statistics: the compass for navigating a data …big data also supplies more raw material for...
TRANSCRIPT
Statistics:The Compass for Navigating
a Data-Centric World
Marie Davidian
Department of StatisticsNorth Carolina State University
January 11, 2013
Statistics2013 Video
Available at http://statistics2013.org
Statistics2013 Video
Available at http://statistics2013.org
Triumph of the geeks
Nate Silver predicted the outcome of the 2012 US presidentialelection in all 50 states
using . . .
Statisticshttp://fivethirtyeight.blogs.nytimes.com/
Silver used a statistical model to combine the results ofstate-by-state polls, weighting them according their previousaccuracy, and to simulate many elections and estimateprobabilities of the outcome
Triumph of the geeks
Nate Silver predicted the outcome of the 2012 US presidentialelection in all 50 states using . . .
Statistics
http://fivethirtyeight.blogs.nytimes.com/
Silver used a statistical model to combine the results ofstate-by-state polls, weighting them according their previousaccuracy, and to simulate many elections and estimateprobabilities of the outcome
Triumph of the geeks
Nate Silver predicted the outcome of the 2012 US presidentialelection in all 50 states using . . .
Statisticshttp://fivethirtyeight.blogs.nytimes.com/
Silver used a statistical model to combine the results ofstate-by-state polls, weighting them according their previousaccuracy, and to simulate many elections and estimateprobabilities of the outcome
Triumph of the geeks
Others did, too. . .
“Dynamic Bayesian forecasting of presidential elections in thestates,” by Drew A. Linzer, Journal of the American StatisticalAssociation, in press
Triumph of the geeks
“Nate Silver-led statistics men crush pundits in election”– Bloomberg Businessweek
“Nate Silver has made statistics sexy again”– Associated Press
“Drew Linzer: The stats man who predicted Obama’s win”– BBC News Magazine
“The allure of the statistics field grows”– Boston Globe
But the interest in statistics didn’t start with theUS elections. . .
Triumph of the geeks
“Nate Silver-led statistics men crush pundits in election”– Bloomberg Businessweek
“Nate Silver has made statistics sexy again”– Associated Press
“Drew Linzer: The stats man who predicted Obama’s win”– BBC News Magazine
“The allure of the statistics field grows”– Boston Globe
But the interest in statistics didn’t start with theUS elections. . .
Statistics in the news
New York Times, August 6, 2009
“I keep saying that the sexy job in the next 10 years will bestatisticians” – Hal Varian, Chief Economist, Google
Statistics in the news
New York Times, January 26, 2012
“I went to parties and heard a little groan when people heardwhat I did. Now they’re all excited to meet me” – Rob
Tibshirani, Department of Statistics, Stanford University
Statistics in the news
New York Times, February 11, 2012
“Statistics are interesting and fun. It’s cool now” – AndrewGelman, Department of Statistics, Columbia University
Statistics in the news
The Wall Street Journal, December 28, 2012
Carl Bialik, The Numbers Guy
Data, data, and more data
Why is there so much talk of statistics andstatisticians?
Data• Administrative (e.g., tax records), government surveys• Genomic, meteorological, air quality, seismic, . . .• Electronic medical records, health care databases• Credit card transactions, point-of-sale, mobile phone• Online search, social networks• Polls, voter registration records
A veritable tsunami/deluge/avalanche of data
Data, data, and more data
Why is there so much talk of statistics andstatisticians?
Data
• Administrative (e.g., tax records), government surveys• Genomic, meteorological, air quality, seismic, . . .• Electronic medical records, health care databases• Credit card transactions, point-of-sale, mobile phone• Online search, social networks• Polls, voter registration records
A veritable tsunami/deluge/avalanche of data
Data, data, and more data
Why is there so much talk of statistics andstatisticians?
Data• Administrative (e.g., tax records), government surveys• Genomic, meteorological, air quality, seismic, . . .• Electronic medical records, health care databases• Credit card transactions, point-of-sale, mobile phone• Online search, social networks• Polls, voter registration records
A veritable tsunami/deluge/avalanche of data
Demand
2011 McKinsey Global Institute report:
Big data: The next frontier for innovation,competition, and productivity
“A significant constraint. . . will be a shortage of . . . people withdeep expertise in statistics and data mining. . . a talent gap of
140K - 190K positions in 2018 (in the US)”
http://www.mckinsey.com/insights/mgi/research/technology and innovation/big data the next frontier for innovation
Opportunities and challenges
• Our ability to collect, store, access, and manipulate vastand complex data is ever-improving
• The potential benefits to science and society of learningfrom these data are enormous
• However, Big Data does not automatically meanBig Information
• Science, decision-making, and policy formulation requirenot only prediction and finding associations and patterns,but uncovering causal relationships
• Which, as we’ll discuss later, is not so easy. . .
Opportunities and challenges
• Our ability to collect, store, access, and manipulate vastand complex data is ever-improving
• The potential benefits to science and society of learningfrom these data are enormous
• However, Big Data does not automatically meanBig Information
• Science, decision-making, and policy formulation requirenot only prediction and finding associations and patterns,but uncovering causal relationships
• Which, as we’ll discuss later, is not so easy. . .
Perils
From “The Age of Big Data”With huge data sets and fine-grained measurement,. . . there isincreased risk of “false discoveries.” The trouble with seeking ameaningful needle in massive haystacks of data, says TrevorHastie, a statistics professor at Stanford, is that “many bits ofstraw look like needles.”
Big Data also supplies more raw material for statisticalshenanigans and biased fact-finding excursions. It offers ahigh-tech twist on an old trick: I know the facts, now let’s find’em. That is, says Rebecca Goldin, a mathematician at GeorgeMason University, “one of the most pernicious uses of data.”
Perils
From “The Age of Big Data”With huge data sets and fine-grained measurement,. . . there isincreased risk of “false discoveries.” The trouble with seeking ameaningful needle in massive haystacks of data, says TrevorHastie, a statistics professor at Stanford, is that “many bits ofstraw look like needles.”
Big Data also supplies more raw material for statisticalshenanigans and biased fact-finding excursions. It offers ahigh-tech twist on an old trick: I know the facts, now let’s find’em. That is, says Rebecca Goldin, a mathematician at GeorgeMason University, “one of the most pernicious uses of data.”
