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Disc Fragments
 
  
The dream of every clinical trial is to come up with something which is inexpensive, definitive and likely to result in media publicity.  “Improved outcome after lumbar microdiscectomy in patients shown their excised disc fragments: a prospective, double blind, randomized, controlled trial” by M.J. Tait, et al [http://www.ncbi.nlm.nih.gov/pubmed/19684238 here] fulfills the desire. 
 
 
According to local Twin Cities website with the heading, [http://www.minnpost.com/healthblog/2009/09/03/11307/seeing_it_appears_is_believing_when_it_comes_to_back_surgery Seeing, it appears, is believing when it comes to back surgery]: “British surgeons report that patients who underwent a surgical procedure (lumbar microdiscectomy) for back pain caused by a spinal disc tear (“slipped disc”) had better outcomes when they received fragments of their removed disc after the operation.  That’s right. Simply taking home a souvenir of the operation in a pot of saline solution improved the patients’ recovery. They reported less leg and back pain, less leg weakness and less “pins and needles” sensations (paresthesia). They also took fewer pain medications after the surgery.”
 
  
The surgeons “said they decided to do the study for two main reasons: They knew that a patient’s anxiety and depression going into surgery for a spinal disc tear has a big impact on the recovery process. They had also noticed, anecdotally, that many of their patients who responded best to the surgery — and who seemed to experience the least anxiety and depression afterwards — were those who had been given their disc fragments.”
+
==Forsooth==
  
The abstract of the journal article notes low p-values to make their case “that presenting the removed disc material to patients after LMD improves patient outcome.”:
+
==Quotations==
 +
“We know that people tend to overestimate the frequency of well-publicized, spectacular
 +
events compared with more commonplace ones; this is a well-understood phenomenon in
 +
the literature of risk assessment and leads to the truism that when statistics plays folklore,
 +
folklore always wins in a rout.”
 +
<div align=right>-- Donald Kennedy (former president of Stanford University), ''Academic Duty'', Harvard University Press, 1997, p.17</div>
  
Lumbar microdiscectomy (LMD) is a commonly performed neurosurgical procedure. We set up a prospective, double blind, randomised, controlled trial to test the hypothesis that presenting the removed disc material to patients after LMD improves patient outcome. METHODS: Adult patients undergoing LMD for radiculopathy caused by a prolapsed intervertebral disc were randomised into one of two groups, termed experimental and control. Patients in the experimental group were given their removed disc fragments whereas patients in the control group were not. Patients were unaware of the trial hypothesis and investigators were blinded to patient group allocation. Outcome was assessed between 3 and 6 months after LMD. Primary outcome measures were the degree of improvement in sciatica and back pain reported by the patients. Secondary outcome measures were the degree of improvement in leg weakness, paraesthesia, numbness, walking distance and use of analgesia reported by the patients. RESULTS: Data from 38 patients in the experimental group and 36 patients in the control group were analysed. The two groups were matched for age, sex and preoperative symptoms. More patients in the experimental compared with the control group reported improvements in leg pain (91.5 vs 80.4%; p<0.05), back pain (86.1 vs 75.0%; p<0.05), limb weakness (90.5 vs 56.3%; p<0.02), paraesthesia (88 vs 61.9%; p<0.05) and reduced analgesic use (92.1 vs 69.4%; p<0.02) than preoperatively. CONCLUSION: Presentation of excised disc fragments is a cheap and effective way to improve outcome after LMD.
+
----
  
The entire paper is only three pages in length and so its calculations can be checked. Below are the calculation results for the three secondary outcomes for which the paper claims statistical significance:
+
"Using scientific language and measurement doesn’t prevent a researcher from conducting flawed experiments and drawing wrong conclusions — especially when they confirm preconceptions."
  
