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Sample Size and Non-Inferiority Margin for Vaccine Efficacy Trials

Source: R/ss_ni_ve.R
ss_ni_ve.Rd

Computes the non-inferiority margin, number of events, and maximum hazard ratio (HR) to declare non-inferiority in vaccine efficacy (VE) trials, based on the approach described by Fleming et al. (2021).

Usage

ss_ni_ve(
  ve_lci,
  alpha = 0.025,
  power = 0.9,
  use70 = FALSE,
  preserve = 0.5,
  ve_exp = NULL,
  ve_ac = NULL
)

Arguments

ve_lci

Numeric. Lower bound of the current vaccine's efficacy (e.g., 0.95 for 95% VE).

alpha

Numeric. Type I error rate (default = 0.025).

power

Numeric. Desired power for the test (default = 0.90).

use70

Logical. If TRUE, assumes at least 30% VE for the new vaccine (the 90–70 rule); otherwise, preserves a fixed fraction of the reference VE.

preserve

Numeric. Proportion of the current vaccine's efficacy to preserve under use70 = FALSE (default = 0.5).

ve_exp

Numeric or NULL (default). Assumed vaccine efficacy of the experimental vaccine versus placebo, used to compute power for the non-inferiority trial. If NULL (the default), the experimental vaccine is assumed to have the same true efficacy as the active comparator (hazard ratio of 1 between them). If specified, ve_ac must also be provided.

ve_ac

Numeric or NULL (default). Point estimate of the active comparator's vaccine efficacy versus placebo (as opposed to ve_lci, which is its confidence interval lower bound). Only used, and required, when ve_exp is specified.

Value

A named list with:

  • Upper limit of the HR used to estimate the sample size: Hazard ratio corresponding to ve_lci.

  • Non-inferior margin in HR scale: Non-inferiority margin expressed as a hazard ratio.

  • Alpha: The type I error used.

  • Power: The power used.

  • Total number of events: Total number of events required in the trial.

  • Max HR to declare NI: Maximum observed hazard ratio that satisfies the non-inferiority criterion.

  • Max number of events in the experimental group: Maximum number of events in the experimental group still compatible with non-inferiority.

  • Non-inferior criteria: Description of the applied non-inferiority rule ("At least 30% VE" or "or preserved effect").

Details

The method applies either the 95–95 rule or 90–70 rule, depending on whether a minimum VE of 30% is assumed (use70 = TRUE) or 50% of the current VE is preserved.

This implementation approximates Tables 1 and 2 of the paper: the total number of events uses Freedman's (1982) log-rank sample size formula, generalized to allow the true experimental-to-comparator hazard ratio assumed for power (ve_exp) to differ from 1; the maximum hazard ratio to declare non-inferiority uses an exact binomial confidence interval via binom.test.

References

Fleming, T.R., Powers, J.H., & Huang, Y. (2021). The use of active controls and non-inferiority studies in evaluating COVID-19 vaccines. Clinical Trials, 18(3), 335–342. doi:10.1177/1740774520988244

Freedman, L.S. (1982). Tables of the number of patients required in clinical trials using the logrank test. Statistics in Medicine, 1(2), 121-129. doi:10.1002/sim.4780010204

Examples

# Table 1: rule out margin delta, assuming EXP has the same true efficacy
# as AC (175-event active-comparator trial, 95% VE, HR upper 95% CI = 0.0855)
ss_ni_ve(ve_lci = 1 - 0.0855, power = 0.9)
#> $`Upper limit of the HR used to estimate the sample size`
#> [1] 0.0855
#> 
#> $`Non-inferior margin in HR scale`
#> [1] 3.419928
#> 
#> $Alpha
#> [1] 0.025
#> 
#> $Power
#> [1] 0.9
#> 
#> $`Total number of events`
#> [1] 36
#> 
#> $`Max HR to declare NI`
#> [1] 1.571429
#> 
#> $`Max number of events in the experimental group`
#> [1] 22
#> 
#> $`Non-inferior criteria`
#> [1] "Preserve at least 50% of the VE in the new vaccine"
#> 

# The 90-70 rule (use70 = TRUE) rules out the more lenient margin delta0
# instead of delta, for the same active-comparator trial as above
ss_ni_ve(ve_lci = 1 - 0.0855, power = 0.9, use70 = TRUE)
#> $`Upper limit of the HR used to estimate the sample size`
#> [1] 0.0855
#> 
#> $`Non-inferior margin in HR scale`
#> [1] 9.785497
#> 
#> $Alpha
#> [1] 0.025
#> 
#> $Power
#> [1] 0.9
#> 
#> $`Total number of events`
#> [1] 16
#> 
#> $`Max HR to declare NI`
#> [1] 2.2
#> 
#> $`Max number of events in the experimental group`
#> [1] 11
#> 
#> $`Non-inferior criteria`
#> [1] "At least 30% VE in new vaccine"
#> 

# Table 2: rule out margin delta0, assuming the experimental vaccine has a
# fixed 60% efficacy versus placebo regardless of AC's own efficacy (here,
# AC has 60% VE, HR upper 95% CI = 0.4997)
ss_ni_ve(ve_lci = 1 - 0.4997, power = 0.9, use70 = TRUE, ve_exp = 0.60, ve_ac = 0.60)
#> $`Upper limit of the HR used to estimate the sample size`
#> [1] 0.4997
#> 
#> $`Non-inferior margin in HR scale`
#> [1] 1.674325
#> 
#> $Alpha
#> [1] 0.025
#> 
#> $Power
#> [1] 0.9
#> 
#> $`Total number of events`
#> [1] 166
#> 
#> $`Max HR to declare NI`
#> [1] 1.213333
#> 
#> $`Max number of events in the experimental group`
#> [1] 91
#> 
#> $`Non-inferior criteria`
#> [1] "At least 30% VE in new vaccine"
#>