Generate Dataset with crossing hazards

Create an empty assumtions data.frame for generate_crossing_hazards

Calculate hr after crossing the hazard functions

Calculate true summary statistics for scenarios with crossing hazards

Usage

generate_crossing_hazards(condition, fixed_objects = NULL)

assumptions_crossing_hazards(print = interactive())

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

cen_rate_from_cen_prop_crossing_hazards(design)

true_summary_statistics_crossing_hazards(
  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 crossing hazards
cutoff_stats: (optionally named) cutoff time, see details
milestones: (optionally named) vector of times at which milestone survival should be calculated

Value

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

For assumptions_crossing_hazards: a design tibble with default values invisibly

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

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

For true_summary_statistics_crossing_hazards: 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
crossing time of crossing of the hazards
hazard_ctrl hazard in the control arm = hazard before onset of treatment effect
hazard_trt_before hazard in the treatment arm before onset of treatment effect
hazard_trt_after 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_crossing_hazards generates a default design data.frame for use with generate_crossing_hazards 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_crossing_from_PH_effect_size calculates the hazard ratio after crossing of hazards 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 crossing of hazards 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_crossing_hazards 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_crossing_hazards(): simulates a dataset with crossing hazards
assumptions_crossing_hazards(): generate default assumptions data.frame
hr_after_crossing_from_PH_effect_size(): Calculate hr after crossing of the hazards from PH effect size
cen_rate_from_cen_prop_crossing_hazards(): calculate censoring rate from censoring proportion
true_summary_statistics_crossing_hazards(): calculate true summary statistics for crossing hazards

Examples

one_simulation <- merge(
    assumptions_crossing_hazards(),
    design_fixed_followup(),
    by=NULL
  ) |>
  head(1) |>
  generate_crossing_hazards()
head(one_simulation)
#>      t trt  evt
#> 1  862   1 TRUE
#> 2  298   1 TRUE
#> 3   41   1 TRUE
#> 4 2273   1 TRUE
#> 5 1927   1 TRUE
#> 6 1050   1 TRUE
tail(one_simulation)
#>        t trt  evt
#> 295  259   0 TRUE
#> 296  245   0 TRUE
#> 297  788   0 TRUE
#> 298 1348   0 TRUE
#> 299 1905   0 TRUE
#> 300  878   0 TRUE
Design <- assumptions_crossing_hazards()
Design
#>   crossing  hazard_ctrl hazard_trt_before hazard_trt_after random_withdrawal
#> 1    0.000 0.0009488668       0.001265156     0.0006325779      0.0001897734
#> 2   60.875 0.0009488668       0.001265156     0.0006325779      0.0001897734
#> 3  121.750 0.0009488668       0.001265156     0.0006325779      0.0001897734
#> 4  182.625 0.0009488668       0.001265156     0.0006325779      0.0001897734
#> 5  243.500 0.0009488668       0.001265156     0.0006325779      0.0001897734
#> 6  304.375 0.0009488668       0.001265156     0.0006325779      0.0001897734
my_design <- merge(
    assumptions_crossing_hazards(),
    design_fixed_followup(),
    by=NULL
  )

my_design$final_events <- ceiling((my_design$n_trt + my_design$n_ctrl)*0.75)
my_design$hazard_trt <- NA
my_design <- hr_after_crossing_from_PH_effect_size(my_design, target_power_ph=0.9)
my_design
#>   crossing  hazard_ctrl hazard_trt_before hazard_trt_after random_withdrawal
#> 1    0.000 0.0009488668       0.001265156     0.0006158887      0.0001897734
#> 2   60.875 0.0009488668       0.001265156     0.0005787618      0.0001897734
#> 3  121.750 0.0009488668       0.001265156     0.0005371313      0.0001897734
#> 4  182.625 0.0009488668       0.001265156     0.0004901248      0.0001897734
#> 5  243.500 0.0009488668       0.001265156     0.0004366293      0.0001897734
#> 6  304.375 0.0009488668       0.001265156     0.0003752012      0.0001897734
#>   n_trt n_ctrl followup recruitment final_events hazard_trt target_median_trt
#> 1   150    150    730.5     182.625          225         NA          1125.442
#> 2   150    150    730.5     182.625          225         NA          1125.442
#> 3   150    150    730.5     182.625          225         NA          1125.442
#> 4   150    150    730.5     182.625          225         NA          1125.442
#> 5   150    150    730.5     182.625          225         NA          1125.442
#> 6   150    150    730.5     182.625          225         NA          1125.442
#>   target_hr
#> 1 0.6490782
#> 2 0.6490782
#> 3 0.6490782
#> 4 0.6490782
#> 5 0.6490782
#> 6 0.6490782
design <- data.frame(
  crossing = c(2, 4, 6),
  hazard_ctrl = c(0.05, 0.05, 0.05),
  hazard_trt_before = c(0.025, 0.025, 0.025),
  hazard_trt_after = c(0.1, 0.1, 0.1),
  censoring_prop = c(0.1, 0.3, 0.2),
  n_trt = c(50, 50, 50),
  n_ctrl = c(50, 50, 50),
  followup = c(200, 200, 200),
  recruitment = c(50, 50, 50)
)
cen_rate_from_cen_prop_crossing_hazards(design)
#>   crossing hazard_ctrl hazard_trt_before hazard_trt_after censoring_prop n_trt
#> 1        2        0.05             0.025              0.1            0.1    50
#> 2        4        0.05             0.025              0.1            0.3    50
#> 3        6        0.05             0.025              0.1            0.2    50
#>   n_ctrl followup recruitment random_withdrawal
#> 1     50      200          50       0.007469191
#> 2     50      200          50       0.029373101
#> 3     50      200          50       0.016885532
my_design <- merge(
    assumptions_crossing_hazards(),
    design_fixed_followup(),
    by=NULL
  )
my_design$follwup <- 15
my_design <- true_summary_statistics_crossing_hazards(my_design)
my_design
#>   crossing  hazard_ctrl hazard_trt_before hazard_trt_after random_withdrawal
#> 1    0.000 0.0009488668       0.001265156     0.0006325779      0.0001897734
#> 2   60.875 0.0009488668       0.001265156     0.0006325779      0.0001897734
#> 3  121.750 0.0009488668       0.001265156     0.0006325779      0.0001897734
#> 4  182.625 0.0009488668       0.001265156     0.0006325779      0.0001897734
#> 5  243.500 0.0009488668       0.001265156     0.0006325779      0.0001897734
#> 6  304.375 0.0009488668       0.001265156     0.0006325779      0.0001897734
#>   n_trt n_ctrl followup recruitment follwup median_survival_trt
#> 1   150    150    730.5     182.625      15            1095.750
#> 2   150    150    730.5     182.625      15            1034.875
#> 3   150    150    730.5     182.625      15             974.000
#> 4   150    150    730.5     182.625      15             913.125
#> 5   150    150    730.5     182.625      15             852.250
#> 6   150    150    730.5     182.625      15             791.375
#>   median_survival_ctrl
#> 1                730.5
#> 2                730.5
#> 3                730.5
#> 4                730.5
#> 5                730.5
#> 6                730.5