I'm not completely clear on the question. It sounds like you may have a supervised learning problem - you have a training set, and want to use that to predict which other stocks are likely to behave in a similar way. Alternatively, perhaps you want to know what your dependent variable really is? What does it mean to "fall early"? Which technique you use will largely be based on whether you're looking for a model which is most interpretable, or a model which is most predictive.
Given that it sounds like you know which stocks fell early (i.e. you know which category they belong to) then you could technically just use SVM for classification. This would allow you to find a maximally separating hyperplane in the feature space, and would probably be the most effective way to predict whether other stocks will behave the same way. LDA, logistic regression, neural networks, random forests can all create strong classifiers, but interpretability of the latter methods is low. If this is what you're looking for, then you can easily create a predictor, as you have known groups.
However, I think the main problem you're going to experience is that you haven't really specified your dependent variable well. You've mentioned that you know which group a variable falls into, but it sounds like you just want to use statistics to justify that decision - generally, that seems like bad practise. You can't use statistics to justify the assignment of a given subject to a group, that's a matter for logic.
Survival analysis would let you analyse the survival curve, but it would require you to set a point below the stock is considered "dead" to the analysis. That point will still be somewhat arbitrary. Because of that, perhaps the real dependent variable you want to analyse is actually some aspect of the price fluctuation following E, such as the volatility, derivative between t1 and t2 etc. Once you decide what you really want to predict, you'll have an easier time choosing the correct technique.
Because of that, I think you need to figure out what it means for a stock to "fall early". Logic is the best way, but if you want to handle things in an atheoretical, data driven way, the best way to do that may be:
- Generate a set of metrics (similar to the ones I mentioned, volatility, derivatives, second derivatives, over various periods)
- See which of those concrete mathematical measures are most correlated with this predefined group of stocks which "fell early".
For example, you might find that having an inflexion point (after smoothing the curve with some parameters) on days t+0 - t+2 was highly correlated with being in the "fell early" group. You may also want to make sure that the measures you're testing (eg. whether there was an inflexion point) are representing significant features in the data, or simply random variability. In pursuit of that goal, you may look to historical data to ascertain the probability that features of that magnitude appear regularly.