Formal:
* As stated by...
* Based on...
* In the words of...
* As per...
* Pursuant to...
* Consistent with...
* In line with...
* As indicated by...
Informal:
* As [person/source] says...
* [Person/source] says...
* [Person/source] reports...
* [Person/source] claims...
* [Person/source] believes...
* [Person/source] suggests...
Other options:
* Based on evidence...
* From what I can tell...
* It seems that...
* I understand that...
* It appears that...
Example:
* Original: According to the doctor, you need to rest.
* Alternative: As the doctor says, you need to rest.
The best phrase to use will depend on the specific situation and the desired tone.