How to politely describe a situation where you have no publication because both you and the advisor are inexperienced in a new research topic? How to politely describe a situation where you have no publication because both you and the advisor are inexperienced in a new research topic?


The lab previously only did research on topic A (e.g. protein factors) and lacked the experimental conditions for conducting research on topic B (e.g. circular RNAs), which is a very hot topic recently. BTW, which word should be used? topic, subject, field or area? 
The student is the first and only one that conducted the project on the new topic.
The student started from scratch and faced many difficulties. The advisor was willing to but sometimes powerless to help when the student got stuck. 
However, there is no publication after several years, since both the student and the advisor lack experience in the new research topic. 


I do not know how to politely describe such situation from two distinct perspectives：


From my advisor’s perspective: I requested my advisor a letter of recommendation for PhD application. He suggested that I write a draft first. 
From my perspective: I need to describe it in my personal statement.


However, I do not know how to politely describe such situation and meanwhile let the reviewer understand why I have no publication on this topic. Also, I am afraid my PS and the ROL draft would make him seem inexperienced in the new field or look like that I’m blaming him, which is rude and arrogant.
I suspect the answer for this strongly depends on cultural context.  My answer is for applications to PhD programs in the US (and probably Canada also), but it may not hold for other countries.

In the US, it's not expected that every student going into a PhD program has written a paper.  (In some subjects, almost no students entering a PhD program has written a paper.)  Your advisor should simply not mention that you haven't written a paper, but explain what you have done successfully (and there are other notions of success than writing a paper!), and what positive character attributes you have that lead him to believe you will be a successful PhD student.  It will be necessary to go into details of your project, but no mention needs to be made about the lack of a paper coming out.

You should have a similar approach in your personal statement, emphasizing what you learned from your research project and your coursework and explaining what research you want to work on for your PhD.

The PhD program will be admitting you as a person, not your package of previous accomplishments (although of course your previous accomplishments will tell them something about you as a person).