design_gsnb: Group sequential design with negative binomial outcomes

In gscounts: Group Sequential Designs with Negative Binomial Outcomes

Description

Design a group sequential trial with negative binomial outcomes

Usage

design_gsnb(
  rate1,
  rate2,
  dispersion,
  ratio_H0 = 1,
  random_ratio = 1,
  power,
  sig_level,
  timing,
  esf = obrien,
  esf_futility = NULL,
  futility = NULL,
  t_recruit1 = NULL,
  t_recruit2 = NULL,
  study_period = NULL,
  accrual_period = NULL,
  followup_max = NULL,
  accrual_speed = 1,
  ...
)

Arguments

rate1	numeric; assumed rate of treatment group 1 in the alternative
rate2	numeric; assumed rate of treatment group 2 in the alternative
dispersion	numeric; dispersion (shape) parameter of negative binomial distribution
ratio_H0	numeric; positive number denoting the rate ratio μ_1/μ_2 under the null hypothesis, i.e. the non-inferiority or superiority margin
random_ratio	numeric; randomization ratio n1/n2
power	numeric; target power of group sequential design
sig_level	numeric; Type I error / significance level
timing	numeric vector; 0 < timing[1] < ... < timing[K] = 1 with K the number of analyses, i.e. (K-1) interim analyses and final analysis. When the timing of efficacy and futility analyses differ, timing should not be defined. Instead, the arguments timing_eff and timing_fut have to be used to specify the timing of the efficacy and futility analyses, respectively.
esf	function; error spending function
esf_futility	function; futility error spending function
futility	character; either "binding", "nonbinding", or NULL for binding, nonbinding, or no futility boundaries
t_recruit1	numeric vector; recruit (i.e. study entry) times in group 1
t_recruit2	numeric vector; recruit (i.e. study entry) times in group 2
study_period	numeric; study duration; to be set when follow-up times are not identical between subjects, NULL otherwise
accrual_period	numeric; accrual period
followup_max	numeric; maximum exposure time of a subject; to be set when follow-up times are to be equal for each subject, NULL otherwise
accrual_speed	numeric; determines accrual speed; values larger than 1 result in accrual slower than linear; values between 0 and 1 result in accrual faster than linear.
...	further arguments. Will be passed to the error spending function.

Details

Denote μ_1 and μ_2 the event rates in treatment groups 1 and 2. This function considers smaller event rates to be better. The statistical hypothesis testing problem of interest is

H_0: \frac{μ_1}{μ_2} ≥ δ vs. H_1: \frac{μ_1}{μ_2} < δ,

with δ=ratio_H0. Non-inferiority of treatment group 1 compared to treatment group 2 is tested for δ\in (1,∞). Superiority of treatment group 1 over treatment group 2 is tested for δ \in (0,1]. The calculation of the efficacy and (non-)binding futility boundaries are performed under the hypothesis H_0: \frac{μ_1}{μ_2}= δ and under the alternative H_1: \frac{μ_1}{μ_2} = rate1 / rate2.

The argument 'accrual_speed' is used to adjust the accrual speed. Number of subjects in the study at study time t is given by f(t)=a * t^b with a = n / accrual_period and b=accrual_speed For linear recruitment, b=1. b > 1 results is slower than linear recruitment for t < accrual_period and faster than linear recruitment for t > accrual_period. Vice verse for b < 1.

Value

A list with class "gsnb" containing the following components:

rate1	as input
rate2	as input
dispersion	as input
power	as input
timing	as input
ratio_H0	as input
ratio_H1	ratio rate1/rate2
sig_level	as input
random_ratio	as input
power_fix	power of fixed design
expected_info	list; expected information under ratio_H0 and ratio_H1
efficacy	list; contains the elements esf (type I error spending function), spend (type I error spend at each look), and critical (critical value for efficacy testing)
futility	list; only part of the output if argument futility is defined in the input. Contains the elements futility (input argument futility), esf (type II error spending function), spend (type II error spend at each look), and critical (critical value for futility testing)
stop_prob	list; contains the element efficacy with the probabilities for stopping for efficacy and, if futility bounds are calculated, the element futility with the probabilities for stopping for futility
t_recruit1	as input
t_recruit2	as input
study_period	as input
followup_max	as input
max_info	maximum information
calendar	calendar times of data looks; only calculated when exposure times are not identical

References

Mütze, T., Glimm, E., Schmidli, H., & Friede, T. (2018). Group sequential designs for negative binomial outcomes. Statistical Methods in Medical Research, <doi:10.1177/0962280218773115>.

Examples

# Calculate the sample sizes for a given accrual period and study period (without futility)
out <- design_gsnb(rate1 = 0.0875, rate2 = 0.125, dispersion = 5, 
                   power = 0.8, timing = c(0.5, 1), esf = obrien,
                   ratio_H0 = 1, sig_level = 0.025,
                   study_period = 3.5, accrual_period = 1.25, random_ratio = 1)
out

# Calculate the sample sizes for a given accrual period and study period with binding futility
out <- design_gsnb(rate1 = 0.0875, rate2 = 0.125, dispersion = 5, 
                   power = 0.8, timing = c(0.5, 1), esf = obrien,
                   ratio_H0 = 1, sig_level = 0.025, study_period = 3.5, 
                   accrual_period = 1.25, random_ratio = 1, futility = "binding", 
                   esf_futility = obrien)
out


# Calculate study period for given recruitment times
expose <- seq(0, 1.25, length.out = 1042)
out <- design_gsnb(rate1 = 0.0875, rate2 = 0.125, dispersion = 5, 
                   power = 0.8, timing = c(0.5, 1), esf = obrien,
                   ratio_H0 = 1, sig_level = 0.025, t_recruit1 = expose, 
                   t_recruit2 = expose, random_ratio = 1)
out

# Calculate sample size for a fixed exposure time
out <- design_gsnb(rate1 = 0.0875, rate2 = 0.125, dispersion = 5, 
                   power = 0.8, timing = c(0.5, 1), esf = obrien,
                   ratio_H0 = 1, sig_level = 0.025,
                   followup_max = 0.5, random_ratio = 1)
                   
# Different timing for efficacy and futility analyses
 design_gsnb(rate1 = 1, rate2 = 2, dispersion = 5,
             power = 0.8, esf = obrien,
             ratio_H0 = 1, sig_level = 0.025, study_period = 3.5,
             accrual_period = 1.25, random_ratio = 1, futility = "binding",
             esf_futility = pocock, 
             timing_eff = c(0.8, 1),
             timing_fut = c(0.2, 0.5, 1))                    

gscounts documentation built on Nov. 2, 2021, 9:07 a.m.