Critical need
Sound, objective methods for modeling,analysis, and interpretation
Statistics
While Big Data have inspired considerable current interest instatistics, statistics has been fundamental in numerous areas ofscience, business, and government for decades
Critical need
Sound, objective methods for modeling,analysis, and interpretation
Statistics
While Big Data have inspired considerable current interest instatistics, statistics has been fundamental in numerous areas ofscience, business, and government for decades
Critical need
Sound, objective methods for modeling,analysis, and interpretation
Statistics
While Big Data have inspired considerable current interest instatistics, statistics has been fundamental in numerous areas ofscience, business, and government for decades
Roadmap
• A brief history
• Statistical stories• Our data-rich future
Roadmap
• A brief history• Statistical stories
• Our data-rich future
Roadmap
• A brief history• Statistical stories• Our data-rich future
What is statistics?
Statistics: The science of learning from dataand of measuring, controlling, andcommunicating uncertainty
The path to what is now the formal discipline of statisticalscience is long and winding. . .
What is statistics?
Statistics: The science of learning from dataand of measuring, controlling, andcommunicating uncertainty
The path to what is now the formal discipline of statisticalscience is long and winding. . .
What is statistics?
Statistics: The science of learning from dataand of measuring, controlling, andcommunicating uncertainty
The path to what is now the formal discipline of statisticalscience is long and winding. . .
Origins – pre-1700
• Sporadic accounts of measurement and data collectionand interpretation date back as early as 5 B.C.
• But it was not until the the mid-1600s that themathematical notions of probability began to be developedby (mainly) mathematicians and physicists (e.g., BlaisePascal), often inspired by games of chance
• The first formal attempt to summarize and learn from datawas by John Graunt, who created a precursor to modernlife tables used in demography
• Christiaan Huygens was among the first to connect suchdata analysis to probability
Origins – pre-1700
• Sporadic accounts of measurement and data collectionand interpretation date back as early as 5 B.C.
• But it was not until the the mid-1600s that themathematical notions of probability began to be developedby (mainly) mathematicians and physicists (e.g., BlaisePascal), often inspired by games of chance
• The first formal attempt to summarize and learn from datawas by John Graunt, who created a precursor to modernlife tables used in demography
• Christiaan Huygens was among the first to connect suchdata analysis to probability
Origins – pre-1700
• Sporadic accounts of measurement and data collectionand interpretation date back as early as 5 B.C.
• But it was not until the the mid-1600s that themathematical notions of probability began to be developedby (mainly) mathematicians and physicists (e.g., BlaisePascal), often inspired by games of chance
• The first formal attempt to summarize and learn from datawas by John Graunt, who created a precursor to modernlife tables used in demography
• Christiaan Huygens was among the first to connect suchdata analysis to probability
Origins – 1700-1750
• From 1700 to 1750, many key results in classicalprobability that underlie statistical theory were derived
• Jakob Bernoulli– law of large numbers, the Bernoulli andbinomial probability distributions
• Abraham de Moivre – The Doctrine of Chances, precursorto the central limit theorem
• Daniel Bernoulli – expected utility, applications ofprobability to measurement problems in astronomy
Origins – 1700-1750
• From 1700 to 1750, many key results in classicalprobability that underlie statistical theory were derived
• Jakob Bernoulli– law of large numbers, the Bernoulli andbinomial probability distributions
• Abraham de Moivre – The Doctrine of Chances, precursorto the central limit theorem
• Daniel Bernoulli – expected utility, applications ofprobability to measurement problems in astronomy
Milestone events – 1750-1820
• Thomas Bayes’ 1763 An essay towards solving a problemin the Doctrine of Chances presented a special case ofBayes’ theorem (posthumously)
• Arien-Marie Legendre described the method of leastsquares in 1805
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Milestone events – 1750-1820
• Thomas Bayes’ 1763 An essay towards solving a problemin the Doctrine of Chances presented a special case ofBayes’ theorem (posthumously)
• Arien-Marie Legendre described the method of leastsquares in 1805
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Milestone events – 1750-1820
• Thomas Bayes’ 1763 An essay towards solving a problemin the Doctrine of Chances presented a special case ofBayes’ theorem (posthumously)
• Arien-Marie Legendre described the method of leastsquares in 1805
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Milestone events – 1750-1820
• Thomas Bayes’ 1763 An essay towards solving a problemin the Doctrine of Chances presented a special case ofBayes’ theorem (pothumously)
• Arien-Marie Legendre described the method of leastsquares in 1805
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Milestone events – 1750-1820
• Thomas Bayes’ 1763 An essay towards solving a problemin the Doctrine of Chances presented a special case ofBayes’ theorem (pothumously)
• Arien-Marie Legendre described the method of leastsquares in 1805
Milestone events – 1750-1820
• Carl Fredrich Gauss connected least squares to Bayestheorem in 1809
• Pierre-Simon Laplace derived the central limit theorem andconnected the normal probability distribution to leastsquares in 1810
Milestone events – 1750-1820
• Carl Fredrich Gauss connected least squares to Bayestheorem in 1809
• Pierre-Simon Laplace derived the central limit theorem andconnected the normal probability distribution to leastsquares in 1810
Milestone events – 1750-1820
• Carl Fredrich Gauss connected least squares to Bayestheorem in 1809
• Pierre-Simon Laplace derived the central limit theorem andconnected the normal probability distribution to leastsquares in 1810
Milestone events – 1750-1820
• Carl Fredrich Gauss connected least squares to Bayestheorem in 1809
• Pierre-Simon Laplace derived the central limit theorem andconnected the normal probability distribution to leastsquares in 1810
More milestones – 1820-1900
• Aldolphe Quetelet pioneered the statistical analysis ofsocial science data – the “average man” (1835) and thenormal distribution as a model for measurements (1842)
