An algorithm to approximate the distribution of fixed -response covariates in logistic regression using smoothing splines

We investigate the use of smoothing splines in logistic regression to estimate the distribution of covariate values that yield a fixed response probability, eg. LC50 or LD50. We develop an algorithm for a monotonic spline fit, approximate the distribution of the resulting probability estimates, and using a Bayesian approach approximate the distribution of the fixed-response covariates. We illustrate our algorithm on data sets from studies of genetic spatial diversity.