Heartdoc -
The reference you cite implies that the Risk of complication from AntiCoagulation Therapy is Cumulative based on your example of multiplying a 2% risk by the number of years. You need to know that this a Mathematical IMPOSSIBILITY. Based on this calculation, with an initial risk of 2%, the annual risk would reach 100% in 50 years. At 51 years this calculated number would be 102%. There is NO SUCH THING as a 102% risk.
FYI, we have some members who have been taking Coumadin/Warfarin for Long Periods of time (30 and 43 years for two I am aware of) who have had NO Serious Bleeding Problems.
There are many examples of Bleeding Issues from AntiCoagulation Therapy that occurred in the Bad Old Days when Prothrombin Time was measured using Reagents that exhibited considerable variability in their characteristics. The INR (International Normalized Ratio) technique which was created in the early 1990's cancels out the reagent characteristics which reduced variability and improved ACT management considerably.
One of our members (Bradley White) who teaches (taught?) statistics at Notre Dame University wrote an explanation of the correct way to analyze the risk that a patient may have had ONE event over time. A copy of that post is reproduced below.
from
www.ValveReplacement.com - Valve Replacement Forum - 2007.2
thread: I'm only 24! - reply #35
Coumadin Risk is NOT Cumulative
QUOTE:
I cannot stress that when risk for ACT complications is given on a "per annum" basis it is not to be taken as cumulative. This is true of any statistic which is laid out as "the risk per patient year is X%". This is a quite basic principle in all biological sciences, especially medicine. I find it astounding that any surgeon would try to say the risk is cumulative!!!! It just makes no sense.
Scary how little medical professionels understand about basic statistics.
If risk were cumulative then that would imply at a risk rate of 3% at 35 years of anti-coagulation the risk would be greater than 100%. This simply isn't true or possible, it is not how statistics works. These risk events are always observed in patient years, one could not reasonable extract that data and attempt to add it up and say that after 35 years everyone would have had an event. That's simply not how statistics works. Anything whose risk is finite in a per year basis will never be 100% over any course of time. It will approach 100% but never reach it.
The cumulative nature of anti-coagulation risk is that every year there is a 3% risk. That means that every year there is a 97% chance of not having an event. As time goes on the chances that you won't have experienced an event decrease due to the recurring risk of 3% per year. You can calculate this risk by taking .97 and using the amount of years you are interested in as the exponent and then subtracting that number from 1 to figure out your chances of HAVING an event in X years:
I have made the following calculations based on a 1%, 2%, and 3% risk at 10 thrugh 50 years. The number represents the chances that you WOULD experience an event by this year if you were on ACT for mechanical valve.
AT THE 1% RISK LEVEL
10 YEARS = 9.6%
20 YEARS = 18.2%
30 YEARS = 26%
40 YEARS = 33.1%
50 YEARS = 39.5%
AT THE 2% RISK LEVEL
10 YEARS = 18.3%
20 YEARS = 33.2%
30 YEARS = 45.5%
40 YEARS = 55.4%
50 YEARS = 63.6%
AT THE 3% RISK LEVEL
10 YEARS = 26.2%
20 YEARS = 45.6%
30 YEARS = 59.9%
40 YEARS = 70.4%
50 YEARS = 78.2%
If anyone doesn't understand how I calculated those risks I can send them the excel file. The thing that stands out the most is the huge long term risk change when one goes from a 1% per annum event rate to a 3% per annum event rate. At 30 years, less than half of those at 3% per annum event rate will have not experienced an event, while at the 1% per annum event rate 74% of individuals should not have experience an event. This a significant reduction in the long term risk of anti-coagulation and represents the major medical reason why self-testing is such a huge advance since it has been shown to decrease the event rate from the 2-3% per annum category to around 1% per annum.
Trust me surgeons and doctors are not infallible, especially when it comes to math. I teach pre-med students a 300-level Fundamentals of Genetics course (decent working knowledge of statistics) at Nortre Dame and it scares me to death to think that some of them could one day be my doctor based on their complete incomprehension of statistics (among other things) at this point in their eduction.
Brad (a.k.a. Bradley White)
Ross Procedure, Dr. Quintessenza, All Children's Hospital, St. Petersburg, FL -- 9/12/2000
Aortic Root and Valve Replacement with 23 mm Homograft, Dr. Joseph Dearani, Mayo Clinic, Rochester, MN -- 12/7/2006
END QUOTE
