Required number of replicates for a target MCSE

Inverts the Monte-Carlo standard error (MCSE) formulas used by performance_measures() to return the number of replicates n required to achieve a target MCSE. Useful for planning a simulation study (a precision / power calculation) before running it.

The MCSE formulas (Morris et al. 2019; rsimsum) invert to:

• coverage (binary 0/1 outcome): MCSE = sqrt(p (1 - p) / n) => n = p (1 - p) / MCSE^2. The default p = 0.5 is the conservative max-variance case (it maximises p (1 - p) and therefore gives the largest required n).

• continuous metrics (bias / mean / model SE): MCSE = sd / sqrt(n) => n = (sd / MCSE)^2. Requires an assumed standard deviation assumed_sd for the per-replicate point estimate (e.g. a guess at the empirical SE of the estimator).

The returned value is ceiling(n) so it is always a whole number of replicates.

Usage

n_replicates_for_target(
  target_mcse,
  metric_type = c("coverage", "continuous"),
  p = 0.5,
  assumed_sd = NULL
)

Arguments

target_mcse

Numeric scalar > 0. The MCSE you want to achieve.

metric_type

Character scalar: "coverage" (binary coverage metrics) or "continuous" (bias / mean / model SE metrics).

p

Numeric scalar in [0, 1]. Assumed coverage probability. Only used when metric_type = "coverage". Defaults to 0.5, the variance-maximising (most conservative) choice.

assumed_sd

Numeric scalar > 0. Assumed standard deviation of the per-replicate point estimate. Required when metric_type = "continuous"; ignored otherwise.

Value

An integer scalar: the number of replicates required (the ceiling of the inverted-MCSE n).

See also

performance_measures() for the MCSE formulas being inverted.

Examples

if (FALSE) { # \dontrun{
# Coverage: target MCSE 0.03 under the conservative p = 0.5.
n_replicates_for_target(0.03, "coverage")

# Coverage at an assumed rate of 0.9.
n_replicates_for_target(0.03, "coverage", p = 0.9)

# Continuous metric (e.g. bias) with assumed sd of the point estimate.
n_replicates_for_target(0.05, "continuous", assumed_sd = 0.5)
} # }