Estimate parameters for a logistic Emax regression model

Fits a logistic Emax regression model for a binary response variable using iterative reweighted least squares (IRLS). For continuous outcomes, use emax_nls() instead.

Usage

emax_logistic(
  structural_model,
  covariate_model,
  data,
  init = NULL,
  opts = NULL
)

Arguments

structural_model

A two-sided formula of the form response ~ exposure

covariate_model

A list of two-sided formulas, each specifying a covariate model for a structural parameter

data

A data frame that includes all relevant variables

init

Initial values and bounds for parameters. See emax_logistic_init()

opts

Model fitting and optimization options. See emax_logistic_options()

Value

An object of class emaxlogistic (which also inherits from emaxnls)

Details

The structural Emax model is placed on the log-odds (logit) scale:

logit(p) = E0 + Emax * x / (x + EC50) (hyperbolic)

logit(p) = E0 + Emax * x^h / (x^h + EC50^h) (sigmoidal)

Estimation uses iterative reweighted least squares (IRLS). At each outer iteration a weighted NLS problem is solved using working weights and a working response derived from the current parameter estimates. This is equivalent to Fisher scoring and produces maximum likelihood estimates at convergence.

The interface mirrors the emax_nls() function for continuous response models: the structural_model and covariate_model arguments have the same specification, including support for sigmoidal models via a logHill term. The response variable in structural_model must be a binary (0/1) numeric vector.

See also

emax_logistic_options(), emax_logistic_init(), emax_nls()

Examples

emax_logistic(
  structural_model = rsp_2 ~ exp_1,
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1),
  data = emax_df,
  opts = emax_logistic_options(max_time = 10)
)
#> Structural model:
#> 
#>   Exposure:       exp_1 
#>   Response:       rsp_2 
#>   Emax type:      hyperbolic 
#>   Response type:  binary (logit link)
#> 
#> Covariate model:
#> 
#>   E0:       E0 ~ cnt_a 
#>   Emax:     Emax ~ 1 
#>   logEC50:  logEC50 ~ 1 
#> 
#> Model fit:
#> 
#>   Observations:  400 
#>   Residual df:   396 
#>   Deviance:      331.4698 
#>   AIC:           339.4698 
#> 
#> Coefficients (95% CI):
#> 
#>   label             estimate std_error  lower  upper
#> 1 E0_cnt_a             0.659    0.0800  0.501  0.816
#> 2 E0_Intercept        -5.00     0.578  -6.14  -3.87 
#> 3 Emax_Intercept       8.12     2.27    5.08  17.6  
#> 4 logEC50_Intercept    9.78     0.518   8.89  11.0  
#> 
#> Use summary() for hypothesis tests.