This is not a complete answer to your question, but it can be argued that each denomination has a doctrinal belief. Though there may be smaller denominations that have not officially organized nor written a catechism/doctrinal belief system, it makes sense that the beliefs in common of people taking part of the community actually do subscribe to a "doctrine."
Wikipedia's definition of doctrine offers a hint to this thinking:
Often doctrine specifically connotes a corpus of religious dogma as it is promulgated by a church, but not necessarily: doctrine is also used to refer to a principle of law, in the common law traditions, established through a history of past decisions, such as the doctrine of self-defense, or the principle of fair use, or the more narrowly applicable first-sale doctrine. In some organizations, doctrine is simply defined as "that which is taught", in other words the basis for institutional teaching of its personnel internal ways of doing business. - Wikipedia, "Doctrine"
Catechism points to belief, explaining what is believed. Peter writes that it's important that we have a reason for what we believe:
"... in your hearts honor Christ the Lord as holy, always being prepared to make a defense to anyone who asks you for a reason for the hope that is in you; yet do it with gentleness and respect" 1 Peter 3:15
Hope this is helpful.