There are accelerometers and then there are accelerometers. If all your are interested in measuring is Parkinson's 'resting tremors' you might be able to get by with a $5 3-axis accelerometer. On the other hand, if you are going to 'deep dive' into diagnosis of Parkinson's and for example test "tandem gait', which should include a measurement of posture, your going to need some a bit more sophisticated than a single accelerometer.
Now we will return to our normal programming..."Decide on what aspects of Parkinson's you are going to measure and make your design decisions based on that".
Here is a helpful reference: About PMC Labs - PMC
Caveat emptor! You can be buried in information from this source. A search for 'parkinson's diagnosis' yields 100686 articles. Far too many for one person to digest. I suggest you time limit your searches to the last 10 years. You will find others that have use 'modern technology' to diagnose PD.
Good luck
AMA