Question about opposite BETA directions in MTAG results when changing input file order

[shaoyu-nanjing]

Hello!

I have a question regarding the BETA directions in MTAG results when the order of input summary statistics files is swapped. Specifically:

I noticed that when I run MTAG with two traits (--sumstats A,B vs. --sumstats B,A), the BETA values for the same SNPs in the output files appear to have opposite signs.
After inspecting the results, it seems the direction of the BETA values is determined by the first input file. For example, when A is the first input file, the BETA values are consistent with the direction of effect in A. However, when B is the first input file, the BETA values appear to reverse their signs.

And I found this change does not affect the values, so I want to confirm:

Is this behavior expected in MTAG?
Does this sign change reflect a difference in the analysis, or is it solely a matter of how MTAG defines the effect allele direction based on the primary input file?
Are there any best practices to standardize the output direction for easier interpretation and downstream analysis?

Thank you for your help!