Sample size calculation for negative binomial distribution

Computes the sample size for comparing two treatment groups assuming a negative binomial distribution for the outcome.

Usage

sample_size_nbinom(
  lambda1,
  lambda2,
  dispersion,
  power = NULL,
  alpha = 0.025,
  sided = 1,
  ratio = 1,
  rr0 = 1,
  accrual_rate,
  accrual_duration,
  trial_duration,
  dropout_rate = 0,
  max_followup = NULL,
  event_gap = NULL
)

Arguments

lambda1: Rate in group 1 (control).
lambda2: Rate in group 2 (treatment).
dispersion: Dispersion parameter k such that \(\mathrm{Var}(Y) = \mu + k \mu^2\). Note that this is equivalent to 1/size in R's stats::rnbinom() parameterization.
power: Power of the test (1 - beta). Default is 0.9.
alpha: Significance level. Default is 0.025.
sided: One-sided or two-sided test. 1 for one-sided, 2 for two-sided. Default is 1.
ratio: Allocation ratio n2/n1. Default is 1.
rr0: Rate ratio under the null hypothesis (lambda2/lambda1). Default is 1 (superiority). For non-inferiority, use a value > 1 (e.g., 1.1). For super-superiority, use a value < 1 (e.g., 0.8).
accrual_rate: Vector of accrual rates (patients per unit time).
accrual_duration: Vector of durations for each accrual rate. Must be same length as accrual_rate.
trial_duration: Total planned duration of the trial. If trial_duration is less than the sum of accrual_duration, accrual is truncated at trial_duration.
dropout_rate: Dropout rate (hazard rate). Default is 0. Can be a vector of length 2.
max_followup: Maximum follow-up time for any patient. Default is NULL (infinite).
event_gap: Gap duration after each event during which no new events are counted. Default is NULL (no gap). If provided, the effective event rate is reduced.

Value

An object of class sample_size_nbinom_result, which is a list containing:

inputs: Named list of the original function arguments.
n1: Sample size for group 1
n2: Sample size for group 2
n_total: Total sample size
alpha: Significance level
sided: One-sided or two-sided test
power: Power of the test
exposure: Average exposure time used in calculation (calendar time). Vector of length 2.
exposure_at_risk_n1: Average at-risk exposure time for group 1 (accounts for event gap)
exposure_at_risk_n2: Average at-risk exposure time for group 2 (accounts for event gap)
events_n1: Expected number of events in group 1
events_n2: Expected number of events in group 2
total_events: Total expected number of events
variance: Variance of the log rate ratio
accrual_rate: Accrual rate used in calculation
accrual_duration: Accrual duration used in calculation

References

Zhu, H., & Lakkis, H. (2014). Sample size calculation for comparing two negative binomial rates. Statistics in Medicine, 33(3), 376–387. doi:10.1002/sim.5947

Friede, T., & Schmidli, H. (2010). Blinded sample size reestimation with negative binomial counts in superiority and non-inferiority trials. Methods of Information in Medicine, 49(06), 618–624. doi:10.3414/ME09-02-0060

Mütze, T., Glimm, E., Schmidli, H., & Friede, T. (2019). Group sequential designs for negative binomial outcomes. Statistical Methods in Medical Research, 28(8), 2326–2347. doi:10.1177/0962280218773115

Examples