Cumulative-response logistic model ($\mathrm{logit}(p_t)=x^T\beta +\gamma {\sum }_{s<t}{Y}_s$)

The accumulated number of previous successes may enter the conditional mean in a history-dependent logistic regression. Its coefficient exponentiates to the conditional success odds ratio per previous success. For a specified future path, update this cumulative predictor after each outcome before multiplying the conditional probabilities.