• The Royal Statistical Society (1834) and AmericanStatistical Association (1839) were founded
• Francis Galton introduced regression analysis (1885) andcorrelation (1888)
• Karl Pearson established the field of biometry anddeveloped fundamental methods, and founded the firststatistical journal, Biometrika (1901)
More milestones – 1820-1900
• Aldolphe Quetelet pioneered the statistical analysis ofsocial science data – the “average man” (1835) and thenormal distribution as a model for measurements (1842)
• The Royal Statistical Society (1834) and AmericanStatistical Association (1839) were founded
• Francis Galton introduced regression analysis (1885) andcorrelation (1888)
• Karl Pearson established the field of biometry anddeveloped fundamental methods, and founded the firststatistical journal, Biometrika (1901)
More milestones – 1820-1900
• Aldolphe Quetelet pioneered the statistical analysis ofsocial science data – the “average man” (1835) and thenormal distribution as a model for measurements (1842)
• The Royal Statistical Society (1834) and AmericanStatistical Association (1839) were founded
• Francis Galton introduced regression analysis (1885) andcorrelation (1888)
• Karl Pearson established the field of biometry anddeveloped fundamental methods, and founded the firststatistical journal, Biometrika (1901)
Modern statistics – 1900-1950s
The modern discipline of statistics was reallyestablished only in the twentieth century
• William Gosset (“Student”), a brewer for Guinness inDublin, derived the Student’s t distribution in 1908
• In the 1920s, Ronald Fisher developed many fundamentalconcepts, including the ideas of statistical models andrandomization, theory of experimental design, the methodof analysis of variance, and tests of significance
• In the 1930s, Jerzy Neyman and Egon Pearson developedthe theory of sampling, the competing approach ofhypothesis testing, and the concept of confidence intervals
• Experimental design became a mainstay of agriculturalresearch
Modern statistics – 1900-1950s
The modern discipline of statistics was reallyestablished only in the twentieth century• William Gosset (“Student”), a brewer for Guinness in
Dublin, derived the Student’s t distribution in 1908
• In the 1920s, Ronald Fisher developed many fundamentalconcepts, including the ideas of statistical models andrandomization, theory of experimental design, the methodof analysis of variance, and tests of significance
• In the 1930s, Jerzy Neyman and Egon Pearson developedthe theory of sampling, the competing approach ofhypothesis testing, and the concept of confidence intervals
• Experimental design became a mainstay of agriculturalresearch
Modern statistics – 1900-1950s
The modern discipline of statistics was reallyestablished only in the twentieth century• William Gosset (“Student”), a brewer for Guinness in
Dublin, derived the Student’s t distribution in 1908• In the 1920s, Ronald Fisher developed many fundamental
concepts, including the ideas of statistical models andrandomization, theory of experimental design, the methodof analysis of variance, and tests of significance
• In the 1930s, Jerzy Neyman and Egon Pearson developedthe theory of sampling, the competing approach ofhypothesis testing, and the concept of confidence intervals
• Experimental design became a mainstay of agriculturalresearch
Modern statistics – 1900-1950s
The modern discipline of statistics was reallyestablished only in the twentieth century• William Gosset (“Student”), a brewer for Guinness in
Dublin, derived the Student’s t distribution in 1908• In the 1920s, Ronald Fisher developed many fundamental
concepts, including the ideas of statistical models andrandomization, theory of experimental design, the methodof analysis of variance, and tests of significance
• In the 1930s, Jerzy Neyman and Egon Pearson developedthe theory of sampling, the competing approach ofhypothesis testing, and the concept of confidence intervals
• Experimental design became a mainstay of agriculturalresearch
Modern statistics – 1900-1950s
The modern discipline of statistics was reallyestablished only in the twentieth century• William Gosset (“Student”), a brewer for Guinness in
Dublin, derived the Student’s t distribution in 1908• In the 1920s, Ronald Fisher developed many fundamental
concepts, including the ideas of statistical models andrandomization, theory of experimental design, the methodof analysis of variance, and tests of significance
• In the 1930s, Jerzy Neyman and Egon Pearson developedthe theory of sampling, the competing approach ofhypothesis testing, and the concept of confidence intervals
• Experimental design became a mainstay of agriculturalresearch
Modern statistics – 1900-1950s
• Fisher/Neyman-Pearson established the paradigm offrequentist statistical inference that is used today
• Also in the 1930s, Bayesian statistical inference wasdeveloped by Bruno de Finetti and others
• In the 1940s, many departments of statistics wereestablished at universities in the US and Europe
• And fundamental theory of statistical inference waspursued by Wald, Cramer, Rao and many others
Modern statistics – 1900-1950s
• Fisher/Neyman-Pearson established the paradigm offrequentist statistical inference that is used today
• Also in the 1930s, Bayesian statistical inference wasdeveloped by Bruno de Finetti and others
• In the 1940s, many departments of statistics wereestablished at universities in the US and Europe
• And fundamental theory of statistical inference waspursued by Wald, Cramer, Rao and many others
Modern statistics – 1900-1950s
• Fisher/Neyman-Pearson established the paradigm offrequentist statistical inference that is used today
• Also in the 1930s, Bayesian statistical inference wasdeveloped by Bruno de Finetti and others
• In the 1940s, many departments of statistics wereestablished at universities in the US and Europe
• And fundamental theory of statistical inference waspursued by Wald, Cramer, Rao and many others
Modern statistics to the present
From the 1950s on, there were numerousadvances in theory, methods, and application• The advent of medical statistics and epidemiological
methods (Richard Doll, Austin Bradford Hill)• The development of methods for analysis of censored
time-to-event data (Paul Meier, D.R. Cox)• The use of the theory of sampling to design surveys and
the US census (Jerzy Neyman, Morris Hansen)• The adoption of statistical quality control and experimental
design in industry (W. Edwards Deming, George Box)• Exploratory data analysis (John Tukey)• And many, many more. . .
