Let’s analyze the terms:
- Nephrology is the study of kidneys.
- Astrology is the study of stars and planets (it is not a medical science).
- Pathology is the study of diseases.
- Mycology is the study of fungi.
Among these, Astrology is different because it is not a medical science, unlike the other fields (Nephrology, Pathology, and Mycology), which are branches of biology or medicine.
Thus, Astrologyis the odd one out.
Therefore, the correct answer is \( \boxed{2} \).