Create a Formula for the Richards Growth Model

set-up a Richards growth model formula to for use in growth_richards_model and in the BayesPharma package. The functional form is

response ~ richards_growth(K, K0, rate, lambda, nu, time)

The parameterization follows (Zwietering, 1990) and grofit:

K      = carrying capacity, K = response(time = Inf). The
         grofit package calls this parameter A. The K parameter has the
         same units as the response.
K0     = initial population size, K0 = response(time = 0). The
         grofit package assumes K0 = 0. The K0 parameter has the same
         units as the response.
rate   = maximum growth rate, rate = max[d(response)/d(time)]. The
         grofit package calls this mu. The rate parameter 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)). The lambda parameter has the
         units of time.
nu     = growth asymmetry before and after the inflection
         point. The nu parameter is unitless.

See the vignettes(topic = "derive_growth_model", package = "BayesPharma") for more details.

Usage

growth_richards_formula(
  treatment_variable = "time",
  treatment_units = "hours",
  response_variable = "response",
  response_units = NULL,
  predictors = 1,
  ...
)

Arguments

treatment_variable

character variable representing time as a treatment

treatment_units

character the units of the time variable

response_variable

character variable representing the response to treatment

response_units

character the units of the response

predictors

Additional formula objects to specify predictors of non-linear parameters. i.e. what perturbations/experimental differences should be modeled separately? (Default: 1) should a random effect be taken into consideration? i.e. cell number, plate number, etc.

...

additional arguments to brms::brmsformula()

Value

a bpformula, which is a subclass of brms::brmsformula() and can be passed to growth_richards_model().

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

See also

brms::brmsformula(), which this function wraps. growth_richards_model() into which the result of this function can be passed.

Examples

if (FALSE) { # \dontrun{
  # Data has a string column drug_id with drug identifiers
  # Fit a separate model for each drug
  BayesPharma::growth_richards_formula(predictors = 0 + drug_id)

  # Data has a string column plate_id with plate identifiers
  # Estimate the change in response for each plate relative to a global
  # baseline.
  BayesPharma::growth_richards_formula(predictors = plate_id)

  # data has columns drug_id and plate_id
  # fit a multilevel model where the drug effect depends on the plate
  BayesPharma::growth_richards_formula(predictors = 0 + (drug_id|plate_id))
} # }