Usage of prepositional Phrase as adverb

[engineer.sunil]

Source: Aristotle SC question Bank

The scientists noted that rats suffering from the rare degenerative disease had begun to die six months earlier, even though they had shown no signs of the disease then.
(A) earlier, even though they had shown no signs of the disease then
(B) earlier, but they were not showing no signs of the disease then
(C) earlier, no outward signs of the disease had been shown in them, however
(D) earlier without any signs of the disease shown then
(E) earlier, even though no signs of it were seen in them at that time

Experts, please advice why option D is incorrect? Isn't prepositional phrase "without any signs of the disease shown then" modifying "to die" and referring to "rats"?

Please explain the usage of prepositional phrase as adverb with example.

[jnelson0612]

Source: Aristotle SC question Bank

The scientists noted that rats suffering from the rare degenerative disease had begun to die six months earlier, even though they had shown no signs of the disease then.
(A) earlier, even though they had shown no signs of the disease then
(B) earlier, but they were not showing no signs of the disease then
(C) earlier, no outward signs of the disease had been shown in them, however
(D) earlier without any signs of the disease shown then
(E) earlier, even though no signs of it were seen in them at that time

Experts, please advice why option D is incorrect? Isn't prepositional phrase "without any signs of the disease shown then" modifying "to die" and referring to "rats"?

Please explain the usage of prepositional phrase as adverb with example.

I don't like D because it says "disease shown then", indicating that the disease was shown. This directly contradicts the sentence's point that the mice died without any sign of the disease. I think D has a major meaning issue.