growth_richards: Richards growth function

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

Richards growth function

Description

Functional form for the Richards growth model.

response(time) =
  K0 + (K - K0)/(
    1 + nu * exp(
      1 + nu + rate/(K - K0) * (1 + nu)^(1 + 1/nu) *
      (lambda - time))) ^ (1/nu)

The parameterization follows (Zwietering, 1990) and grofit:

K      = **carrying capacity**, `K = response(time = Inf)`. The
         \pkg{grofit} package calls this parameter `A`. `K` has the same
         units as the `response`.
K0     = **initial population size** `K0 = response(time = 0)`. The
         \pkg{grofit} package assumes `K0=0`. `K0` has the same units as
         the `response`.
rate   = **maximum growth rate** `rate = max[d(response)/d(time)]`. The
         \pkg{grofit} package calls this `mu`. `rate` has the units of
         `response/time`
lambda = **duration of the lag-phase** the time point at which the
         tangent through the growth curve when it achieves the maximum
         growth rate crosses the initial population size `K0`. (see
         Figure 2 in (Kahm et al., 2010)).
nu     = **growth asymmetry** before and after the inflection

Usage

growth_richards(K, K0, rate, lambda, nu, time)

Arguments

K	numeric the carrying capacity
K0	numeric the baseline response
rate	numeric the maximum growth rate
lambda	numeric duration of the lag-phase
nu	numeric growth asymmetry before and after the inflection point
time	numeric time point at which to evaluate the response

Value

numeric response given the time and parameters

References

Zwietering M. H., Jongenburger I., Rombouts F. M., van 't Riet K., (1990) Modeling of the Bacterial Growth Curve. Appl. Environ. Microbiol., 56(6), 1875-1881 https://doi.org/10.1128/aem.56.6.1875-1881.1990

Kahm, M., Hasenbrink, G., Lichtenberg-Fraté, H., Ludwig, J., & Kschischo, M. (2010). grofit: Fitting Biological Growth Curves with R. J. Stat. Softw., 33(7), 1–21. https://doi.org/10.18637/jss.v033.i07

Examples

## Not run: 
 # Generate Richards growth curve
 data <- data.frame(
   time = seq(0, 2, length.out = 101)) |>
     dplyr::mutate(
       response = stats::rnorm(
         n = length(time),
         mean = BayesPharma::growth_richards(
           K = 1,
           K0 = 0,
           rate = 2,
           lambda = 0.5,
           nu = 2,
           time = time),
       sd = .2))

## End(Not run)

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