Construct an exact Gaussian confidence region from replicated doses

Assumes fixed distinct doses including zero and `D`, independent Gaussian observations with a common unknown positive variance, at least three dose levels, and positive pure-error degrees of freedom. No observations are removed, imputed, binned, recoded, or transformed. Within-dose variation supplies the pooled variance estimate.

Usage

emax_region(
  x,
  y,
  D = max(x),
  alpha = 0.05,
  calibration = c("contrast", "mean")
)

Arguments

x: Nonempty numeric vector of observed doses.
y: Corresponding numeric response vector, without missing values.
D: Positive upper dose endpoint. Defaults to the maximum supplied dose.
alpha: Error probability strictly between zero and one.
calibration: Either `"contrast"` (primary method) or `"mean"` (full mean-region benchmark).

Value

An `emax_region` object containing the unchanged sufficient statistics, calibration rank, and squared F-region radius.

Details

Contrast calibration removes the unrestricted intercept and has rank `m - 1`; mean calibration uses the full `m`-dimensional mean region. Both use an exact F pivot under the stated assumptions. Projection onto the integrated response can be conservative. The standard contrast pivot itself is not a claim of a new statistical model.

Examples

x <- rep(c(0, 0.5, 1), each = 4)
y <- rep(c(0.2, 0.6, 0.8), each = 4) + rep(c(-0.1, 0.1, -0.2, 0.2), 3)
region <- emax_region(x, y)
region$calibration_rank
#> [1] 2