Polypharmacy, patients suffering with extremely many kinds of drugs for particular diseases, has been critical issues in aging society. It is not trivial to explore primary factors associated with polypharmacy because it requires huge amount of confidential personal healthcare data. In this study, we propose a new methodology applying local perturbation ensuring differential privacy to the healthcare data to identify risk factors in polypharmacy. With a large-scale, anonymized 390,000 health insurance claims for over-60-years-old individuals, we apply two-dimensional randomized responses to reveal relative risks of suffering polypharmacy for each of potential factors.