Compute parameters for logistic dose toxicity model

Usage

Find_AB(dose_vec, prob_vec, ref_dose, logb = FALSE)

Arguments

dose_vec: a length-2 numeric vector giving the doses
prob_vec: a length-2 numeric vector giving the DLT probability of the dose_vec
ref_dose: a numeric scalar, the reference dose.
logb: boolean, whether to return log(b) or b in original scale. Refer to details for more information about the model settings

Value

A length-2 numerical vector c(a, b) for the logistic toxicity model. Or c(a, log(b)) if logb is set to TRUE.

Details

Denote p the DLT probability and the logistic model is assumed to be

$$logit(p) = a + b * log(d / ref\_dose),$$

where

$$logit(p) = log(p / (1 - p)).$$

Therefore, given two doses (ds) in dose_vec, there corresponding DLT probabilities (ps) in prob_vec and the reference dose ref_dose, we can solve for a and b.

In BLRM, a bivariate-normal assumption is assumed for $(a, log(b))$. And different tools may uses different parameterization of the model. By changing the values of logb, one can control what this function returns about b, either in original scale, or log(b).

Examples

ref_dose <- 300
dose_vec <- c(0.15, ref_dose)
prob_vec <- c(0.01, 0.20)

Find_AB(dose_vec, prob_vec, ref_dose)
#> [1] -1.3862944  0.4221638

Find_AB(dose_vec, prob_vec, ref_dose, logb = TRUE)
#> [1] -1.386294 -0.862362