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Estimating equation for delta-effective dose (log-logistic)

Source: R/ee-pharma.R
ee_loglogistic_ed.Rd

Computes the effective dose at level delta from the log-logistic model. Should be stacked with ee_loglogistic().

Usage

ee_loglogistic_ed(theta, dose, delta, lower, upper, ed50, steepness)

Arguments

theta

Numeric scalar. The ED(delta) parameter.

dose

Numeric vector (used for dimension only).

delta

Numeric effective dose level of interest.

lower

Numeric lower limit parameter.

upper

Numeric upper limit parameter.

ed50

Numeric estimated ED50.

steepness

Numeric steepness parameter.

Value

A 1-by-n matrix.

See also

ee_loglogistic(), the dose-response equation this one is stacked with.

Examples

# The lower limit is held at zero instead of being estimated: root length
# cannot fall below zero, and the five-parameter stack diverges on these
# data. The lower-limit row of the log-logistic equation is therefore
# dropped, leaving the upper limit, ED50, and steepness to be estimated
# alongside the ED90.
psi <- function(theta) {
  loglogistic <- ee_loglogistic(
    c(0, theta[1:3]),
    dose = inderjit$dose,
    response = inderjit$response
  )
  ed90 <- ee_loglogistic_ed(
    theta[4],
    dose = inderjit$dose,
    delta = 0.9,
    lower = 0,
    upper = theta[1],
    ed50 = theta[2],
    steepness = theta[3]
  )
  rbind(loglogistic[-1, , drop = FALSE], ed90)
}

# This stacked system is sensitive to its starting values, so a reasonable
# init matters more here than it does for most equations.
m <- m_estimate(stacked_equations = psi, init = c(8, 2, 1, 5))

# Upper limit, ED50, steepness, and the ED90. Stacking is what gives the ED90
# a standard error of its own, so summary() rather than coef() shows the
# gain.
summary(m)
#> ── MEstimator Results ──────────────────────────────────────────────────────────
#> Observations: 24
#> Parameters: 4
#> 
#>           Estimate    Std.Err    Z-score    95% LCL    95% UCL    P-value    S-value
#> theta_1     7.8554     0.1540    51.0194     7.5537     8.1572     <2e-16        Inf
#> theta_2     3.2634     0.2657    12.2813     2.7426     3.7842     <2e-16   112.7546
#> theta_3     2.4703     0.2924     8.4490     1.8973     3.0434     <2e-16    54.9177
#> theta_4     7.9423     1.2765     6.2220     5.4405    10.4442   4.91e-10    30.9244