Binary classification supervisor definition help I need help with defining the supervisor for a ML model.
Background: I’m predicting if a customer will respond positively to a marketing campaign. The response is a binary variable that I am given at each step of the campaign and a positive response stays positive for the remainder of the campaign, but negative can change to positive. The marketing campaigns are all similar (or the same) but some have different numbers of steps.
Current Approach: I’m looking at this on the customer level, specifically if the response to the most recent campaign step is 1 or 0. This supervisor definition obviously does not take into account the step number, or if the campaign is complete. Some customers have a 1 with one step completed, some are done with a campaign and still at a 0, others are halfway through and currently a 0.
Questions/Alternative Approaches:

*

*I’m wondering if I should instead build the supervisor based on response to the very first step of the campaign. Is that going to be a more accurate supervisor, since the number of outreach steps will be the same across the board? And then build a second model for positive response on step two for all who were negative on step one?


*Alternatively, I could build the supervisor based on completed campaigns. However, not all customers complete their campaigns and some switch campaigns halfway through. If I did this, I would use any data for the customer up to the time of the first marketing step. Any issues with this approach?


*Finally, I could take each step as a row where the supervisor is “will the customer respond positively to this step” (instead of “will the customer respond positively to this campaign”).
Sorry for so many questions. I work alone and would appreciate any feedback!
 A: This is equivalent to survival analysis, except that what in survival theory is called "death" would in your case be called "success of the campaign". Both types of problems have in common that you want to do regression/classification with the extra problem that trials might end prematurely. In survival analysis, those trials are called censored.
Survival analysis is not the easiest of all theories, but fortunately, there are good tutorials and even pretty good implementations of the simpler algorithms, e.g. here and here.
But maybe you are not interested in all the sophisticated results of survival analysis and wonder whether there is an easier way out. Let's fix some notation:
IIUC, you have a couple of features ($\mathbf{x}$) (covariates) that describe your individuals, and you have a binary response ($y$), telling you whether the campaign was successful ($y=0$ for failure, $y=1$ for success). Finally, define the binary random variable $d$, which is equal to the stage of the campaign before drop-out: E.g., if your campaign has three stages, then $d=1$ if the proband drops out after the first stage, and $d=3$ would mean proband didn't drop out. Then the most general situation would be the following causal graph:

Now, let's presume that you would be satisfied with the knowledge of the probability of campaign success for a given individual without regard to whether the individual dropped out or not. This would be the marginalization of d:
$$
p(y |\,\mathbf{x}) = \sum_{i=1}^{|d|} p(y, d=i|\,\mathbf{x}),
$$
where $|d|$ is the number of stages in the campaign. For you, this means you just use your complete dataset and just record for each test person whether there was a campaign success or not (you don't care whether there was early drop-out or not). This is a very reasonable thing to do.
On the other hand, you wondered in your OP whether it is a good idea to only consider those that don't drop out, i.e. to condition on $d=|d|$. Well, in case there is really an arrow going from $\mathbf{x}$ to $y$, this is not a good idea. Imagine the situation that because of some weird reason, those that don't drop out are exactly those on which the campaign never succeeds, while the campaign always succeeds on those that do drop out prematurely (the success is then before the drop-out). Conditioning on $d$:
$$
p(y\,|\,\mathbf{x}, d=|d|)
$$
is thus a very bad idea, provided this arrow from $\mathbf{x}$ to $d$ exists.
If, on the other hand, this arrow does not exist, the situation is fine, the random variable $d$ becomes a "good control", which is even likely to be helpful in improving precision. See for instance:

*

*Cinelli, Carlos, Andrew Forney, and Judea Pearl. "A crash course in good and bad controls." Available at SSRN 3689437 (2020).

Hopefully, your domain knowledge tells you whether $\mathbf{x}$ actually causally affects $d$. If that is not the case, you would have to figure this out from the data and/or special experiments, using methods of "causal discovery", which is again a completely different subject.