Modern statistics to the present
Computing fundamentally altered the field ofstatistics forever• Complex calculations became feasible• Much larger and more complicated data sets could be
created and analyzed• Sophisticated models and methods could be applied
• Statistical software implementing popular methods becamewidespread (e.g., SAS, developed at NC State in the1960s/70s)
• Simulation to investigate performance of statisticalmethods became possible
• Bayesian statistical methods became feasible in complexsettings (Markov chain Monte Carlo – MCMC)
Modern statistics to the present
Computing fundamentally altered the field ofstatistics forever• Complex calculations became feasible• Much larger and more complicated data sets could be
created and analyzed• Sophisticated models and methods could be applied• Statistical software implementing popular methods became
widespread (e.g., SAS, developed at NC State in the1960s/70s)
• Simulation to investigate performance of statisticalmethods became possible
• Bayesian statistical methods became feasible in complexsettings (Markov chain Monte Carlo – MCMC)
Modern statistics to the present
Computing fundamentally altered the field ofstatistics forever• Complex calculations became feasible• Much larger and more complicated data sets could be
created and analyzed• Sophisticated models and methods could be applied• Statistical software implementing popular methods became
widespread (e.g., SAS, developed at NC State in the1960s/70s)
• Simulation to investigate performance of statisticalmethods became possible
• Bayesian statistical methods became feasible in complexsettings (Markov chain Monte Carlo – MCMC)
Today
Statistical methods are used routinely inscience, industry/business, and government• Pharmaceutical companies employ statisticians, who work
in all stages of drug development
• Statisticians are ubiquitous in medical and public healthresearch, working with health sciences researchers todesign studies, analyze data, and draw conclusions
• Google, Facebook, LinkedIn, credit card companies, globalretailers employ statisticians to develop and implementmethods to mine their vast data
• Government science, regulatory, and statistical agenciesemploy statisticians to design surveys, make forecasts,develop estimates of income, review new drug applications,assess evidence of health effects of pollutants, . . .
Today
Statistical methods are used routinely inscience, industry/business, and government• Pharmaceutical companies employ statisticians, who work
in all stages of drug development• Statisticians are ubiquitous in medical and public health
research, working with health sciences researchers todesign studies, analyze data, and draw conclusions
• Google, Facebook, LinkedIn, credit card companies, globalretailers employ statisticians to develop and implementmethods to mine their vast data
• Government science, regulatory, and statistical agenciesemploy statisticians to design surveys, make forecasts,develop estimates of income, review new drug applications,assess evidence of health effects of pollutants, . . .
Today
Statistical methods are used routinely inscience, industry/business, and government• Pharmaceutical companies employ statisticians, who work
in all stages of drug development• Statisticians are ubiquitous in medical and public health
research, working with health sciences researchers todesign studies, analyze data, and draw conclusions
• Google, Facebook, LinkedIn, credit card companies, globalretailers employ statisticians to develop and implementmethods to mine their vast data
• Government science, regulatory, and statistical agenciesemploy statisticians to design surveys, make forecasts,develop estimates of income, review new drug applications,assess evidence of health effects of pollutants, . . .
Today
Statistical methods are used routinely inscience, industry/business, and government• Pharmaceutical companies employ statisticians, who work
in all stages of drug development• Statisticians are ubiquitous in medical and public health
research, working with health sciences researchers todesign studies, analyze data, and draw conclusions
• Google, Facebook, LinkedIn, credit card companies, globalretailers employ statisticians to develop and implementmethods to mine their vast data
• Government science, regulatory, and statistical agenciesemploy statisticians to design surveys, make forecasts,develop estimates of income, review new drug applications,assess evidence of health effects of pollutants, . . .
Statistical stories
Some diverse examples where statistics andstatisticians are essential. . .
The controlled clinical trial
The gold standard study for comparison oftreatments (a question of cause and effect)
• An experiment designed to compare a new treatment to acontrol treatment
• Subjects are randomized to receive one treatment or theother⇒ unbiased, fair comparison using statisticalmethods (hypothesis testing)
• In addition, blinding, placebo• The first such clinical trial was conducted in the UK by the
Medical Research Council in 1948, comparingstreptomycin+bed rest to bed rest alone in tuberculosis
• In 1954, 800K children in the US were randomized to theSalk polio vaccine or placebo to assess the vaccine’seffectiveness in preventing paralytic polio
The controlled clinical trial
The gold standard study for comparison oftreatments (a question of cause and effect)• An experiment designed to compare a new treatment to a
control treatment• Subjects are randomized to receive one treatment or the
other⇒ unbiased, fair comparison using statisticalmethods (hypothesis testing)
• In addition, blinding, placebo• The first such clinical trial was conducted in the UK by the
Medical Research Council in 1948, comparingstreptomycin+bed rest to bed rest alone in tuberculosis
• In 1954, 800K children in the US were randomized to theSalk polio vaccine or placebo to assess the vaccine’seffectiveness in preventing paralytic polio
The controlled clinical trial
The gold standard study for comparison oftreatments (a question of cause and effect)• An experiment designed to compare a new treatment to a
control treatment• Subjects are randomized to receive one treatment or the
other⇒ unbiased, fair comparison using statisticalmethods (hypothesis testing)
• In addition, blinding, placebo• The first such clinical trial was conducted in the UK by the
Medical Research Council in 1948, comparingstreptomycin+bed rest to bed rest alone in tuberculosis
• In 1954, 800K children in the US were randomized to theSalk polio vaccine or placebo to assess the vaccine’seffectiveness in preventing paralytic polio
The controlled clinical trial
• In 1969, evidence from a randomized clinical trial becamemandatory for a new product to receive approval from theUS Food and Drug Administration (FDA)
• Because a trial involves only a sample of patients from theentire population, the results are subject to uncertainty
• Statistical methods are critical for determining the samplesize required to ensure that a real difference can bedetected with a specified degree of confidence
• Which is why regulatory bodies like the FDA employ 100sof statisticians
• In the last 4 decades, statisticians have developed newmethods to handle ethical and practical considerations
• E.g., group sequential trials that allow interim analyses atwhich the trial can be stopped early without compromisingthe ability to make a valid comparison
The controlled clinical trial
• In 1969, evidence from a randomized clinical trial becamemandatory for a new product to receive approval from theUS Food and Drug Administration (FDA)
• Because a trial involves only a sample of patients from theentire population, the results are subject to uncertainty
• Statistical methods are critical for determining the samplesize required to ensure that a real difference can bedetected with a specified degree of confidence
• Which is why regulatory bodies like the FDA employ 100sof statisticians
• In the last 4 decades, statisticians have developed newmethods to handle ethical and practical considerations
• E.g., group sequential trials that allow interim analyses atwhich the trial can be stopped early without compromisingthe ability to make a valid comparison
The controlled clinical trial
• In 1969, evidence from a randomized clinical trial becamemandatory for a new product to receive approval from theUS Food and Drug Administration (FDA)
• Because a trial involves only a sample of patients from theentire population, the results are subject to uncertainty
• Statistical methods are critical for determining the samplesize required to ensure that a real difference can bedetected with a specified degree of confidence
• Which is why regulatory bodies like the FDA employ 100sof statisticians
• In the last 4 decades, statisticians have developed newmethods to handle ethical and practical considerations
• E.g., group sequential trials that allow interim analyses atwhich the trial can be stopped early without compromisingthe ability to make a valid comparison
The controlled clinical trial
• In 1969, evidence from a randomized clinical trial becamemandatory for a new product to receive approval from theUS Food and Drug Administration (FDA)
• Because a trial involves only a sample of patients from theentire population, the results are subject to uncertainty
• Statistical methods are critical for determining the samplesize required to ensure that a real difference can bedetected with a specified degree of confidence
• Which is why regulatory bodies like the FDA employ 100sof statisticians
• In the last 4 decades, statisticians have developed newmethods to handle ethical and practical considerations
• E.g., group sequential trials that allow interim analyses atwhich the trial can be stopped early without compromisingthe ability to make a valid comparison
The controlled clinical trial
National forest inventory
Next stop, Bhutan• The Kingdom of Bhutan, in South Asia, transitioned to a
constitutional democracy in 2008• The new constitution mandates that Bhutan maintain 60%
forest cover in perpetuity• A National Forest Inventory was called for. . .
