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.
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.