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Statistical Models: The Rest of the Story. Scott L. Zeger Hurley-Dorrier Professor and Chair Department of Biostatistics The Johns Hopkins University Bloomberg School. What is a model?. What is a statistical model?. Tool for those empirical sciences where signals come embedded in noise.

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statistical models the rest of the story

Statistical Models: The Rest of the Story

Scott L. Zeger

Hurley-Dorrier Professor and Chair

Department of Biostatistics

The Johns Hopkins University Bloomberg School

what is a statistical model
What is a statistical model?

Tool for those empirical sciences where signals come embedded in noise

Lens through which to view data to better understand the signal

Tool for quantifying the evidence in data about a particular truth we seek

empirical science search for truth
Empirical science: search for “truth”

Probability – statistical model

Observed Value

for a Representative

Sample

Truth for

Population

Statistical inference

how to choose the best model

You can not choose the best model because there isn’t one

You can choose a useful model based upon prior scientific knowledge

You can explore and report how your scientific findings vary over a set of other useful models

You can average your results across useful models

How to Choose the Best Model
  • Miminize the mean squared error
  • Minimize the Akaike Information Criterion (AIC)
  • Minimize the Bayesian Information Criterion (BIC)
  • Maximize the likelihood function
  • Cross-validate
  • Jackknife
  • Bootstrap
  • Boost, then bag
  • etc
causal model

Dollars

Smoking

Disease

Death

Causal Model
what do we know about smoking and medical expenditures
What Do We Know about Smoking and Medical Expenditures
  • WHO, U.S. Surgeon General and IARC say smoking causes 13 major diseases:
    • Lung cancer; COPD; atherosclerosis; MI; stroke; ….
  • In the U.S., most people receive treatment for major chronic diseases (e.g. lung cancer)
  • It cost money to treat your disease
what we know little about
What we know LITTLE about
  • Whether smoking causes people to use more or less medical services to treat smoking caused diseases
  • Whether smoking causes people without a major disease to seek more or less medical services
    • “I hate my doctor, she tries to take my cigs away”
    • “I go as often as I can afford; got to watch out for those diseases that can kill me”
competing causal models

Smoking

Disease

Dollars

Smoking

Dollars

Competing Causal Models
smoking attributable burden for cohort of 60 million who started under 21 years old 1954 2000
Smoking Attributable Burden for Cohort of 60 Million Who Started Under 21 Years Old, 1954-2000
slide17

“Know this”:

$1 Trillion +- 0.2 T for 10% of pop

Smoking

Disease

Dollars

???

Estimate well what you can; estimate poorly what you must.

Don’t dilute decent causal estimates with causal speculates (unless you intend to make everything uncertain)

what we know well
What We Know Well
  • 2,237 U.S. soldiers (DoD)
  • 99 British soldiers (British Govt)

What We Know Less Well

  • 4,027 Iraqi police (News reports compiled by iCasualties.org)
  • 28,198 - 31,800 Iraqi civilians (IBC web-site)
    • The count includes civilian deaths caused by coalition military action and by military or paramilitary responses to the coalition presence (e.g. insurgent and terrorist attacks). It also includes excess civilian deaths caused by criminal action resulting from the breakdown in law and order which followed the coalition invasion. Compiled from eye-witness reports and news articles
slide20

Iraq invasion

Violence

Death

~30,000 Iraqi deaths

Lack of sanitation

Lack of clean water

Poor nutrition

Limited access to medical care

Extreme stress and grief

summary
Summary
  • A model defines the boundaries of an analysis and can determine what will be learned from data
    • Like a lens determines what you will see
  • Same model for two problems
    • Separate what can be estimated precisely from what can not
    • Prior knowledge about pathway
  • Too much uncertainty invalidates, whether it should or not
slide25

Timing of Proceeds Relative to Smoking Attributable Expenditures for Major Diseases Only