• My friend Tim Gregoire of Yale University, an expert inforest biometry, was consulted to help plan and implementBhutan’s comprehensive NFI
National forest inventory
Next stop, Bhutan• The Kingdom of Bhutan, in South Asia, transitioned to a
constitutional democracy in 2008• The new constitution mandates that Bhutan maintain 60%
forest cover in perpetuity• A National Forest Inventory was called for. . .• My friend Tim Gregoire of Yale University, an expert in
forest biometry, was consulted to help plan and implementBhutan’s comprehensive NFI
National forest inventory
National forest inventory
A NFI is an assessment based on statisticalsampling and estimation of the forest resourcesof a nation• Set policy on forest resource management• Monitor biodiversity, habitat type and extent, land
conversion rates• Measure quantity/quality of wood fiber for commodities• Measure non-wood forest products• Measure carbon storage and change• Reference spatially where resources are located
Statistics is critical to developing the sampling plan for bothremote sensing and field data and to estimation of abundanceof resources based on 100s of measurements
National forest inventory
A NFI is an assessment based on statisticalsampling and estimation of the forest resourcesof a nation• Set policy on forest resource management• Monitor biodiversity, habitat type and extent, land
conversion rates• Measure quantity/quality of wood fiber for commodities• Measure non-wood forest products• Measure carbon storage and change• Reference spatially where resources are located
Statistics is critical to developing the sampling plan for bothremote sensing and field data and to estimation of abundanceof resources based on 100s of measurements
National forest inventory
Pharmacokinetics
What’s behind a drug label?• A drug should be safe and effective• Labeling provides guidance on dose, conditions under
which a drug should/should not be taken• Partly behind this – pharmacokinetics (PK), the science of
“what the body does to the drug”
• Key: Understanding Absorption, Distribution, Metabolism,Excretion in the population and how these processes varyacross patients and are altered by conditions
• Statistical modeling is an integral part of the science
Pharmacokinetics
What’s behind a drug label?• A drug should be safe and effective• Labeling provides guidance on dose, conditions under
which a drug should/should not be taken• Partly behind this – pharmacokinetics (PK), the science of
“what the body does to the drug”• Key: Understanding Absorption, Distribution, Metabolism,
Excretion in the population and how these processes varyacross patients and are altered by conditions
• Statistical modeling is an integral part of the science
Pharmacokinetics
A hierarchical statistical model that allows these processes tovary across patients and conditions is fitted to drugconcentration-time data
Pharmacokinetics
Conc(t) =ka Dose
V (ka − Cl/V )[exp{−(Cl/V )t} − exp(−kat)]
ka = absorption rate, V = volume of distribution, Cl = clearance
Forensic science
An area where statisticians and better statisticsare desperately needed!• Fingerprints, DNA analysis, bite marks, firearm toolmarks,
hair specimens, writing samples, toxicological analysis,. . .• Laboratory- or expert interpretation-based• 2009 US National Academy of Sciences report
• The report cites examples of lack of sufficient recognitionof sources of variability and their effects on uncertainties inmany types of forensic science analyses. . .
Forensic science
“With the exception of nuclear DNA analysis, however, no forensicmethod has been rigorously shown to have the capacity toconsistently, and with a high degree of certainty, demonstrate aconnection between evidence and a specific individual or source.”
“A body of research is required to establish the limits and measuresof performance and to address the impact of sources of variabilityand potential bias.”
“The development of quantifiable measures of uncertainty in theconclusions of forensic analyses . . . and of quantifiable measures ofthe reliability and accuracy of forensic analyses (are needed).”
Basically, the report recommends that current and new forensicpractices should be developed and assessed using properlydesigned experiments and statistical methods!
The hazards of haphazard data
When data are simply observed and collected,without a principled design and randomization,be wary!• Investigations of causal relationships can be compromised
by confounding• E.g., comparison of the effects of competing treatments• When individual patients and their providers decide which
treatment to take, there may be factors that are associatedwith both the choice of treatment and outcome
• Failure to recognize/identify such confounding factors canlead to misleading conclusions
Simpson’s paradox
Data on 2 treatments from a healthcare database
Ave
rage
Out
com
e
Avg Trt A
Avg Trt B
Simpson’s paradox
Data on 2 treatments from a healthcare database
Ave
rage
Out
com
e
Trt A
Trt A
Trt B
Trt B
Male Female
Simpson’s paradox
Data on 2 treatments from a healthcare database
Ave
rage
Out
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Trt A
Trt A
Trt B
Trt B
Avg Trt A
Avg Trt B
A: 80%/20% M/F B: 20%/80% M/F
Male Female
Confounding and other threats
• Statistical methods are available to take confounding intoappropriate account
• . . . but the confounding factors must be recorded in thedatabase!
Other threats• Missing information – why are some factors not recorded
for some individuals?• Drop out – sicker patients may disappear sooner in a
longitudinal study• Etc
Comparative effectiveness research, which strivesto recommend best uses for existing treatment throughanalyses of such databases, requires statistics!
