Confidence intervals for Emax regression model parameters

Computes profile likelihood confidence intervals for the model parameters. Profile likelihood intervals are generally preferred over Wald intervals in nonlinear settings because they do not assume the likelihood surface is quadratic near the estimates.

Usage

# S3 method for class 'emaxnls'
confint(
  object,
  parm = NULL,
  level = 0.95,
  back_transform = FALSE,
  simultaneous = FALSE,
  ...
)

Arguments

object: An emaxnls or emaxlogistic object
parm: A specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If parm = NULL, all parameters are considered.
level: The confidence level required
back_transform: Should log-scaled parameters (logEC50, logHill) be back-transformed to original scale?
simultaneous: If TRUE, return simultaneous (joint) Wald confidence intervals rather than the default profile likelihood intervals. Defaults to FALSE.
...: Ignored

Value

A matrix (or vector) with columns giving lower and upper confidence limits for each parameter. These will be labeled as (1-level)/2 and 1 - (1-level)/2 in % (by default 2.5% and 97.5%).

Details

By default, and when simultaneous = FALSE, this calls stats::confint.nls() for emaxnls objects. For emaxlogistic objects, the same profiling approach is applied to the final NLS fit from the IRLS algorithm at convergence. If profile likelihood computation fails (which can occur for sigmoidal models), a warning is issued and Wald intervals are returned instead.

When simultaneous = TRUE, a single critical value is derived from the joint multivariate normal distribution of the standardized parameter estimates (via mvtnorm::qmvnorm()). The resulting intervals have simultaneous coverage at level across all parameters and will be wider than the individual (pointwise) intervals. This matches the intervals produced by summary(object, simultaneous = TRUE).

Setting back_transform = TRUE exponentiates the confidence limits for logEC50 and logHill, expressing them on the concentration scale rather than the log-concentration scale on which they are estimated, and drops the log prefix from their row names.

Examples

mod_c <- 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)
)

# 95% confidence interval on the estimation scale
confint(mod_c)
#>                        2.5%      97.5%
#> E0_cnt_a          0.4634245  0.5088686
#> E0_Intercept      4.9055018  5.2041150
#> Emax_Intercept    9.7525268 10.1914700
#> logEC50_Intercept 8.1908985  8.3454640

# 90% confidence interval on the estimation scale
confint(mod_c, level = 0.9)
#>                          5%        95%
#> E0_cnt_a          0.4670913  0.5052018
#> E0_Intercept      4.9295962  5.1800202
#> Emax_Intercept    9.7872831 10.1553642
#> logEC50_Intercept 8.2035751  8.3331788

# 95% confidence interval with log-scale parameters back-transformed
confint(mod_c, back_transform = TRUE)
#>                        2.5%        97.5%
#> E0_cnt_a          0.4634245    0.5088686
#> E0_Intercept      4.9055018    5.2041150
#> Emax_Intercept    9.7525268   10.1914700
#> EC50_Intercept 3607.9625359 4211.0361735

# simultaneous (joint) confidence intervals
confint(mod_c, simultaneous = TRUE)
#>                        2.5%     97.5%
#> E0_cnt_a          0.4579834  0.514310
#> E0_Intercept      4.8697415  5.239874
#> Emax_Intercept    9.6975604 10.241890
#> logEC50_Intercept 8.1729527  8.364728

mod_b <- 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)
)
confint(mod_b)
#>                         2.5%      97.5%
#> E0_cnt_a           0.5014985  0.8160269
#> E0_Intercept      -6.1357553 -3.8667186
#> Emax_Intercept     5.0800762 17.6084133
#> logEC50_Intercept  8.8920970 11.0482722