We have quasimultinomial model, which tries to fit all the growth advantages at once. There exists a simpler model, which targets only the proportion $p(t) = \frac{y_1(t)}{y_1(t) + y_0(t)}$ and estimates a growth advantage directly, using a two parameter model $p(t) = \mathrm{logit}^{-1}(g t - b)$.
Prepare the functions that: