Is it permissible for a medical student to participate in a scientific research study on the role of istibra' (purification after urination) in preventing prostate cancer, knowing that some scholars consider istibra' an innovation and not authentically reported from the Prophet (peace be upon him)?

Istibra' (purification/cleansing) is used in two senses: The first is purification from what exits from the two private parts, and the second is the cleansing of the womb from pregnancy. None of the scholars of Islam have ever stated that either of these is an innovation (bid'ah).

If, by istibra', you mean shaking or squeezing the penis after urination, some scholars have indeed mentioned that it is an innovation, while others have said that the ruling varies depending on the individual.

As for the cleansing of the womb from pregnancy, it is generally agreed upon by jurists, even though they differ on some of its forms, and whether it is obligatory or recommended.