sigmoid_hill_to_slope: Convert Hill to Slope Parameters a the Sigmoid Functional...

In maomlab/BayesPharma: Tools for Bayesian Analysis of Non-Linear Pharmacology Models

Convert Hill to Slope Parameters a the Sigmoid Functional Form

Description

The hill parameter controls the slope at the ac50 (slope) but the slope also depends on the top and bottom parameters. This helper function facilitates computing the slope from the parameters.

To prove the this function is correct, consider the derivative of the response of the sigmoid() function with respect to the log_dose:

  d(response)/d(log_dose) =
    hill * log(10) * (top - bottom) * 10 ^ ((ac50 - log_dose) * hill) /
    ((10 ^ ((ac50 - log_dose) * hill) + 1) ^ 2)

Evaluating this derivative at log_dose == ac50 simplifies the exponents:

  slope = hill * log(10) * (top - bottom) / (1 + 1) ^ 2)
        = hill * log(10) * (top - bottom) / 4

Usage

sigmoid_hill_to_slope(hill, top, bottom)

Arguments

hill	numeric the hill coefficient for the sigmoid() function.
top	numeric the top parameter for the sigmoid() function.
bottom	numeric the bottom parameter for the sigmoid() function.

Value

numeric the slope of the sigmoid() function at the ac50.

See Also

sigmoid() sigmoid_slope_to_hill()

maomlab/BayesPharma documentation built on Aug. 24, 2024, 8:45 a.m.