pkpd.Release (version 0.1.0)

sigmoid_imax: Sigmoid Imax (Inhibitory Hill Model) for Dose-Response Analysis

Description

Fits pharmacodynamic dose-response data to the inhibitory Hill (Sigmoid Imax) model using nonlinear least squares regression.

The inhibitory Hill model describes decreasing pharmacological effects with increasing dose (or concentration) according to:

$$ E = E_0 - \frac{I_{max} \cdot D^n}{IC_{50}^n + D^n} $$

An equivalent parameterization is:

$$ E = E_{min} + \frac{(E_0 - E_{min}) \cdot IC_{50}^n}{IC_{50}^n + D^n} $$

where \(E_0\) is the baseline response, \(I_{max}\) is the maximum inhibitory effect, \(IC_{50}\) is the dose producing 50 inhibition, and \(n\) is the Hill coefficient.

This model is appropriate when the observed response decreases monotonically with increasing dose.

Value

A list containing:

fitted_parameters

Data frame with E0, Imax, IC50, Hill coefficient (n), RMSE, AIC, and BIC values for each group.

data

The processed dataset used for model fitting and plotting.

Arguments

data

A data frame containing dose-response experimental data.

dose_col

Character string specifying the column name for dose or concentration.

response_col

Character string specifying the column name for measured response.

group_col

Optional character string specifying a column for grouping.

log_dose

Logical; if TRUE, dose values are log10-transformed for plotting (model fitting uses original dose values).

plot

Logical; if TRUE, generates a dose-response plot with fitted Hill curves.

annotate

Logical; if TRUE, annotates the plot with model parameters and fit metrics (only if <=1 group).

Author

Paul Angelo C. Manlapaz

References

Holford, N. H. G. & Sheiner, L. B. (1981) <doi:10.2165/00003088-198106060-00002> Understanding the dose-effect relationship. Clinical Pharmacokinetics, 6(6), 429–453.

Examples

# Example I: Single inhibitory dose-response dataset
df <- data.frame(
  dose = c(0.1, 0.3, 1, 3, 10, 30, 100),
  response = c(95, 90, 75, 45, 20, 8, 3)
)
sigmoid_imax(
  data = df,
  dose_col = "dose",
  response_col = "response"
)

# Example II: Two treatment groups (e.g., two inhibitors or conditions)
df2 <- data.frame(
  dose = rep(c(0.1, 0.3, 1, 3, 10, 30), 2),
  response = c(
    92, 85, 65, 40, 18, 7,    # Group A (stronger inhibitor)
    95, 88, 72, 50, 30, 15    # Group B (weaker inhibitor)
  ),
  treatment = rep(c("Group A", "Group B"), each = 6)
)
sigmoid_imax(
  data = df2,
  dose_col = "dose",
  response_col = "response",
  group_col = "treatment",
  log_dose = TRUE
)

# Example III: Multiple subjects (population-style inhibitory pharmacodynamics)
df_subjects <- data.frame(
  dose = rep(c(0.1, 0.3, 1, 3, 10, 30), 5),
  response = c(
    94, 86, 68, 42, 20, 9,    # Subject 1
    96, 88, 70, 45, 22, 10,   # Subject 2
    93, 84, 65, 40, 18, 8,    # Subject 3
    95, 87, 69, 44, 21, 9,    # Subject 4
    97, 89, 72, 48, 25, 12    # Subject 5
  ),
  subject = rep(paste0("S", 1:5), each = 6)
)
sigmoid_imax(
  data = df_subjects,
  dose_col = "dose",
  response_col = "response",
  group_col = "subject",
  log_dose = TRUE
)