1.  Improved Leg Weakness--the paper states that the p-value is less that .02.  Minitab shows that the p-value from Fisher’s exact test is .024.
+
<div align=right>-- Blaise Agüera y Arcas, Margaret Mitchell and Alexander Todoorov, quoted in: The racist history behind facial recognition, ''New York Times'', 10 July 2019</div>
  
Test and CI for Two Proportions    [leg weakness]
+
==In progress==
 +
[https://www.nytimes.com/2018/11/07/magazine/placebo-effect-medicine.html What if the Placebo Effect Isn’t a Trick?]<br>
 +
by Gary Greenberg, ''New York Times Magazine'', 7 November 2018
  
Sample  :::: X  ::N      ::::::Sample p<BR>
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[https://www.nytimes.com/2019/07/17/opinion/pretrial-ai.html The Problems With Risk Assessment Tools]<br>
1::::          ::::::::9  ::::16      ::::::0.562500<BR>
+
by Chelsea Barabas, Karthik Dinakar and Colin Doyle, ''New York Times'', 17 July 2019
2 ::::::::              ::::::::::::::::19  ::21      ::::::0.904762
 
  
::The second analysi
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==Hurricane Maria deaths==
Difference = p (1) - p (2)
+
Laura Kapitula sent the following to the Isolated Statisticians e-mail list:
Estimate for difference:  -0.342262
 
95% CI for difference:  (-0.615844, -0.0686795)
 
Test for difference = 0 (vs not = 0):  Z = -2.45  P-Value = 0.014
 
  
Fisher's exact test: P-Value = 0.024
+
:[Why counting casualties after a hurricane is so hard]<br>
 +
:by Jo Craven McGinty, Wall Street Journal, 7 September 2018
  
2. Parathaesia--The paper states that the p-value is less that .05. Minitab shows that the p-value is from Fisher’s exact test is .08.
+
The article is subtitled: Indirect deaths—such as those caused by gaps in medication—can occur months after a storm, complicating tallies
 +
 +
Laura noted that  
 +
:[https://www.washingtonpost.com/news/fact-checker/wp/2018/06/02/did-4645-people-die-in-hurricane-maria-nope/?utm_term=.0a5e6e48bf11 Did 4,645 people die in Hurricane Maria? Nope.]<br>
 +
:by Glenn Kessler, ''Washington Post'', 1 June 2018
  
Test and CI for Two Proportions    [parathaesia]
+
The source of the 4645 figure is a [https://www.nejm.org/doi/full/10.1056/NEJMsa1803972 NEJM article].  Point estimate, the 95% confidence interval ran from 793 to 8498.
  
Sample  X  N    Sample p
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President Trump has asserted that the actual number is
1            22 25    0.880000
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[https://twitter.com/realDonaldTrump/status/1040217897703026689 6 to 18].
2            13  21    0.619048
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The ''Post'' article notes that Puerto Rican official had asked researchers at George Washington University to do an estimate of the death toll. That work is not complete.
 +
[https://prstudy.publichealth.gwu.edu/ George Washington University study]
  
 +
:[https://fivethirtyeight.com/features/we-still-dont-know-how-many-people-died-because-of-katrina/?ex_cid=538twitter We sttill don’t know how many people died because of Katrina]<br>
 +
:by Carl Bialik, FiveThirtyEight, 26 August 2015
  
Difference = p (1) - p (2)
+
----
Estimate for difference: 0.260952
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[https://www.nytimes.com/2018/09/11/climate/hurricane-evacuation-path-forecasts.html These 3 Hurricane Misconceptions Can Be Dangerous. Scientists Want to Clear Them Up.]<br>
95% CI for difference: (0.0173021, 0.504603)
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[https://journals.ametsoc.org/doi/abs/10.1175/BAMS-88-5-651 Misinterpretations of the “Cone of Uncertainty” in Florida during the 2004 Hurricane Season]<br>
Test for difference = 0 (vs not = 0):  Z = 2.10 P-Value = 0.036
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[https://www.nhc.noaa.gov/aboutcone.shtml Definition of the NHC Track Forecast Cone]
 +
----
 +
[https://www.popsci.com/moderate-drinking-benefits-risks Remember when a glass of wine a day was good for you? Here's why that changed.]
 +
''Popular Science'', 10 September 2018
 +
----
 +
[https://www.economist.com/united-states/2018/08/30/googling-the-news Googling the news]<br>
 +
''Economist'', 1 September 2018
  
Fisher's exact test: P-Value = 0.080
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[https://www.cnbc.com/2018/09/17/google-tests-changes-to-its-search-algorithm-how-search-works.html We sat in on an internal Google meeting where they talked about changing the search algorithm — here's what we learned]
 +
----
 +
[http://www.wyso.org/post/stats-stories-reading-writing-and-risk-literacy Reading , Writing and Risk Literacy]
  
3. Reduced Analgesic Use--The paper states that the p-value is less that .02.  Minitab shows that the p-value from Fisher’s exact test is .017.
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[http://www.riskliteracy.org/]
 +
-----
 +
[https://twitter.com/i/moments/1025000711539572737?cn=ZmxleGlibGVfcmVjc18y&refsrc=email Today is the deadliest day of the year for car wrecks in the U.S.]
  
Test and CI for Two Proportions
+
==Some math doodles==
 +
<math>P \left({A_1 \cup A_2}\right) = P\left({A_1}\right) + P\left({A_2}\right) -P \left({A_1 \cap A_2}\right)</math>
  
Sample   X  N    Sample p
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<math>P(E)   = {n \choose k} p^k (1-p)^{ n-k}</math>
1             35  38    0.921053
 
2            25  36    0.694444
 
  
 +
<math>\hat{p}(H|H)</math>
  
Difference = p (1) - p (2)
+
<math>\hat{p}(H|HH)</math>
Estimate for difference:  0.226608
 
95% CI for difference:  (0.0534229, 0.399793)
 
Test for difference = 0 (vs not = 0):  Z = 2.49  P-Value = 0.013
 
  
Fisher's exact test: P-Value = 0.017
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==Accidental insights==
  
The primary outcomes, leg pain and (low) back pain for the treatment vs. the control were not calculated in a similar manner to the way the secondary outcomes were. Instead of using a two-sample test of proportions, the results for “pain” were calculated by having five categories: “Much better,” Little better,” “Same,” “Little worse,” and “Much worse. That is, an ordinal scale was employed.  Because the accompanying graphs, Figure 1A and 1B in the paper, are not precise enough to determine the number in each category, a nonparametric calculation is hard to carry out.
+
My collective understanding of Power Laws would fit beneath the shallow end of the long tail. Curiosity, however, easily fills the fat endI long have been intrigued by the concept and the surprisingly common appearance of power laws in varied natural, social and organizational dynamics.  But, am I just seeing a statistical novelty or is there meaning and utility in Power Law relationships? Here’s a case in point.
 
 
Nevertheless, ignoring the breakdown into five categories, here are Minitab results for leg pain and back pain, respectively; note that the p-values are much different from the claimed <.05:
 
 
 
Test and CI for Two Proportions [leg pain]
 
Sample  X  N    Sample p             
 
1            35  38    0.921053
 
2            29  36    0.805556
 
 
  
Difference = p (1) - p (2)
+
While carrying a pair of 10 lb. hand weights one, by chance, slipped from my grasp and fell onto a piece of ceramic tile I had left on the carpeted floor. The fractured tile was inconsequential, meant for the trash.  
Estimate for difference:  0.115497
+
<center>[[File:BrokenTile.jpg | 400px]]</center>
95% CI for difference: (-0.0396318, 0.270626)
+
As I stared, slightly annoyed, at the mess, a favorite maxim of the Greek philosopher, Epictetus, came to mind: “On the occasion of every accident that befalls you, turn to yourself and ask what power you have to put it to use. Could this array of large and small polygons form a Power Law? With curiosity piqued, I collected all the fragments and measured the area of each piece.
Test for difference = 0 (vs not = 0): Z = 1.46 P-Value = 0.144
 
 
Fisher's exact test: P-Value = 0.185
 
  
Test and CI for Two Proportions [back pain]
+
<center>
Sample  X  N    Sample p           
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{| class="wikitable"
1           33 38  0.868421
+
|-
2            27 36  0.750000
+
! Piece !! Sq. Inches !! % of Total
   
+
|-
 +
| 1 || 43.25 || 31.9%
 +
|-
 +
| 2 || 35.25 ||26.0%
 +
|-
 +
| 3 || 23.25 || 17.2%
 +
|-
 +
| 4 || 14.10 || 10.4%
 +
|-
 +
| 5 || 7.10 || 5.2%
 +
|-
 +
| 6 || 4.70 || 3.5%
 +
|-
 +
| 7 || 3.60 || 2.7%
 +
|-
 +
| 8 || 3.03 || 2.2%
 +
|-
 +
| 9 || 0.66 || 0.5%
 +
|-
 +
| 10 || 0.61 || 0.5%
 +
|}
 +
</center>
 +
<center>[[File:Montante_plot1.png | 500px]]</center>
 +
The data and plot look like a Power Law distribution. The first plot is an exponential fit of percent total area. The second plot is same data on a log normal format. Clue: Ok, data fits a straight line.  I found myself again in the shallow end of the knowledge curve. Does the data reflect a Power Law or something else, and if it does what does it reflect? What insights can I gain from this accident? Favorite maxims of Epictetus and Pasteur echoed in my head:
 +
“On the occasion of every accident that befalls you, remember to turn to yourself and inquire what power you have to turn it to use” and “Chance favors only the prepared mind.”
  
Difference = p (1) - p (2)
+
<center>[[File:Montante_plot2.png | 500px]]</center>
Estimate for difference: 0.118421
 
95% CI for difference:  (-0.0592271, 0.296069)
 
Test for difference = 0 (vs not = 0):  Z = 1.31  P-Value = 0.191
 
 
   
 
   
Fisher's exact test: P-Value = 0.242  
+
My “prepared” mind searched for answers, leading me down varied learning paths. Tapping the power of networks, I dropped a note to Chance News editor Bill Peterson. His quick web search surfaced a story from ''Nature News'' on research by Hans Herrmann, et. al. [http://www.nature.com/news/2004/040227/full/news040223-11.html Shattered eggs reveal secrets of explosions]As described there, researchers have found power-law relationships for the fragments produced by shattering a pane of glass or breaking a solid object, such as a stone. Seems there is a science underpinning how things break and explode; potentially useful in Forensic reconstructions.
 
+
Bill also provided a link to [http://cran.r-project.org/web/packages/poweRlaw/vignettes/poweRlaw.pdf a vignette from CRAN] describing a maximum likelihood procedure for fitting a Power Law relationship. I am now learning my way through that.
Discussion
 
 
 
1. Why might an individual report a better outcome because he was handed his disc fragment?  Why might he feel worse?
 
 
 
2. Assuming that the p-values reported in the article are correct, what criticism might still remain?
 
  
3.  A disc fragment is one form of excised body part.  What other excised body part might have a similar positive result?  What other excise body part might have a distinctly negative result?
+
Submitted by William Montante
  
4. This study took place in London, England.  Why might patient reaction be different in, let us say, Asia or Africa?
+
----

Latest revision as of 15:58, 17 July 2019


Forsooth

Quotations

“We know that people tend to overestimate the frequency of well-publicized, spectacular events compared with more commonplace ones; this is a well-understood phenomenon in the literature of risk assessment and leads to the truism that when statistics plays folklore, folklore always wins in a rout.”

-- Donald Kennedy (former president of Stanford University), Academic Duty, Harvard University Press, 1997, p.17

"Using scientific language and measurement doesn’t prevent a researcher from conducting flawed experiments and drawing wrong conclusions — especially when they confirm preconceptions."

-- Blaise Agüera y Arcas, Margaret Mitchell and Alexander Todoorov, quoted in: The racist history behind facial recognition, New York Times, 10 July 2019

In progress

What if the Placebo Effect Isn’t a Trick?
by Gary Greenberg, New York Times Magazine, 7 November 2018

The Problems With Risk Assessment Tools
by Chelsea Barabas, Karthik Dinakar and Colin Doyle, New York Times, 17 July 2019

Hurricane Maria deaths

Laura Kapitula sent the following to the Isolated Statisticians e-mail list:

[Why counting casualties after a hurricane is so hard]
by Jo Craven McGinty, Wall Street Journal, 7 September 2018

The article is subtitled: Indirect deaths—such as those caused by gaps in medication—can occur months after a storm, complicating tallies

Laura noted that

Did 4,645 people die in Hurricane Maria? Nope.
by Glenn Kessler, Washington Post, 1 June 2018

The source of the 4645 figure is a NEJM article. Point estimate, the 95% confidence interval ran from 793 to 8498.

