pkpd.Release (version 0.1.0)

sigmoid_emax: Sigmoid Emax (Stimulatory Hill Model) for Dose-Response Analysis

Description

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

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

$$ E = E_0 + \frac{E_{max} \cdot D^n}{EC_{50}^n + D^n} $$

where \(E_0\) is the baseline effect, \(E_{max}\) is the maximum stimulatory effect, \(EC_{50}\) is the dose producing 50 \(E_{max}\), and \(n\) is the Hill coefficient.

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

Value

A list containing:

fitted_parameters

Data frame with E0, Emax, EC50, 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

Hill, A. V. (1910) The possible effects of the aggregation of the molecules of hæmoglobin on its dissociation curves. The Journal of Physiology, 40(4), iv–vii.

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 dose-response dataset
df <- data.frame(
  dose = c(0.1, 0.3, 1, 3, 10, 30, 100),
  response = c(5, 10, 25, 55, 80, 92, 98)
)
sigmoid_emax(
  data = df,
  dose_col = "dose",
  response_col = "response"
)

# Example II: Two treatment groups
df2 <- data.frame(
  dose = rep(c(0.1, 0.3, 1, 3, 10, 30), 2),
  response = c(
    3, 8, 20, 45, 70, 85,     # Group A
    2, 6, 15, 35, 60, 78      # Group B
  ),
  treatment = rep(c("Group A", "Group B"), each = 6)
)
sigmoid_emax(
  data = df2,
  dose_col = "dose",
  response_col = "response",
  group_col = "treatment",
  log_dose = TRUE
)

# Example III: Multiple subjects (population-style dose-response pharmacodynamics)
df_subjects <- data.frame(
  dose = rep(c(0.1, 0.3, 1, 3, 10, 30), 5),
  response = c(
    5, 13, 30, 56, 80, 92,   # Subject 1
    4, 12, 28, 54, 78, 90,   # Subject 2
    6, 15, 33, 59, 83, 95,   # Subject 3
    5, 14, 31, 57, 81, 93,   # Subject 4
    3, 11, 26, 52, 76, 88    # Subject 5
  ),
  subject = rep(paste0("S", 1:5), each = 6)
)
sigmoid_emax(
  data = df_subjects,
  dose_col = "dose",
  response_col = "response",
  group_col = "subject",
  log_dose = TRUE
)