pkpd.Release (version 0.1.0)

td50_model: Toxic Dose 50 (TD50) Pharmacodynamic Model

Description

Fits quantal toxicity response data to a logistic dose-response model to estimate the Toxic Dose 50 (TD50), defined as the dose producing toxicity in 50

The model uses binomial logistic regression and supports optional grouping (e.g., sex, species, formulation) and stratification by experimental conditions (e.g., exposure route).

In addition to TD50 estimation, the model provides the following interpretable parameters:

• Slope: Represents the steepness of the dose-response curve. A larger slope indicates a rapid increase in toxicity with small increases in dose (narrow tolerance or high population sensitivity), whereas a smaller slope reflects a more gradual response, suggesting greater inter-individual variability in susceptibility.

• Intercept: Represents the baseline log-odds of observing toxicity at zero dose. A strongly negative intercept indicates minimal background toxicity, while a positive intercept suggests appreciable toxicity in the absence of administered dose, which may indicate experimental bias or background risk.

• TD50 95% Confidence Interval: An approximate 95 interval for the TD50, computed using the delta method. This provides an uncertainty range around the estimated dose causing 50

• McFadden Pseudo-R\(^2\): A likelihood-based measure of model goodness-of-fit that quantifies how much better the fitted model explains the data compared to a null (intercept-only) model. Values between 0.1 and 0.2 indicate acceptable biological fit, while values above 0.3 suggest a strong and reliable dose-response relationship.

The function can generate dose-response plots with fitted curves and annotate TD50, slope, intercept, TD50 confidence intervals, and McFadden pseudo-R\(^2\).

Value

A list containing:

fitted_parameters

Data frame with TD50, 95 slope, intercept, and pseudo-R2 values for each group.

data

The processed data used for model fitting and plotting.

Arguments

data

A data frame containing toxicity response data.

dose_col

Character string specifying the dose column.

response_col

Character string specifying the binary toxicity response (0 = no toxicity, 1 = toxic response).

group_col

Optional character string specifying a grouping variable.

condition_col

Optional character string specifying an experimental condition.

plot

Logical; if TRUE, generates dose-response plots.

annotate

Logical; if TRUE, annotates the plot with TD50, confidence intervals, and model parameters (only if <=2 groups).

Author

Paul Angelo C. Manlapaz

References

Bliss, C. I. (1935) <doi:10.1111/j.1744-7348.1935.tb07713.x> The calculation of the dosage-mortality curve. Annals of Applied Biology, 22(1), 134–167.

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

Examples

# Example I: Single population toxicity study
df1 <- data.frame(
  dose = c(5, 10, 20, 40, 80, 160),
  toxic = c(0, 0, 0, 1, 1, 1)
)
td50_model(
  data = df1,
  dose_col = "dose",
  response_col = "toxic"
)

# Example II: Grouped analysis (Male vs Female)
df2 <- data.frame(
  dose = rep(c(5, 10, 20, 40, 80), 2),
  toxic = c(0,0,1,1,1, 0,0,0,1,1),
  sex = rep(c("Male","Female"), each = 5)
)
td50_model(
  data = df2,
  dose_col = "dose",
  response_col = "toxic",
  group_col = "sex"
)

# Example III: Grouped by formulation and exposure route
df3 <- data.frame(
  dose = rep(c(10, 25, 50, 100), 4),
  toxic = c(0,0,1,1, 0,1,1,1, 0,0,0,1, 0,0,1,1),
  formulation = rep(c("A","B"), each = 8),
  route = rep(c("Oral","IV"), each = 4, times = 2)
)
td50_model(
  data = df3,
  dose_col = "dose",
  response_col = "toxic",
  group_col = "formulation",
  condition_col = "route"
)