Introduction
This vignette illustrates how the
sim_power_equivalence_normal() function can be used to
estimate the empirical power of an equivalence test under the assumption
of normally distributed outcomes. The method simulates repeated trials
and determines whether all pairwise confidence intervals for differences
in group means fall within user-specified equivalence limits.
Example: Equivalence Among Vaccine Lots
An evaluation is conducted to determine whether three manufacturing
lots of a vaccine produce equivalent immune responses. The outcome is
the antibody concentration measured on the
scale, assumed to follow a normal distribution with a standard deviation
of 0.4.
Equivalence is declared if the confidence intervals for the ratio of all
pairwise comparisons fall entirely within the range [2/3, 3/2].
Since the analysis is conducted on the
scale, the equivalence limits are transformed to log10(2/3)
and log10(3/2).
A total of 1,000 trials is simulated with 172 subjects per group and a 95% confidence level:
set.seed(12345)
sim_power_equivalence_normal(
ngroups = 3,
npergroup = 172,
sd = 0.4,
llimit = log10(2/3),
ulimit = log10(3/2),
nsim = 1000,
t_level = 0.95
)
#> Empirical Power Result
#> -----------------------
#> Power: 0.9130
#> 95% CI: [0.8938, 0.9297]
#> Simulations: 1000The result shows the proportion of simulations in which all pairwise comparisons satisfy the equivalence criterion.
A power calculation in nQuery® shows that a Two One-Sided Equivalence
Test (TOST) for a two-group design, with an alpha level of 0.025, 172
participants per group, a standard deviation of 0.4, and equivalence
limits of log10(2/3) and log10(3/2), has a
power of 96.98%. When extended to three comparisons, assuming
independence, the joint probability of all three satisfying the
equivalence condition is approximately:
.