President Trump has asserted that the actual number is 6 to 18. The Post article notes that Puerto Rican official had asked researchers at George Washington University to do an estimate of the death toll. That work is not complete. George Washington University study

We sttill don’t know how many people died because of Katrina
by Carl Bialik, FiveThirtyEight, 26 August 2015

These 3 Hurricane Misconceptions Can Be Dangerous. Scientists Want to Clear Them Up.
Misinterpretations of the “Cone of Uncertainty” in Florida during the 2004 Hurricane Season
Definition of the NHC Track Forecast Cone


Remember when a glass of wine a day was good for you? Here's why that changed. Popular Science, 10 September 2018


Googling the news
Economist, 1 September 2018

We sat in on an internal Google meeting where they talked about changing the search algorithm — here's what we learned


Reading , Writing and Risk Literacy

[1]


Today is the deadliest day of the year for car wrecks in the U.S.

Some math doodles

<math>P \left({A_1 \cup A_2}\right) = P\left({A_1}\right) + P\left({A_2}\right) -P \left({A_1 \cap A_2}\right)</math>

<math>P(E) = {n \choose k} p^k (1-p)^{ n-k}</math>

<math>\hat{p}(H|H)</math>

<math>\hat{p}(H|HH)</math>

Accidental insights

My collective understanding of Power Laws would fit beneath the shallow end of the long tail. Curiosity, however, easily fills the fat end. I long have been intrigued by the concept and the surprisingly common appearance of power laws in varied natural, social and organizational dynamics. But, am I just seeing a statistical novelty or is there meaning and utility in Power Law relationships? Here’s a case in point.

While carrying a pair of 10 lb. hand weights one, by chance, slipped from my grasp and fell onto a piece of ceramic tile I had left on the carpeted floor. The fractured tile was inconsequential, meant for the trash.

BrokenTile.jpg

As I stared, slightly annoyed, at the mess, a favorite maxim of the Greek philosopher, Epictetus, came to mind: “On the occasion of every accident that befalls you, turn to yourself and ask what power you have to put it to use.” Could this array of large and small polygons form a Power Law? With curiosity piqued, I collected all the fragments and measured the area of each piece.

Piece Sq. Inches % of Total
1 43.25 31.9%
2 35.25 26.0%
3 23.25 17.2%
4 14.10 10.4%
5 7.10 5.2%
6 4.70 3.5%
7 3.60 2.7%
8 3.03 2.2%
9 0.66 0.5%
10 0.61 0.5%
Montante plot1.png

The data and plot look like a Power Law distribution. The first plot is an exponential fit of percent total area. The second plot is same data on a log normal format. Clue: Ok, data fits a straight line. I found myself again in the shallow end of the knowledge curve. Does the data reflect a Power Law or something else, and if it does what does it reflect? What insights can I gain from this accident? Favorite maxims of Epictetus and Pasteur echoed in my head: “On the occasion of every accident that befalls you, remember to turn to yourself and inquire what power you have to turn it to use” and “Chance favors only the prepared mind.”

Montante plot2.png

My “prepared” mind searched for answers, leading me down varied learning paths. Tapping the power of networks, I dropped a note to Chance News editor Bill Peterson. His quick web search surfaced a story from Nature News on research by Hans Herrmann, et. al. Shattered eggs reveal secrets of explosions. As described there, researchers have found power-law relationships for the fragments produced by shattering a pane of glass or breaking a solid object, such as a stone. Seems there is a science underpinning how things break and explode; potentially useful in Forensic reconstructions. Bill also provided a link to a vignette from CRAN describing a maximum likelihood procedure for fitting a Power Law relationship. I am now learning my way through that.

Submitted by William Montante