Confronting our data-rich future
I hope I have convinced you that statistics and statisticians areessential to our data-rich future!
Big Data have enormous potential for new generating newknowledge and improving human welfare. However, Big Datawithout statistics have enormous potential to mislead.
“The future demands that scientists, policy-makers, and thepublic be able to interpret increasingly complex information andrecognize both the benefits and pitfalls of statistical analysis.Embedding statistics in science and society will pave the routeto a data-informed future, and statisticians must lead thischarge.”– Davidian and Louis, Science, April 6, 2012
Confronting our data-rich future
I hope I have convinced you that statistics and statisticians areessential to our data-rich future!
Big Data have enormous potential for new generating newknowledge and improving human welfare. However, Big Datawithout statistics have enormous potential to mislead.
“The future demands that scientists, policy-makers, and thepublic be able to interpret increasingly complex information andrecognize both the benefits and pitfalls of statistical analysis.Embedding statistics in science and society will pave the routeto a data-informed future, and statisticians must lead thischarge.”– Davidian and Louis, Science, April 6, 2012
Confronting our data-rich future
I hope I have convinced you that statistics and statisticians areessential to our data-rich future!
Big Data have enormous potential for new generating newknowledge and improving human welfare. However, Big Datawithout statistics have enormous potential to mislead.
“The future demands that scientists, policy-makers, and thepublic be able to interpret increasingly complex information andrecognize both the benefits and pitfalls of statistical analysis.Embedding statistics in science and society will pave the routeto a data-informed future, and statisticians must lead thischarge.”– Davidian and Louis, Science, April 6, 2012
2013 – the International Year of Statistics
A celebration of the contributions of statistics islong overdue!
http://statistics2013.org
References and further reading
Aldrich, J. Figures from the history of probability and statistics.http://www.economics.soton.ac.uk/staff/aldrich/Figures.htm
Davidian, M. and Louis, T.A. (2012). Why statistics? Science, 336, 12.
Feinberg, S.E. (1992). A brief history of statistics in three and onehalf chapters: A review essay. Statistical Science, 7, 208–225.
Stigler, S.M. (1986). The History of Statistics: The Measurement ofUncertainty Before 1900. Harvard University Press.
Personalized Medicine:The Right Treatment for the
Right Patient
Marie Davidian
Department of StatisticsNorth Carolina State University
January 11, 2013
“The right treatment for the right patient(at the right time) ”
So why is a statistician talking to you aboutpersonalized medicine?
My goal: To convince you that the quantitativesciences, and especially statistics, are essentialin the quest for personalized medicine!
So why is a statistician talking to you aboutpersonalized medicine?
My goal: To convince you that the quantitativesciences, and especially statistics, are essentialin the quest for personalized medicine!
Roadmap
• Some background
• What is personalized medicine?• Statistics, mathematics, and personalized
medicine
Roadmap
• Some background• What is personalized medicine?
• Statistics, mathematics, and personalizedmedicine
Roadmap
• Some background• What is personalized medicine?• Statistics, mathematics, and personalized
medicine
Modern expectationThere should be a treatment for that!
“Treatments” – drugs, biologic products, medicaldevices, surgical procedures, behavioraltherapies – are omnipresent in today’s world• Cholesterol-lowering medications, anti-platelet therapies• Anti-depressants, anti-psychotics, cognitive therapies• Chemotherapies, tamoxifen (Nolvadex), bevacizumab
(Avastin), rituximab (Retuxan)• Antiretroviral therapies, e.g., PIs, NNRTIs, FIs• Artificial hips, implants
How are treatments developed?
Who decides if they “work?” How is thisdecided?
How are treatments developed and evaluated?
Main players• Pharmaceutical, biotechnology, device companies• University and government research
Who decides? And how? Today• US: Food and Drug Administration (FDA)• EU: European Medicines Agency (EMA)• Japan: Pharmaceuticals and Medical Devices Agency• International Conference on Harmonisation (ICH)• Safety – can people take it?• Efficacy – does it do anything in humans?• Effectiveness – is it better or at least as good as what is
currently available?• Do the benefits outweigh the risks?
How are treatments developed and evaluated?
Main players• Pharmaceutical, biotechnology, device companies• University and government research
Who decides? And how? Today• US: Food and Drug Administration (FDA)• EU: European Medicines Agency (EMA)• Japan: Pharmaceuticals and Medical Devices Agency• International Conference on Harmonisation (ICH)• Safety – can people take it?• Efficacy – does it do anything in humans?• Effectiveness – is it better or at least as good as what is
currently available?• Do the benefits outweigh the risks?
Regulatory process
Today, the process of deciding is highlyregulated
But it wasn’t always like this. . .
Regulatory process
Today, the process of deciding is highlyregulated
But it wasn’t always like this. . .
No regulatory process
At the beginning of the 20th century, there wasessentially no regulation anywhere!• Manufacturers could advertise any product as a treatment
for anything, with no evidence• Drugs like opium, heroin, cocaine were freely available• No requirements for labeling or a list of ingredients• A “free-for-all”
Path to modern regulatory agencies
Little by little, steps were taken• To create what is now the modern FDA in the US (1927)• To require evidence of safety in the US (1938)• To introduce the concept of a prescription in the US (1951)
The bombshell: 1962 – Thalidomide• Anecdotal reports of birth defects in Europe• A FDA medical officer argued for keeping the drug off the
US market⇒ public support for stronger drug regulation• Legislation enacted in the US requiring demonstration of
safety and effectiveness for the first time by “substantialevidence” from “well-controlled studies”
Today
1962 to present• The Declaration of Helsinki was developed by the World
Medical Association to set forth ethical principles forresearch involving human subjects (1964)
• Similarly, the Belmont Report in the US (1979)• The current, highly regulated process of bringing a new
treatment to market was established
Fundamental – the controlled clinical trial• Evaluation of effectiveness• Comparison of a new treatment to standard of care• Comparison of existing treatments to establish new uses
The controlled clinical trial
Basics of a “confirmatory” clinical trial• A sample of subjects with the disease/disorder is recruited• 100s to 1000s of subjects• Subjects are randomized to treatments under study⇒ eliminate bias, allow fair comparison
• A clinical outcome is ascertained for each subject• E.g., survival time in cancer, viral load level in human
immunodeficiency virus (HIV) infection after 1 year
The controlled clinical trial
Effectiveness• Compare some summary measure of clinical outcomes
between/among treatments• E.g., the average• “Is the average outcome if all patients in the population
took treatment A different from (better than) that if they allinstead took treatment B?”
