There are several key pieces of evidence in a long-term disability claim that will be reviewed by the insurance adjuster handling your case.
First and foremost is your medical records. That's the most important part of your case. Those medical records will determine the full extent and severity of your medical conditions to support the case.
Second, the insurance company may ask for forms to be filled out by your doctor, called Attending Physician Statements. You can either use the insurance company's form or you can use a custom form, such as the forms we use in our office, but the purpose of these forms is to identify the extent and severity of your condition, not just what you have, but how it limits you.
Third, the insurance company may have your file reviewed by one of their doctors where their doctor will review your medical records and give their opinion about what your limitations are.
Some other types of evidence that might be considered are social media profiles and posts, an interview with you where the insurance adjuster will interview you about your limitations, but those are the key pieces of evidence that are used in a disability case.