Authorship for design and data analysis
This sound like a classic case of clinician-statistician interaction. Both sides tend to under-appreciate the contribution of the other, and conflicts like this happen a lot. For the future, the lesson is to discuss authorship as early as possible when engaging on any projects.
For now, I'd add two things to consider:

Even assuming that the entire intellectual contribution so far has come from you, the other postdoc would not be entirely freeloading. The first author has a lot of responsibilities, such as deciding on the overall presentation, writing the manuscript, presenting the results in conferences, responding to reviews etc., and I personally think that is a significant intellectual effort. It may be unfair that you were passed over, but in the end the other person will still have to put in a lot of intellectual work, while you are free to move on to other projects.

Ask yourself if your analysis method is a sufficiently strong advance to stand as a publication on its own, i.e. could you write a methods paper using some simulated or publicly-available data. If so, pitch that to your PI, along the lines of &quot;I believe I have found some more general methods to improve PET data analysis, and I would like to write that up with a technical focus, in an appropriate journal. By the way, this won't actually need [other postdoc]'s data&quot;. The PI will surely see the cause of this, but as long you're being honest and tactful, nobody should be offended, and whatever the outcome, this should help all parties understand each other's contribution better.