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==A coin puzzle==
==Renal denervation==
[http://wordplay.blogs.nytimes.com/2014/03/17/coin/?module=BlogPost-Title&version=Blog%20Main&contentCollection=Numberplay&action=Click&pgtype=Blogs&region=Body A coin problem]<br>
by Gary Antonik, Numberplay blog, ''New York Times'', 17 March 2014


The post begins with this simple problem, posed by Daniel Finkel:
[http://www.nytimes.com/2014/03/30/health/setback-for-promising-high-blood-pressure-treatment.html?hp&_r=0 Denise Grady] of the New York Times points out that
<blockquote>
<blockquote>
Consider this simple game: flip a fair coin twice. You win if you get two heads, and lose otherwise. It’s not hard to calculate that the chances of winning are 1/4… . Your challenge is to design a game, using only a fair coin, that you have a 1/3 chance of winning.
In the United States, 67 million people have high blood pressure, and it resists treatment [by drugs] in about 10 percent of them.
</blockquote>
</blockquote>
Finkel continues, "And here is my recipe for getting the most out of this problem: if you can solve it, do not stop with one answer. Rather, see how many answers you can come up with. I’ve posed this problem to many people, and I continue to hear novel solutions."


Here are three familiar solutions (I notice the these also turned up quickly in readers' comments to the ''NYT''!):
Thus, the interest in  
*  Toss the coin until the first head appears.  You win if this takes an even number of tosses
<blockquote>
*  Toss the coin twice.  You win on HH and lose on HT or TH.  If TT appears, ignore the result and make another two tosses.
 
*  Toss the coin until the first appearance of HTT or HHT on consecutive tosses.  You win HTT.
The treatment, called renal denervation, [which] involves threading a tube through blood vessels into the renal arteries, [and] then zapping them with radio-frequency energy to kill nerve endings.  
<br><br>
The procedure was thought to be a lifesaver for people whose high blood pressure could not be lowered even with multiple drugs. Uncontrolled hypertension increases the risk of strokes, heart attacks and other problems.
</blockquote>


The third is an instance of the game [http://en.wikipedia.org/wiki/Penney's_game Penney-Ante], invented by William Penney. It is a famous example of a non-transitive game:  whatever triple the first player chooses, the second can choose a triple that has a better than even chance of coming up first.  So if the you choose HTT, then second I will choose HHT, giving me a 2/3 chance of winning.
Previous “case reports and studies had found astounding drops in blood pressure after the [renal denervation] treatment — as much as 30 millimeters of mercury in systolic pressure, the top number in a blood pressure reading.”  Therefore, to the surprise of many, renal denervation [http://www.nejm.org/doi/pdf/10.1056/NEJMoa1402670
failed in a large, rigorous study].


But I was not aware, until searching for an online description of Penney-Ante, that there is a variation with cards, called the Humble-Nishiyama Randomness Game.  As described  [http://en.wikipedia.org/wiki/Penney's_game#Variation_with_playing_cards here]
Unlike earlier, unblinded studies, this so-called SYMPLICITY HTN-3 study was
<blockquote>
<blockquote>
At the start of a game each player decides on their three colour sequence for the whole game. The cards are then turned over one at a time and placed in a line, until one of the chosen triples appears. The winning player takes the upturned cards, having won that "trick". The game continues with the rest of the unused cards, with players collecting tricks as their triples come up, until all the cards in the pack have been used. The winner of the game is the player that has won the most tricks.
 
a prospective, single-blind, randomized, sham-controlled trial. Patients
with severe resistant hypertension were randomly assigned in a 2:1 ratio to undergo renal denervation or a sham procedure.
<br><br>
The primary efficacy end point was the change in office systolic blood pressure at 6 months; a secondary efficacy end point was the change in mean 24-hour ambulatory systolic blood pressure.
</blockquote>
</blockquote>
In this scenario, the advantage of choosing second is even greater.  For example, if the first player chooses BRR, the second should choose BBR.  Now there is only a 5.18% that the first player wins, and 88.29% chance that the second player wins, and a 6.53% chance of a draw (a full table is available at the above link).


'''Discussion'''<br>
From the figures below, it can be seen that the treatment (renal denervation) and the control (sham treatment) are virtually identical for the primary and secondary efficacy, respectively.  That is, for primary efficacy, the treatment failed to beat the control by at least 5 mm HG and for secondary efficacy, the treatment failed to beat the control by at least 2 mm Hg.
What other solutions can you come up with to Finkel's original puzzle?
 
