I would like to study the effectiveness of counterterrorism strategies and I would like to know whether there is any quantitative and empirical method to do it.
As far as I know, there are no quantitative or empirical methods that are specific to the subject area described. Or in other words: If the available data allow it and if it makes sense in the face of the research question, regression oder correlation analysis, ANOVA etc. can be used because these tools are not restricted to specific content. A fundamentally important question for the selection of methods is whether the research should be exploratory or confirmatory resp. whether you have hypotheses or not. Many greetings, Axel Faix
beyond what Axel said: You have to be more specific. What's the data that you can generate or use? If you are using secondary data, perhaps a interrupted time series design would be possible in which you have a substantial series of one or more outcome variables repeatedly measured before the strategies started and after that. The strength of the design--among others--depends on whether there was a clear onset of the strategies as this should lead to a structural break. Optimally you would gather this data on a comparable region/country, in which no strategies were implemented--with "comparable" meaning with regard to terrorism-determining variables.