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Sample size calculation for negative binomial distribution

Source: R/sample_size_nbinom.R
sample_size_nbinom.Rd

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,
  accrual_rate,
  accrual_duration,
  trial_duration,
  dropout_rate = 0,
  max_followup = NULL,
  event_gap = NULL,
  method = "zhu"
)

Arguments

lambda1

Rate in group 1 (control).

lambda2

Rate in group 2 (treatment).

dispersion

Dispersion parameter k such that \(Var(Y) = \mu + k \mu^2\). 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.

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.

dropout_rate

Dropout rate (hazard rate). Default is 0.

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.

method

Method for sample size calculation. "zhu" for Zhu and Lakkis (2014), or "friede" for Friede and Schmidli (2010) / Mütze et al. (2019).

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

exposure

Average exposure time used in calculation (calendar time)

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)

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

See also

vignette("sample-size-nbinom", package = "gsDesignNB") for a detailed explanation of the methodology.

Examples

# Calculate sample size for lambda1 = 0.5, lambda2 = 0.3, dispersion = 0.1
# with fixed recruitment of 10/month for 20 months, 24 month trial duration
x <- sample_size_nbinom(
  lambda1 = 0.5, lambda2 = 0.3, dispersion = 0.1, power = 0.8,
  accrual_rate = 10, accrual_duration = 20, trial_duration = 24
)
class(x)
#> [1] "sample_size_nbinom_result" "list"                     
summary(x)
#> Fixed sample size design for negative binomial outcome (zhu method), total
#> sample size 38 (n1=19, n2=19), 80 percent power, 2.5 percent (1-sided) Type I
#> error. Control rate 0.5000, treatment rate 0.3000, risk ratio 0.6000,
#> dispersion 0.1000. Accrual duration 20.0, trial duration 24.0, average exposure
#> 14.00. Expected events 212.8. Randomization ratio 1:1.
#> 

# With piecewise accrual
# 5 patients/month for 3 months, then 10 patients/month for 3 months
# Trial ends at month 12.
x2 <- sample_size_nbinom(
  lambda1 = 0.5, lambda2 = 0.3, dispersion = 0.1, power = 0.8,
  accrual_rate = c(5, 10), accrual_duration = c(3, 3),
  trial_duration = 12
)
summary(x2)
#> Fixed sample size design for negative binomial outcome (zhu method), total
#> sample size 52 (n1=26, n2=26), 80 percent power, 2.5 percent (1-sided) Type I
#> error. Control rate 0.5000, treatment rate 0.3000, risk ratio 0.6000,
#> dispersion 0.1000. Accrual duration 6.0, trial duration 12.0, average exposure
#> 8.50. Expected events 176.8. Randomization ratio 1:1.
#>