_rate_from_cen_prop_subgroup(design)
#>   hazard_ctrl hazard_trt hazard_subgroup prevalence censoring_prop followup
#> 1         0.2       0.02            0.01        0.2           0.10      100
#> 2         0.2       0.02            0.01        0.5           0.10      100
#> 3         0.2       0.02            0.01        0.2           0.25      100
#> 4         0.2       0.02            0.01        0.5           0.25      100
#> 5         0.2       0.02            0.01        0.2           0.01      100
#> 6         0.2       0.02            0.01        0.5           0.01      100
#>   n_trt n_ctrl random_withdrawal
#> 1    50     50      0.0030440737
#> 2    50     50      0.0026408014
#> 3    50     50      0.0108976367
#> 4    50     50      0.0095627716
#> 5    50     50      0.0002558513
#> 6    50     50      0.0002211651