How can I refactor this elixir code

Extracting the case statement to a function would also mandate that function have 2 parameters: participant and user_id. And since your case statement is only 5 lines long I don’t think the extraction would make the code better in any way.

I think the code is fine. Do always run mix format though, I’d write DateTime.utc_now() and not DateTime.utc_now – always put parentheses even when calling functions without an argument.

I’d split it into few more specific functions so that each of them does less and has less variables, something like this:

def start_conversation(chat_id, user_id, %{gender: "female", user_id: participant_user_id}) do
  create_conversation(chat_id, participant_user_id, user_id)
end

def start_conversation(chat_id, user_id, %{gender: "male", user_id: participant_user_id}) do
  create_conversation(chat_id, user_id, participant_user_id)
end

defp create_conversation(chat_id, first_user_id, second_user_id) do  
  Db.Conversation.create(%{
      chat_id: chat_id,
      start_time: DateTime.utc_now,
      first_user_id: first_user_id,
      second_user_id: second_user_id
    })
end