pkpd.Release (version 0.1.0)

logistic_4pl: 4PL Logistic Dose-Response Model (Emax/Imax)

Description

Fits pharmacodynamic dose-response data to a 4-parameter logistic (4PL) model using nonlinear least squares regression.

The model can handle **both increasing (Stimulatory / Emax)** and **decreasing (Inhibitory / Imax)** dose-response curves automatically.

The 4PL model generalizes the Hill/Sigmoid model:

$$ E = E_{min} + \frac{E_{max} - E_{min}}{1 + (EC_{50} / D)^n} \quad \text{for increasing curves} $$

$$ E = E_{min} + \frac{E_{max} - E_{min}}{1 + (D / IC_{50})^n} \quad \text{for decreasing curves} $$

Key features: * Automatically detects increasing vs decreasing responses * \(E_{min}\) = minimum response (floor) * \(E_{max}\) = maximum response (ceiling) * \(EC_{50}/IC_{50}\) = dose producing half-maximal effect * \(n\) = Hill coefficient (steepness) * Symmetric sigmoid curve about midpoint

Value

A list containing:

fitted_parameters

Data frame with E_min, E_max, EC50, n, RMSE, AIC, and BIC for each group.

data

Processed data used for fitting and plotting.

Arguments

data

A data frame containing dose-response experimental data.

dose_col

Character string specifying the column name for dose.

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.

plot

Logical; if TRUE, generates a dose-response plot with fitted 4PL curves.

annotate

Logical; if TRUE, annotates the plot with model parameters and fit metrics.

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.

Finney, D. J. (1971) <isbn:9780521080415> Probit Analysis, 3rd Edition. Cambridge University Press, Cambridge.

Examples

# Example I: Single increasing curve (Emax)
df_emax <- data.frame(
  dose = c(0.1, 0.3, 1, 3, 10, 30, 100),
  response = c(5, 12, 28, 55, 75, 90, 98)
)
logistic_4pl(
  data = df_emax,
  dose_col = "dose",
  response_col = "response"
)

# Example II: Single decreasing curve (Imax)
df_imax <- data.frame(
  dose = c(0.1, 0.3, 1, 3, 10, 30, 100),
  response = c(95, 88, 70, 50, 30, 15, 5)
)
logistic_4pl(
  data = df_imax,
  dose_col = "dose",
  response_col = "response"
)

# Example III: Two treatment groups, mixed Emax/Imax
df_groups <- data.frame(
  dose = rep(c(0.1, 0.3, 1, 3, 10, 30), 2),
  response = c(
    4, 10, 25, 55, 78, 92,   # Group A: increasing (Emax)
    90, 75, 55, 35, 20, 10   # Group B: decreasing (Imax)
  ),
  treatment = rep(c("Group A", "Group B"), each = 6)
)
logistic_4pl(
  data = df_groups,
  dose_col = "dose",
  response_col = "response",
  group_col = "treatment",
  log_dose = TRUE
)