I am running a piecewise logistic model to generate the survival curves of students not dropping out of school. The model-based probabilities are something like
$$ p_1=P(\texttt{dropping out at }t=1) \\ p_2=P(\texttt{dropping out at }t=2) \\ \ldots $$
Once I have those, I am interested in $P(\texttt{not dropping out at }t=6)$ which I am calculating as:
$$ (1-p_1)(1-p_2)...(1-p_6) $$
I do this for different student profiles and now I am interested in calculating the significance of the difference between the two profiles. I can get the p-value of say two students one of profile A and one B who both dropped out in a given time/grade, but is there a way with the info I have to get the significance of the difference between the two profiles who did NOT drop out in say $t=4$?