 
 
 
 
 
 
 
 
 
===Discussion===
 
1.  Franz H. Messerli [http://www.nejm.org/doi/full/10.1056/NEJMe1402388?query=featured_home wrote an editorial in the NEJM] entitled “Renal Denervation for Resistant Hypertension?” in which he questioned the enthusiasm for the procedure.  It has not been approved in the United States but according to Grady,”it has been approved in more than 80 countries and performed on thousands of patients.”  She quotes Messerli as saying
<blockquote>
 
You have to perhaps congratulate the Food and Drug Administration that they were not as eager to approve this procedure based on the little evidence there was, as opposed to the Europeans and the Australians.
<br><br>
It [SYMPLICITY HTN-3] is absolutely a landmark study.  I hope it will have an impact and will override some of the zeal of the European investigators.
</blockquote>
 
2.  As indicated above, the (15) authors of the study regard “clinical (i.e., practical) significance” to be a primary superiority of at least 5 mm Hg or a secondary superiority of at least 2 mm Hg of the treatment over the control.  Neither was achieved but with the help of any convenient statistics software, use the numbers in Figure 1 and Figure 2 to show that “statistical” significance was also not achieved in either case for the respective differences between treatment and control.
 
3.  The study also looked at subgroups such as race, gender, age, etc. 
<blockquote>
 
Although the differences between groups in some subgroups were nominally significant, the absolute magnitude of the differences was small (<10 mm Hg), and the differences were not significant with the use of a superiority margin of 5 mm Hg or after adjustment for multiple comparisons.
</blockquote>
 
Which “significances” are being discussed here?
 
4.  Point out the similarities of a sham treatment to the use of a placebo when testing drugs.  Point out the differences between a sham treatment and a placebo.


Submitted by Bill Peterson
Submitted by Paul Alper

Revision as of 01:49, 8 April 2014

Renal denervation

Denise Grady of the New York Times points out that

In the United States, 67 million people have high blood pressure, and it resists treatment [by drugs] in about 10 percent of them.

Thus, the interest in

The treatment, called renal denervation, [which] involves threading a tube through blood vessels into the renal arteries, [and] then zapping them with radio-frequency energy to kill nerve endings.

The procedure was thought to be a lifesaver for people whose high blood pressure could not be lowered even with multiple drugs. Uncontrolled hypertension increases the risk of strokes, heart attacks and other problems.

Previous “case reports and studies had found astounding drops in blood pressure after the [renal denervation] treatment — as much as 30 millimeters of mercury in systolic pressure, the top number in a blood pressure reading.” Therefore, to the surprise of many, renal denervation [http://www.nejm.org/doi/pdf/10.1056/NEJMoa1402670 failed in a large, rigorous study].

Unlike earlier, unblinded studies, this so-called SYMPLICITY HTN-3 study was

a prospective, single-blind, randomized, sham-controlled trial. Patients with severe resistant hypertension were randomly assigned in a 2:1 ratio to undergo renal denervation or a sham procedure.

The primary efficacy end point was the change in office systolic blood pressure at 6 months; a secondary efficacy end point was the change in mean 24-hour ambulatory systolic blood pressure.

From the figures below, it can be seen that the treatment (renal denervation) and the control (sham treatment) are virtually identical for the primary and secondary efficacy, respectively. That is, for primary efficacy, the treatment failed to beat the control by at least 5 mm HG and for secondary efficacy, the treatment failed to beat the control by at least 2 mm Hg.







Discussion

1. Franz H. Messerli wrote an editorial in the NEJM entitled “Renal Denervation for Resistant Hypertension?” in which he questioned the enthusiasm for the procedure. It has not been approved in the United States but according to Grady,”it has been approved in more than 80 countries and performed on thousands of patients.” She quotes Messerli as saying

You have to perhaps congratulate the Food and Drug Administration that they were not as eager to approve this procedure based on the little evidence there was, as opposed to the Europeans and the Australians.

It [SYMPLICITY HTN-3] is absolutely a landmark study. I hope it will have an impact and will override some of the zeal of the European investigators.

2. As indicated above, the (15) authors of the study regard “clinical (i.e., practical) significance” to be a primary superiority of at least 5 mm Hg or a secondary superiority of at least 2 mm Hg of the treatment over the control. Neither was achieved but with the help of any convenient statistics software, use the numbers in Figure 1 and Figure 2 to show that “statistical” significance was also not achieved in either case for the respective differences between treatment and control.

3. The study also looked at subgroups such as race, gender, age, etc.

Although the differences between groups in some subgroups were nominally significant, the absolute magnitude of the differences was small (<10 mm Hg), and the differences were not significant with the use of a superiority margin of 5 mm Hg or after adjustment for multiple comparisons.

Which “significances” are being discussed here?

4. Point out the similarities of a sham treatment to the use of a placebo when testing drugs. Point out the differences between a sham treatment and a placebo.

Submitted by Paul Alper