Patient Right to Independent Appeal Act of 1998 - Amends the Public Health Service Act and the Employee Retirement Income Security Act of 1974 to require a group health plan, and a health insurer offering group coverage, (and, for the Public Health Service Act, health coverage offered in the individual market) to provide for an external appeals process for certain adverse determinations if the denial or failure: (1) involves a determination that a treatment is experimental; (2) is based on a determination that services are not medically necessary and the amount is over a threshold; or (3) jeopardizes the patient's life or health. Requires that the appeal be conducted under a contract between the plan or issuer and one or more appeal entities unless: (1) for health insurance issuers, the State selects the appeal entity; or (2) for group health plans, the Secretary of Health and Human Services designates the appeal entity. Provides for certification of appeal entities.

Amends the Internal Revenue Code to require a group health plan to provide for an external appeals process for certain adverse determinations if the denial or failure: (1) involves a determination that a treatment is experimental; (2) is based on a determination that services are not medically necessary and the amount is over a threshold; or (3) jeopardizes the patient's life or health. Requires that the appeal be conducted under a contract between the plan or issuer and one or more appeal entities unless the Secretary of Health and Human Services designates the appeal entity. Provides for certification of appeal entities.

Authorizes the Secretary of Health and Human Services to apply this Act's requirements relating to the Public Health Service Act to entities offering coverage under titles XVIII (Medicare) and XIX (Medicaid) of the Social Security Act to the extent that such requirements provide greater protections for enrollees and do not conflict directly with requirements otherwise imposed by law.