Generate Dataset with delayed effect

Create an empty assumtions data.frame for generate_delayed_effect

Calculate hr after onset of treatment effect

Calculate true summary statistics for scenarios with delayed treatment effect

Usage

generate_delayed_effect(condition, fixed_objects = NULL)

assumptions_delayed_effect(print = interactive())

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

cen_rate_from_cen_prop_delayed_effect(design)

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

Arguments

condition: condition row of Design dataset
fixed_objects: additional settings, see details
print: print code to generate parameter set?
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
Design: Design data.frame for delayed effect
cutoff_stats: (optionally named) cutoff times, see details
milestones: (optionally named) vector of times at which milestone survival should be calculated

Value

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

For assumptions_delayed_effect: a design tibble with default values invisibly

For hr_after_onset_from_PH_effect_size: the design data.frame passed as argument with the additional column hazard_trt.

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

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

Details

Condidtion has to contain the following columns:

n_trt number of paitents in treatment arm
n_ctrl number of patients in control arm
delay time until onset of effect
hazard_ctrl hazard in the control arm = hazard before onset of treatment effect
hazard_trt hazard in the treatment arm afert onset of treatment effect

If fixed_objects is given and contains an element t_max, then this is used as the cutoff for the simulation used internally. If t_max is not given in this way the 1-(1/10000) quantile of the survival distribution in the control or treatment arm is used (which ever is larger).

assumptions_delayed_effect generates a default design data.frame for use with generate_delayed_effect. 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.)

hr_after_onset_from_PH_effect_size calculates the hazard ratio after onset of treatment effect 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 arm under this hazard ratio and proportional hazards are calculated. Finally the hazard rate of the treatment arm after onset of treatment effect is 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_delayed_effect 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.

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.

Functions

generate_delayed_effect(): simulates a dataset with delayed treatment effect
assumptions_delayed_effect(): generate default assumptions data.frame
hr_after_onset_from_PH_effect_size(): Calculate hr after onset of treatment effect of the hazards from PH effect size
cen_rate_from_cen_prop_delayed_effect(): calculate censoring rate from censoring proportion
true_summary_statistics_delayed_effect(): calculate true summary statistics for delayed effect

Examples

one_simulation <- merge(
    assumptions_delayed_effect(),
    design_fixed_followup(),
    by=NULL
  ) |>
  head(1) |>
  generate_delayed_effect()
head(one_simulation)
#>      t trt  evt
#> 1 5593   1 TRUE
#> 2 3411   1 TRUE
#> 3  955   1 TRUE
#> 4 1498   1 TRUE
#> 5 6771   1 TRUE
#> 6  421   1 TRUE
tail(one_simulation)
#>        t trt  evt
#> 295  158   0 TRUE
#> 296 1428   0 TRUE
#> 297  578   0 TRUE
#> 298  964   0 TRUE
#> 299 2495   0 TRUE
#> 300  572   0 TRUE
Design <- assumptions_delayed_effect()
Design
#>     delay  hazard_ctrl   hazard_trt random_withdrawal
#> 1   0.000 0.0009488668 0.0006325779      0.0001897734
#> 2  60.875 0.0009488668 0.0006325779      0.0001897734
#> 3 121.750 0.0009488668 0.0006325779      0.0001897734
#> 4 182.625 0.0009488668 0.0006325779      0.0001897734
#> 5 243.500 0.0009488668 0.0006325779      0.0001897734
#> 6 304.375 0.0009488668 0.0006325779      0.0001897734
my_design <- merge(
  assumptions_delayed_effect(),
  design_fixed_followup(),
  by=NULL
)

my_design$hazard_ctrl <- 0.05
my_design$final_events <- ceiling((my_design$n_trt + my_design$n_ctrl)*0.75)
my_design$hazard_trt <- NA
my_design <- hr_after_onset_from_PH_effect_size(my_design, target_power_ph=0.9)
#> Warning: Median survival is shorter than delay of treatment effect, calculation not possible
#> Warning: Median survival is shorter than delay of treatment effect, calculation not possible
#> Warning: Median survival is shorter than delay of treatment effect, calculation not possible
#> Warning: Median survival is shorter than delay of treatment effect, calculation not possible
#> Warning: Median survival is shorter than delay of treatment effect, calculation not possible
my_design
#>     delay hazard_ctrl hazard_trt random_withdrawal n_trt n_ctrl followup
#> 1   0.000        0.05 0.03245391      0.0001897734   150    150    730.5
#> 2  60.875        0.05         NA      0.0001897734   150    150    730.5
#> 3 121.750        0.05         NA      0.0001897734   150    150    730.5
#> 4 182.625        0.05         NA      0.0001897734   150    150    730.5
#> 5 243.500        0.05         NA      0.0001897734   150    150    730.5
#> 6 304.375        0.05         NA      0.0001897734   150    150    730.5
#>   recruitment final_events target_median_trt target_hr
#> 1     182.625          225          21.35789 0.6490782
#> 2     182.625          225          21.35789 0.6490782
#> 3     182.625          225          21.35789 0.6490782
#> 4     182.625          225          21.35789 0.6490782
#> 5     182.625          225          21.35789 0.6490782
#> 6     182.625          225          21.35789 0.6490782
design <- expand.grid(
  delay=seq(0, 10, by=5),            # delay of 0, 1, ..., 10 days
  hazard_ctrl=0.2,                   # hazard under control and before treatment effect
  hazard_trt=0.02,                   # hazard after onset of treatment effect
  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_delayed_effect(design)
#>   delay hazard_ctrl hazard_trt censoring_prop followup n_trt n_ctrl
#> 1     0         0.2       0.02           0.10      100    50     50
#> 2     5         0.2       0.02           0.10      100    50     50
#> 3    10         0.2       0.02           0.10      100    50     50
#> 4     0         0.2       0.02           0.25      100    50     50
#> 5     5         0.2       0.02           0.25      100    50     50
#> 6    10         0.2       0.02           0.25      100    50     50
#> 7     0         0.2       0.02           0.01      100    50     50
#> 8     5         0.2       0.02           0.01      100    50     50
#> 9    10         0.2       0.02           0.01      100    50     50
#>   random_withdrawal
#> 1      0.0043517713
#> 2      0.0047198579
#> 3      0.0050796441
#> 4      0.0150805823
#> 5      0.0162247001
#> 6      0.0173312396
#> 7      0.0003698016
#> 8      0.0004022565
#> 9      0.0004341304
my_design <- merge(
    assumptions_delayed_effect(),
    design_fixed_followup(),
    by=NULL
  )
my_design <- true_summary_statistics_delayed_effect(my_design)
my_design
#>     delay  hazard_ctrl   hazard_trt random_withdrawal n_trt n_ctrl followup
#> 1   0.000 0.0009488668 0.0006325779      0.0001897734   150    150    730.5
#> 2  60.875 0.0009488668 0.0006325779      0.0001897734   150    150    730.5
#> 3 121.750 0.0009488668 0.0006325779      0.0001897734   150    150    730.5
#> 4 182.625 0.0009488668 0.0006325779      0.0001897734   150    150    730.5
#> 5 243.500 0.0009488668 0.0006325779      0.0001897734   150    150    730.5
#> 6 304.375 0.0009488668 0.0006325779      0.0001897734   150    150    730.5
#>   recruitment median_survival_trt median_survival_ctrl
#> 1     182.625           1095.7500                730.5
#> 2     182.625           1065.3125                730.5
#> 3     182.625           1034.8750                730.5
#> 4     182.625           1004.4375                730.5
#> 5     182.625            974.0000                730.5
#> 6     182.625            943.5625                730.5