Estimate parameters for an Emax regression model

Fits an Emax regression model for a continuous response variable using nonlinear least squares. For binary outcomes, use emax_logistic() instead.

Usage

emax_nls(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_nls_init()
opts: Model fitting and optimization options. See emax_nls_options()

Value

An object of class emaxnls

Details

Pass a two-sided formula to structural_model to specify the response and exposure variables (e.g., response ~ exposure), and a list of formulas to covariate_model to specify covariates. At a minimum the covariate model requires formulas for E0, Emax, and logEC50. A formula like E0 ~ age + group includes age and group as covariates on the baseline response; use Emax ~ 1 when no covariates are to be added for a parameter.

To fit a sigmoidal Emax model (estimating the Hill parameter), include a formula for logHill in covariate_model, e.g. logHill ~ 1. Without this term a hyperbolic model is fitted. Interaction terms in the covariate model are not currently supported.

Starting values are constructed automatically via emax_nls_init() unless the init argument is supplied manually. Three optimization algorithms are available; see emax_nls_options() for details.

Examples

emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df,
  opts = emax_nls_options(max_time = 10)
)
#> Structural model:
#> 
#>   Exposure:       exp_1 
#>   Response:       rsp_1 
#>   Emax type:      hyperbolic 
#>   Response type:  continuous
#> 
#> Covariate model:
#> 
#>   E0:       E0 ~ cnt_a 
#>   Emax:     Emax ~ 1 
#>   logEC50:  logEC50 ~ 1 
#> 
#> Model fit:
#> 
#>   Observations:         400 
#>   Residual df:          396 
#>   Residual std. error:  0.5108 
#>   AIC:                  603.6431 
#> 
#> Coefficients (95% CI):
#> 
#>   label             estimate std_error lower  upper
#> 1 E0_cnt_a             0.486    0.0116 0.463  0.509
#> 2 E0_Intercept         5.05     0.0759 4.91   5.20 
#> 3 Emax_Intercept       9.97     0.112  9.75  10.2  
#> 4 logEC50_Intercept    8.27     0.0394 8.19   8.35 
#> 
#> Use summary() for hypothesis tests.