We consider a situation in which a decision maker takes sequential and adaptive sensing actions to collect measurements and estimate an unknown parameter taking finitely many values, in the presence of an adversary who also collects measurements whenever a sensing action is taken. This situation can be viewed as an abstraction in which to analyze the mitigation of information leakage inherent to control actions in systems with feedback, such as cyber-physical systems. Specifically, we formulate an evasive active hypothesis problem in which the objective is for the decision maker to control the risk of its test while minimizing the detection ability of the adversary, measured in terms of the asymptotic error exponent ratio between the adversary and the decision maker. We develop bounds on the exponent ratio that offer insight into optimal strategies that the decision maker can deploy to evade the adversary's detection. We illustrate the results with a numerical example corresponding to the detection of a wireless transmission.