Medicare and other third party payers pay have specific rules for paying physicians of the same specialty in a group.  Here is what the Medicare Claims Processing Manual says:

30.6.5 - Physicians in Group Practice
(Rev. 1, 10-01-03)
Physicians in the same group practice who are in the same specialty must bill and be paid
as though they were a single physician.  If more than one evaluation and management
(face-to-face) service is provided on the same day to the same patient by the same
physician or more than one physician in the same specialty in the same group, only one
evaluation and management service may be reported unless the evaluation and
management services are for unrelated problems.  Instead of billing separately, the
physicians should select a level of service representative of the combined visits and
submit the appropriate code for that level.
Physicians in the same group practice but who are in different specialties may bill and be
paid without regard to their membership in the same group.

This definition is important when considering whether a patient is new or established, and whether or not a second subsequent hospital visit is payable.  The two important factors are specialty and group membership.

When a physician enrolls with Medicare or a private insurance plan, the two digit specialty code of the physician is submitted.  There are about 40 specialty designations defined by Medicare.  Some subspecialties (Orthopedics with a subspecialty in spine, for example) are not considered specialties by Medicare.  Even with fellowship training in a specific area, such as sleep medicine, the specialty designation will remain the same.  Why does that matter?  A patient seen by Pulmonologist, whose care is transferred to another Pulmonary Physician in the same group with a specialty in sleep, is an established patient, not a new patient.  Both the physicians have the same specialty designation.  It is important to know the specialty designation for all physicians when submitting claims.