Returns the predictor value at which a binomial logit model reaches probability p (e.g. L50 for p = 0.5) with a 95% delta-method confidence interval.
Details
The estimate is \(x_p = (logit(p) - b_0) / b_1\). Its variance is approximated by the delta method, \(Var(x_p) = g^T V g\), where \(V\) is the variance-covariance matrix of the intercept and slope (vcov(model)) and \(g = (-1/b_1, -x_p/b_1)\) is the gradient of \(x_p\). The confidence interval is \(x_p \pm z_{0.975} SE\). This accounts for the (typically strong negative) correlation between intercept and slope and is equivalent to MASS::dose.p().