• Use statistical methods to evaluate the strength of theevidence in the data from the sample supporting a realdifference in the population
Results
Thus, usually• Assesment of effectiveness and regulatory approval are
based on a summary measure (e.g., an average) acrossthe entire population
• Statistics is key
Success• Countless treatments have been approved on this basis• And have benefited numerous patients
However. . .• All patients are not created equal
Patient heterogeneity
Patient heterogeneity
We’re all different• Physiological, demographic characteristics• Medical history• Genetic/genomic characteristics
What works for a patient with one set ofcharacteristics might not work for another
Patient heterogeneity
We’re all different• Physiological, demographic characteristics• Medical history• Genetic/genomic characteristics
What works for a patient with one set ofcharacteristics might not work for another
An (admittedly contrived) example
Average outcome in the patient population• Larger outcomes are better (survival time)• If all patients took treatment A = 9 months• If all patients took treatment B =18 months• Treatment B is better on average
Genetic mutation• 20% have it, 80% don’t• If all patients took treatment A = (0.2)(25) + (0.8)(5) = 9• If all patients took treatment B = (0.2)(10) + (0.8)(20) = 18• That is, patients with the mutation do much better on
treatment A! (25 months vs. 10 months)
An (admittedly contrived) example
Average outcome in the patient population• Larger outcomes are better (survival time)• If all patients took treatment A = 9 months• If all patients took treatment B =18 months• Treatment B is better on average
Genetic mutation• 20% have it, 80% don’t
• If all patients took treatment A = (0.2)(25) + (0.8)(5) = 9• If all patients took treatment B = (0.2)(10) + (0.8)(20) = 18• That is, patients with the mutation do much better on
treatment A! (25 months vs. 10 months)
An (admittedly contrived) example
Average outcome in the patient population• Larger outcomes are better (survival time)• If all patients took treatment A = 9 months• If all patients took treatment B =18 months• Treatment B is better on average
Genetic mutation• 20% have it, 80% don’t• If all patients took treatment A = (0.2)(25) + (0.8)(5) = 9
• If all patients took treatment B = (0.2)(10) + (0.8)(20) = 18• That is, patients with the mutation do much better on
treatment A! (25 months vs. 10 months)
An (admittedly contrived) example
Average outcome in the patient population• Larger outcomes are better (survival time)• If all patients took treatment A = 9 months• If all patients took treatment B =18 months• Treatment B is better on average
Genetic mutation• 20% have it, 80% don’t• If all patients took treatment A = (0.2)(25) + (0.8)(5) = 9• If all patients took treatment B = (0.2)(10) + (0.8)(20) = 18
• That is, patients with the mutation do much better ontreatment A! (25 months vs. 10 months)
An (admittedly contrived) example
Average outcome in the patient population• Larger outcomes are better (survival time)• If all patients took treatment A = 9 months• If all patients took treatment B =18 months• Treatment B is better on average
Genetic mutation• 20% have it, 80% don’t• If all patients took treatment A = (0.2)(25) + (0.8)(5) = 9• If all patients took treatment B = (0.2)(10) + (0.8)(20) = 18• That is, patients with the mutation do much better on
treatment A! (25 months vs. 10 months)
Patient heterogeneity
Moral• “One size does not fit all”• Use a patient’s characteristics to determine which
treatment option might be best for him/her
• Genomic information may hold great potential• Personalized medicine
Patient heterogeneity
Moral• “One size does not fit all”• Use a patient’s characteristics to determine which
treatment option might be best for him/her• Genomic information may hold great potential• Personalized medicine
Patient heterogeneity
Not so fast . . .• How do we do this?• What are the challenges and possible pitfalls?
Popular persepective on personalized medicine
Subgroup identification and targeted treatment• Can we determine subgroups of patients who share
certain characteristics and who are more likely to do betteron a particular treatment than on others?
• Can biomarkers be developed to identify such patients?• In fact, can a new treatment be developed to target a
subgroup that is likely to benefit?• Can clinical trials and approval be focused on particular
subgroups of patients?
Focus on finding and treating a subgroup
Popular persepective on personalized medicine
Subgroup identification and targeted treatment• Can we determine subgroups of patients who share
certain characteristics and who are more likely to do betteron a particular treatment than on others?
• Can biomarkers be developed to identify such patients?• In fact, can a new treatment be developed to target a
subgroup that is likely to benefit?• Can clinical trials and approval be focused on particular
subgroups of patients?
Focus on finding and treating a subgroup
Popular persepective on personalized medicine
Another perspective on personalized medicine
Can we determine how best to treat the entirepopulation?• Given information on any patient’s characteristics, can we
determine the treatment most likely to benefit him/her?• In fact, can we come up with “rules” that take a patient’s
chacteristics as input and output the best option forhim/her?
Focus on treating everyone
Another perspective on personalized medicine
Can we determine how best to treat the entirepopulation?• Given information on any patient’s characteristics, can we
determine the treatment most likely to benefit him/her?• In fact, can we come up with “rules” that take a patient’s
chacteristics as input and output the best option forhim/her?
Focus on treating everyone
Challenge
In either case• It’s all about identifying “tailoring variables”• Knowledge of the biology integrated with statistics
Finding tailoring variables
Ave
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Trt A
Trt A
No Mutation Mutation
Finding tailoring variables
Ave
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Trt A
Trt A
Trt B
Trt B
No Mutation Mutation
Finding tailoring variables
Ave
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Trt A
Trt A
No Mutation Mutation
Finding tailoring variables
Ave
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Trt A
Trt A
Trt B
Trt B
No Mutation Mutation
Result
Moral• Need to identify tailoring variables• This is a statistical problem. . .
Challenge, more precisely
High dimensional data!• Must sift through 1000s of characteristics to identify the
right combination of key tailoring variables• Based on data from a sample of patients (10s, 100s,
1000s)
Challenge, more precisely
Pitfalls• Computational complexity• Chance to miss important characteristics• Chance of false discovery• Statistical methods must be used
Can we treat everyone “optimally?”
