The Sardinian Pika (Prolagus sardus), used to live on the islands of Sardinia and Corsica. It was bigger than a rabbit and slightly smaller than a Pika. This genus evolved on these islands and like other such species was not very numerous to begin with.
However, with the coming of the Romans, and the introduction of predators followed by rabbits and rodents, the Pika went extinct during Roman times. Polybius in his “Histories” describes it as looking like a hare from afar but when captured, looking and tasting (emphasis mine) different. So the Romans killed off more than some Gauls and Goths during Pax Romana.
In all seriousness, the amount of damage that can be done through introduction of foreign fauna, particularly on island species, is catastrophic. Tales abound of such behavior by humans. Some is inadvertent, other instances can be downright malicious or just plain stupid. For example, the introduction of rabbits in Australia, with foxes to follow them. Also, the introduction of red deer in New Zealand for hunting. When such introduced species find no predators and a comfortable niche, their populations shoot up and they literally elbow aside less resilient species.
Such is what happened to the Sardinian Pika. Some natives talk of hold-outs in outer islands until the 17th century but that is mostly conjecture. The little animal is undoubtedly extinct.