I have some data corresponding to changes in a binomial variable - i.e, in month 1 there were n1 trials and k1 successes, and in month 2 there were n2 trials and k2 successes. Say I have M of these cases, and in between month 1 and month 2 there were performed a number of different operations (so for case 1 we might have tried treatments a and b, and for case 2 b,c,and d), each of which could have increased or decreased the success rate. I would like to examine the effects of these treatments by regressing on the categorical covariates corresponding to the presence or absence of a,b,c,d,etc - what is the best way to go about this? I suppose I am looking for something analogous to a binomial ancova, but using change in the dependent variable.
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You are still looking for binomial regression. You have to rearrange the data so that each observation is one set of binomial trials (separately for pre- and post), adding a "time" and "subject" variable. The effect of "time" on the probability of success is like the pre-post difference (on the logit scale), its interactions with the type of treatment are the differential effects of each treatment. The model will need a subject effect as well to capture the baseline of each subject. This could be a fixed or random effect. You should also watch out for overdispersion, and use a quasi-binomial model.
If you don't understand the above, you might need to consult a statistician in real life - there is no simple solution to your problem, and it is easy to mess up.