Function estimate_effect_3 

pub fn estimate_effect_3(
    a: f64,
    b: f64,
    c: f64,
    alpha12: f64,
    alpha13: f64,
    alpha23: f64,
    alpha123: f64,
    h1: f64,
    h2: f64,
    h3: f64,
) -> f64

Computes the effect metric for the three-site Greco response-surface model.

This is the three-drug extension published by Snyder et al. (PMID 10722511). With positive M, the canonical residual is

r(M) = 1 - a/M^h1 - b/M^h2 - c/M^h3
       - (alpha12*a*b)/M^((h1+h2)/2)
       - (alpha13*a*c)/M^((h1+h3)/2)
       - (alpha23*b*c)/M^((h2+h3)/2)
       - (alpha123*a*b*c)/M^((h1+h2+h3)/3)

The function brackets positive roots across characteristic concentration scales and uses multi-start Nelder-Mead for any remaining least-squares minima, then returns M / (1 + M). Each normalized exposure below 1e-5 is treated as zero. Consequently, the model reduces exactly to estimate_effect_2 when one site is absent and to the corresponding closed-form single-site equation when two sites are absent. Finite negative interaction parameters are valid and represent antagonism.

The exponent arguments are H_i = 1 / m_i, where m_i are the conventional Hill coefficients used in the source publication. Pairwise and three-way interaction exponents are therefore the arithmetic means of these reciprocal Hill coefficients.

Arguments

• a, b, c - Nonnegative finite normalized drug exposures.
• alpha12, alpha13, alpha23 - Finite pairwise interaction coefficients.
• alpha123 - Finite three-way interaction coefficient.
• h1, h2, h3 - Positive finite reciprocal Hill exponents H1, H2, and H3.

Returns

The effect M / (1 + M). Malformed inputs and search failures without a meaningful finite scalar return NaN. If no exact positive root exists, the best finite least-squares candidate found by the bounded log-space search is returned.

Example

use pharmsol::estimate_effect_3;

// With all exponents equal to one, M is the sum of all seven coefficients.
let effect = estimate_effect_3(1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0);
assert!((effect - 0.8).abs() < 1e-6);