generate_crossing_hazards {SimNPH}

Generate Dataset with crossing hazards

Description

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

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.

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,

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)
tail(one_simulation)
Design <- assumptions_crossing_hazards()
Design
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
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)
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