Run sigmoidal Emax model fit with formula notation
Usage
stan_emax(
formula,
data,
gamma.fix = 1,
e0.fix = NULL,
emax.fix = NULL,
priors = NULL,
param.cov = NULL,
...
)Arguments
- formula
a symbolic description of variables for Emax model fit.
- data
an optional data frame containing the variables in the model.
- gamma.fix
a (positive) numeric or NULL to specify gamma (Hill coefficient) in the sigmoidal Emax model. If NULL, gamma will be estimated from the data. If numeric, gamma is fixed at the number provided. Default = 1 (normal Emax model).
- e0.fix
a numeric or NULL to specify E0 in the Emax model. If NULL, E0 will be estimated from the data. If numeric, E0 is fixed at the number provided. Default = NULL (estimate from the data).
- emax.fix
a numeric or NULL to specify Emax in the Emax model. If NULL, Emax will be estimated from the data. If numeric, Emax is fixed at the number provided. Default = NULL (estimate from the data).
- priors
a named list specifying priors of parameters (ec50, emax, e0, gamma, sigma). Each list item should be length 2 numeric vector, one corresponding to mean and another corresponding to standard deviation. Currently only supports normal distribution for priors.
- param.cov
a named list specifying categorical covariates on parameters (ec50, emax, e0). Convert a column into factor if specific order of covariates are needed.
- ...
Arguments passed to rstan::sampling (e.g. iter, chains).
Details
The following structure is used for the Emax model: $$Response = e_0 + e_{max} \times exposure ^{\gamma} / (ec50 ^{\gamma} + exposure ^ {\gamma}) + \epsilon$$ $$\epsilon \sim N(0, \sigma^2)$$
Examples
if (FALSE) { # \dontrun{
data(exposure.response.sample)
fit1 <- stan_emax(response ~ exposure,
data = exposure.response.sample,
# the next line is only to make the example go fast enough
chains = 1, iter = 500, seed = 12345
)
print(fit1)
# Set priors manually, also estimate gamma instead of the default of fix to 1
fit2 <- stan_emax(response ~ exposure,
data = exposure.response.sample, gamma.fix = NULL,
priors = list(
ec50 = c(100, 30), emax = c(100, 30), e0 = c(10, 5),
gamma = c(0, 3), sigma = c(0, 30)
),
# the next line is only to make the example go fast enough
chains = 1, iter = 500, seed = 12345
)
print(fit2)
data(exposure.response.sample.with.cov)
# Specify covariates
fit3 <- stan_emax(
formula = resp ~ conc, data = exposure.response.sample.with.cov,
param.cov = list(emax = "cov2", ec50 = "cov3", e0 = "cov1"),
# the next line is only to make the example go fast enough
chains = 1, iter = 500, seed = 12345
)
print(fit3)
} # }