Showing posts with label mathematics. Show all posts
Showing posts with label mathematics. Show all posts

Sunday, April 19, 2020

COVID-19 and County Health Rankings in PA: Which Variables Predict Cases and Deaths

The trend in Covid-19 Cases in Cambria County

Last week I posted on how county health rankings overall measures predicted the number of cases and deaths in each county in Pennsylvania.  These measures were composites of dozens of more specific county level measures.  There are too many univariate correlations to summarize here.  The cases used in the analysis are from April 18. The variables were added one at a time and stayed in the Poisson regression model if they were significant.

The final Poisson model for the number of cases is:

ln(cases) = -1.033 + 0.000002*(population) + 0.045*(% with access to exercise opportunities) - 0.070*(Social Association Rate) + 0.13*(% who Drive Alone to Work) + 
0.41*(% not proficient in English) + 0.14*(% with severe housing problems)

  • Access to exercise opportunities, is a component of health behaviors and is positively associated with the number of cases in each county.  
  • The social association rate is the number of membership organizations per 100,000 people and is negatively associated with the number of cases.  This measure is a component of the social and economic z-score.
  • The percent who drive alone to work is also a component of social and economic z-score and is positively associated with the number of cases.  
  • The percent with severe housing problems is a component of the physical environment z-score and is positively associated with the number of cases.  It is correlated with poor length of life outcomes.
  • The percent not proficient in English is a demographic variable that is not a component of the rankings.  It has the strongest association with the number of cases.
The model for deaths last week was:

ln(number of deaths) = -0.14 - 7.97*(health behavior z-score) + 2.83*(social economic z score) + 1.62*(quality of life z score) + 0.000003*(population)

The final model with the submeasures that was settled on was:

ln(number of deaths) = -4.94 + 0.000001*(population) + 0.07*(% with access to exercise opportunities) + 0.78*(%Unemployed) - 0.16*(% of Children in poverty) + 0.46*(% not proficient in English)
  • Access to exercise opportunities, is a component of health behaviors and is positively associated with the number of deaths in each county.  
  • The percent unemployed is a component of the social and economic factors z-score and is positively associated with the number of deaths.
  • The percent of children in poverty is also a component of the social and economic factors z-score and is negatively associated with the number of deaths.  This seems counter intuitive but counties with higher rates of child poverty may have less social interaction with more susceptible populations such as the elderly.
  • Like the number of cases, The percent not proficient in English was positively associated with the number of deaths.  This variable and the % unemployed could be positively correlated with poor quality of life.
These variables would be better to study at the individual level than the county level.  I looked at these variables as they were readily available.  The graph above shows the trend in cases in my home county, Cambria County.  It does provide some clues as to what factors may be exacerbating this pandemic.


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Thursday, March 14, 2019

Happy 3.14159..... Day

I have an interview published on the website Manufacturing Chemist on healthcare analytics which you are welcome to check out.  



Today is pi Day (march 14 or 3/14).  Which is more celebrated now than March 15 or the Ides of March, the day Julius Caesar was killed.  Of course it's not as celebrated as St. Patrick's day everywhere but in Ireland itself.  

Pi is the ratio of the circumference of a circle to its diameter.  It is used to calculate the area of a circle, the circumference of a circle, and the volume of a sphere.  It is also used in the famous normal distribution in statistics, aka the bell shaped curve as seen in the formula below.  Here the probability value of x is conditioned on the variables mean mu and variance sigma squared.  Pi is a constant in this equation.
There are many other uses for pi in math.  Many of which I am not aware so I will leave it here.


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Friday, September 21, 2018

New Sports and Math Post On Darply and an Update on Trump's Approval Ratings

I have a new post on sports and statistics on the news site Darply. Featured prominently in this article is former Baltimore Ravens center John Urschel who retired from the NFL to pursue a PhD at MIT in Mathematics.  You can see another interview he recently gave on Amanpour and Company at the link below.  

John Urschel | Video | Amanpour: Walter Isaacson sits down with John Urschel, a rising star who walked away from a lucrative football career in the NFL to pursue a doctorate in mathematics at MIT.  

As a Steeler fan and a statistician I must say I'm glad he retired.

 

I also have an update on Trump's approval ratingsHis ratings have taken a 2%-3% dip in the events surrounding the convictions of Paul Manafort and Michael Cohen and Sen John McCain's funeral.  It's worth noting but still not in Nixon territory for impeachment to happen.  Things have been hectic for me lately but I will begin work on my 8th anniversary post.

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Tuesday, August 9, 2016

Specialized Practical vs. Universal Theoretical Math


Andrew Hacker, a political scientist has written a book called The Math Myth.  In it he argues that the emphasis on everyone learning algebra, geometry and for the elite students calculus is misguided and the curriculum should be tailored to meet individual needs.  He says "At most, 5 percent of people really use math, advanced math, in their work."

I've never been a fan of the one size fits all approach to education.  A group of experts in a room decide what is best for everyone and mandate it.  Of course this is the objection to the Common Core federally mandated curriculum we hear from the right who prefer local control so intelligent design can be taught along side the theory of evolution as a competing theory.  


