CEA numbers frighten me... needlessly! (aka, looking at the world from the patient's perspective)

Apologies - this is a long, and at times technical post - but it represents, for me at least, a really classic example of the challenge the doctors face in being "patient centric"; one of my biggest interests in the management of serious illness by the medical professions. 

 In summary -

• If a key "wellness marker" in a healthy person is a "2", and cancer patients aspire to a "20", then if my marker is "500", then that's frightening and, more importantly, appears to be quite misleading.  
• But if a different numbering scheme (such as is used for deciBels and the Richter Scale) were used, these marker values would be a "3", "13" and "27" - far less daunting, and a much better indication of reality.

But before getting into detail, let me explain why this is of such interest to me.  Consider three points of view - those of:

1. The Oncologist - whose primary focus is on the cancer and its treatment regime (with a fair amount of interest in the physiological impact that has on the patient).
2. The Chemo-nurse - whose primary interests include the readiness of the patient's physiology to take that regime, as well as their real-time and between-times state of health and the management of these "side effects".
3. The Patient - whose many interests include an understanding of "how am I doing?  Am I getting better or worse, and can I cope with more?"

Notice the difference between the "outside-in" centric viewpoints in the first two cases, but the "inside-out" emphasis of the third...  This is starkly exemplified by the way the CEA number is presented:  while the professionals understand the underlying meaning of the number itself without any "emotional baggage" about the absolute values, the patient just sees "500!!!!".  We need some way of retaining the number's meaning for the Oncologist and Nurse, while easing the nerves of the patient...

 The Detail -

The CEA number is one of the markers used to determine the activity level of colon cancer.  While it is never used in isolation by the medical staff - and anyway they are far more interested in its change than absolute value - it can be hugely "influential" on the patient as an easy way of comparing notes with other patients, as well as their own "level of illness".

  This next part is for anyone with an interest in maths.. and that means you!!!!

It seems that the CEA number, unlike almost all of the other numbers we get to tell us "how we're doing" is not what mathematicians call an arithmetic progression, but closer to a geometric progression.  In other words, most other "markers" and indicators change in a simple way - the difference in significance between a "2" and  a "3" is the same as between a "12" and a "13", or a "72" and a "73".  Therefore if my number is 12 and yours is 2, we can say we're "pretty much the same" (the difference is only 10) whereas the difference between 12 and 72 is "massive" (a whopping 60!!)

But geometric progressions are different - the numeric gap between successive values gets bigger and bigger, rather than staying constant.  And the CEA number seems to be one of these geometric progressions - as it gets bigger, the gap also gets bigger between "significant numbers", meaning the impact of a change from "2" to "3" (1.5 times bigger) is the same as a change from 20 to 30 or from 200 to 300.

  OK - you can start reading again...

A "good" CEA value is a 2 or a 3 - that'll be your number.  An acceptable target for a cancer patient is in the 10's.  But mine was 900 two weeks' ago!!!!  Oh boy, that's BIG!!!!  It's now 500, and all the professionals are delighted.  But 900!!!! even 500!!! when the target is 20-50!!!!  Oh crikey!!!!

The CEA number does not work like that - it seems the number "runs away from you" as it gets bigger - hence the "ease" with which a huge chunk (400) was lopped off my number in just 14 days (and of course, in much the same way, it can increase in a frightening way in the first place).  In other words, it just so happens that the difference between your level of a "2" and my target of say "20" is the same as me getting from "200" to "20", or "500" to "50" - each bigger number is 10 times the smaller one.

Which can of course instil a false sense of the challenge - "only another 450 to go (500 to 50), and I managed 400 in a fortnight!".  The reality is that getting from a 900 to a 500 has a difficulty of, say 1.8 (900/500), whereas 500 to 50 has a difficulty of 10 (500/50) - which is why one inevitably fails to see a "constant improvement" and feels depressed as a consequence...

Is there a different way, which would still satisfy the medics as well as not frightening me?

YES!!! It's to adopt the same approach as is used for other similarly behaved measurements, such the strength of an earthquake (the Richter Scale) or deciBels, as used in audio and electronic systems

 OK, more maths...
The trick is to use a logarithmic scale, in which the absolute number ("2", "20" or "900") is converted to it's "log-base-10" value. For example a "20" becomes 1.3.  If the same convention is then used as for deciBels, we'd refine this to a "13".
   You can start reading again...

In this approach, a "2" becomes 3, a "20" is 13, "500" is 27 and "900" 29.  This instantly does two things:

• It's less frightening - if my target is 13, which is a whole 10 higher than a healthy 3, then getting from 27 to 13 is about the same "gap", and therefore I feel happier that I need "only get half way" to the healthy number.
  
  
• It presents a more accurate representation of the number's meaning - the reduction from 29 to 27 seems to be is a more realistic representation of my recent "improvement", without giving false hope of "getting to 13 in two weeks" - rather, if it were at all possible to achieve to a smooth trajectory downwards, then three months might be more reasonable... not that cancer is ever reasonable!