Clinical practice: Treatment decisions over time• Fixed schedule• Event(s) necessitating a decision
Clinical decision-making• Clinical judgment used to synthesize all information
available, make a “personalized” treatment decision• Can this be formalized?• That is, can we construct decision rules?
Cancer treatment
Two decision points• Decision 1: Induction chemotherapy (C)• Decision 2: Maintenance treatment (M) for patients who
respond, Salvage chemotherapy (S) for those who don’t• Several options for each• Goal: Prolong survival
Sequential decision-making
• Decision rule 1: Genetic/genomic profile, demographics,physiological characteristics, medical history,. . .⇒ which of2 chemotherapies C to use
• Decision rule 2: Previous info + responder status,intermediate physiological/clinical measures, sideeffects,. . .⇒ which of 2 maintenance therapies M(responders) or 2 salvage chemotherapies S(non-responders) to use
Sequential decision-making
• Decision rule 1: Genetic/genomic profile, demographics,physiological characteristics, medical history,. . .⇒ which of2 chemotherapies C to use
• Decision rule 2: Previous info + responder status,intermediate physiological/clinical measures, sideeffects,. . .⇒ which of 2 maintenance therapies M(responders) or 2 salvage chemotherapies S(non-responders) to use
Decision rules
• Decision rule 1: “If age < 50, progesterone receptor level< 10 fmol, RAD51 mutation, then give C1, else, give C2”
• Decision rule 2: “If patient responds, age < 60, CEA > 10ng/mL, progesterone receptor level < 8 fmol, give M1, else,give M2; if does not respond, age > 65, P53 mutation, CA15-3 > 25 units/mL, then give S1, else, give S2”
Decision rules
• Decision rule 1: “If age < 50, progesterone receptor level< 10 fmol, RAD51 mutation, then give C1, else, give C2”
• Decision rule 2: “If patient responds, age < 60, CEA > 10ng/mL, progesterone receptor level < 8 fmol, give M1, else,give M2; if does not respond, age > 65, P53 mutation, CA15-3 > 25 units/mL, then give S1, else, give S2”
Statistical problem
Construct (estimate) rules from data• At each decision, identify the tailoring variables and the
right function of them to give a decision rule• Goal: Find the decision rules that would lead to best
expected outcome if followed by all patients• Each rule must take account of what might happen later
when deciding what to do now• How to do this: Statistical modeling, dynamic programming
Treatment of acute HIV infection
47 year old male goes to the ER• 102.5 ◦F fever, headache, nausea/vomiting, rash, . . .• MSM, recent unprotected sex, . . .• Tests for cytomegalovirus (CMV), Epstein-Barr virus
(EBV), influenza negative• HIV test positive• HIV RNA (viral load ) > 750,000 copies/ml• CD4+ T cell count = 432 cells/µL
Diagnosis – Acute HIV infection
Treatment of acute HIV infection
47 year old male goes to the ER• 102.5 ◦F fever, headache, nausea/vomiting, rash, . . .• MSM, recent unprotected sex, . . .• Tests for cytomegalovirus (CMV), Epstein-Barr virus
(EBV), influenza negative• HIV test positive• HIV RNA (viral load ) > 750,000 copies/ml• CD4+ T cell count = 432 cells/µL
Diagnosis – Acute HIV infection
Treatment of acute HIV infection
Treatment of acute HIV infection
Should this patient be started on antiretroviraltherapy (ART)?
• Disadvantages: Cost, side effects, eventual drugresistance, limit future ART options
• Advantages: “Train” the immune system through cycles oftreatment “interruption” – cycles of treatment and viralexposure may allow patient to maintain control of virus
More generally• Can we determine the “best” way to use ART to manage
the infection and prolong time to AIDS?
Treatment of acute HIV infection
Should this patient be started on antiretroviraltherapy (ART)?• Disadvantages: Cost, side effects, eventual drug
resistance, limit future ART options• Advantages: “Train” the immune system through cycles of
treatment “interruption” – cycles of treatment and viralexposure may allow patient to maintain control of virus
More generally• Can we determine the “best” way to use ART to manage
the infection and prolong time to AIDS?
Treatment of acute HIV infection
Should this patient be started on antiretroviraltherapy (ART)?• Disadvantages: Cost, side effects, eventual drug
resistance, limit future ART options• Advantages: “Train” the immune system through cycles of
treatment “interruption” – cycles of treatment and viralexposure may allow patient to maintain control of virus
More generally• Can we determine the “best” way to use ART to manage
the infection and prolong time to AIDS?
Mathematical modeling
HIV dynamic model• Represent mechanisms involved in virus-immune system
interaction mathematically• System of differential equations• Over-simplification of complex biology, but can be useful• Predict viral load, CD4 count at any time under any ART
strategy
Dynamical system model
Dynamical system model
T1 = λ1 − d1T1 − {1− ε1u(t)}k1VIT1
T ∗1 = {1− ε1u(t)}k1VIT1 − δT ∗
1 −m2ET ∗1
T2 = λ2 − d2T2 − {1− f ε1u(t)}k2VIT2
T ∗2 = {1− f ε1u(t)}k2VIT2 − δT ∗
2 −m2ET ∗2
VI = {1− ε2u(t)}103NT δ(T ∗1 + T ∗
2 )− cVI
−{1− ε1u(t)}ρ1103k1T1VI
− {1− f ε1u(t)}ρ2103k2T2VI
VNI = ε2u(t)103NT δ(T ∗1 + T ∗
2 )− cVNI
E = λE +bE(T ∗
1 + T ∗2 )
(T ∗1 + T ∗
2 ) + KbE −
dE(T ∗1 + T ∗
2 )
(T ∗1 + T ∗
2 ) + KdE − δEE
Model-based treatment
Add statistics• Fit the model to data on many subjects using statistical
methods• Use the fitted model + control theory to design ART
interruption strategies• Use the model to study the consequences of different ART
interruption strategies on “virtual patients” (simulation)• Study the promising ones on real patients in a clinical trial
Model-based treatment
Model-based treatment
Wrap-up
• The goal of truly personalized medicine isstill elusive
• But it is attainable!• Combining quantitative sciences (statistics,
mathematics, computer science,. . . ) withbiological, biomedical sciences is one keythat will pave the way