Some would argue that there has to be some core skills citizens should have in order to be functioning citizens in a democracy.  They argue further that the problem solving skills acquired from studying higher mathematics are just as essential as learning facts.  Hacker argues that these skills can be acquired by tailoring curricula to individual needs and abilities for real world problems.  

When I taught general statistics for science majors (a course with many real world applications if I do say so myself) the students who had calculus struggled to grasp the concepts probability and statistics (This is partly why casinos are so profitable as I have discussed before).  They were well versed in calculus but struggled applying the formulas to real world problems.   

In this blog I have applied a wide variety of statistical methods to show how they can shed light on everyday phenomena.  There are theoretical underpinnings to these methods which involve calculus and linear algebra.  I have seldom discussed them in this blog as they would be confusing to the average reader.  Most applications in statistics can be explained and used without understanding these underpinnings.  The dilemma for educators is how far should they go in the theory to explain the practical applications which Hacker believes is more important to have functioning citizens in a society.

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Friday, July 12, 2013

Numbers and Catholicism

The Vatican announced this week that Popes John Paul II and John XXIII were cleared to be canonized saints. The former was fast tracked for sainthood when crowds were chanting "Santo Subito (Sainthood Soon)" at his funeral in 2005.  The latter mentioned Pope's bid for sainthood was delayed as there was no second miracle as "objective proof" of his favor with God.  Pope Francis I waived the required second miracle for John XXIII  to be canonized because he is known as "the good Pope" who called for the Second Vatican Council which modernized the church by, for example, having the Mass in local languages.

Pope John Paul II (r: 1978-2005) had reduced the required number of miracles from three to two.  A miracle on that saint's behalf is if you pray to that person's soul in heaven to intercede with God for you for something and it is granted it is proof of that soul's favor with the almighty.  If this happens on two (the church used to require three) separate occasions then the church considers this "empirical proof" of divine favor. 


Not surprisingly many more canonizations (sainthood) were granted under John Paul II than any of his predecessors.  Most famously Mother Teresa, Padre Pio, and controversially to Father Maximillian Kolbe.  

All of this reliance on numbers and objective evidence to make decisions while accepting on faith other tenets such as the resurrection of Jesus Christ which others reject is what really interests me.  For example, the church has 7 sacraments, 7 commandments (in addition to the 10 commandments given to Moses on Mount Sinai), and 7 corporal and 7 spiritual works of mercy to go with 7 deadly sins.  The rosary has it's own numerology with 5 joyful, 5 sorrowful and 5 glorious mysteries which accompany the long list of the Lord's Prayers, 10 Hail Mary's and one Glory Be that accompany each mystery.  Finally there are 40 days of fasting for Lent followed by 50 days of feasting after Easter (40 days until Ascension Thursday followed by 10 more until Pentecost Sunday).

All of this seems orderly and rational with in the cosmos (Greek for the natural order of things) until you get to the Trinity which is enunciated at every Catholic Mass (and every Orthodox plus many Protestant services) in the Nicene Creed set at the council of Nicea by the Emperor Constantine in 325 AD.  It states that there are three separate individuals, the Father, Son and Holy Spirit but only one God.  Skeptics may state that this was just a ploy by the early church to attract polytheistic pagans (especially number loving Greeks) to the faith in the early centuries AD and that saints also took the place of their many gods.  Believers counter that God exists beyond the laws of the universe and human abilities of comprehension.  Islam rejected this type of complex symbolism and has had no trouble spreading faith in the later centuries.  Which of these opinions about God is true among the many that exist?  It's all a leap of faith now isn't it?

It's hard to know where to draw the line between faith and reason. We all make leaps of faith on things we do not or cannot know.  Darwin took a leap of faith on evolution based on the information in front of him without knowing about genetics which would've strengthened his argument.  The issue is what do we do with those leaps.  Pope Francis I is taking a leap of faith on his two predecessors. 


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Friday, April 26, 2013

How Do You Use and Consume Math?


People often assume that because I am a statistician I am a whiz at high math.  The graph above from a survey by Northeastern University seems to explain why.  The vast majority of Americans do not use any math above fractions (an estimated 78% or 1-22% which is the opposite of the any more advanced category on the graph above).  The graph below shows what type of job uses what type of math with upper blue collar like upper level trades and mechanics using each type except statistics which is upper white collar.



Although an estimated 78% of Americans do not use advanced math on a daily basis, 100% depend on them, often without question, to make decisions everyday.  Below is an example on The Colbert Report of how this blind faith can go seriously wrong.



Here is an interview with Stephen Colbert by the UMASS grad student who exposed their error in an Excel spreadsheet.  One can learn a lot by simply doing a little digging.  Some say it is not necessary to teach advanced math to our school students if they are not going to use it in their work but the critical thinking skills that are gained can come in handy if we choose to use them in other areas.


Mathematics above calculus is a different world altogether as can be seen in the BBC documentary from 1984 A Mathematical Mystery Tour which describes how the philosopher Bertrand Russell needed 362 pages to prove that 1+1=2.  I added an online poll to survey users of this blog on their background and comfort level in math.  The polling will be open until May 26.



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