Fundamentals of Applied Statistics

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Fundamentals of Applied Statistics

• Gerald van Belle
• Department Biostatistics, Department of
  Occupational and Environmental Health Sciences
• University of Washington,
• Seattle, WA.

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Damaged Spitfire
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Vulnerability Analysis of Spitfires (sample
15/400)
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Vulnerability analysis
Abraham Wald Advice Reinforce planes Where they
have Not been hit
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(No Transcript)
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Theme for this Week

• Variation
• Causation

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Basic BiostatisticsTheme for this Week

• What is the question?
• Is it measurable?
• Where will you get the data?
• What do you think the data are telling you?

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Outline of talk

• Variation Causation
• Question
• Measurable
• Get data
• Interpret

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Two definitions

• A.N. Whitehead (1925) on science
• a vehement and passionate interest in the
  relation of general principles to irreducible and
  stubborn facts.
• Statistics
• A vehement and passionate interest in the
  relation of general principles to
  variationvariation observed, variation managed,
  and variation induced.

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What is the question? Is it measurable?
Not everything that can be counted counts and
not everything that counts can be
counted. Albert Einstein
(The things that really count cant be countedor
are very difficult to count)
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Questions that count and may be countable

• Are pesticides neurotoxic?
• Does air pollution cause ill health?
• Is obesity increasing in Costa Rica?
• Does Prozac increase suicide rate?
• Why does it take 10 years to get a new drug on
  the market?
• Your question?

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Issues in measurability

• Not measurable e.g. ethical imperative
• Latent trait, e.g. cognition
• Takes too long, e.g. survival in clinical
  trialSurrogate outcomes .e.g. blood pressure
• Measurement destroys object, e.g. light bulb
• Measurement alters response e.g. Hawthorne
• Other issues?
• May not be able to summarize with one number
  (next slide)

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Statistician drowning in river of average depth
25 cm
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A. Working with variation

• Describing and classifying variation
• Selection
• Controlling variation
• Inducing variation
• Working with variation
• Dealing with missing data

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1. Describing and classifying variation

• We tell stories of abnormality Air travel
  horror stories, laptop disasters,
• We sort into genres art, biology, literature
  Concept of population Characteristics of
  population and sample
• Variation in time, space, social structures,
  Waves on beach (non-stationarity) Hierarchy,
  social class
• We make inferences based on limited data And
  often get the wrong population Basis for a
  great deal of humor Switch in expectation

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2. Selection in the face of variation

• Need to know selection mechanismRandom selection
  as gold standard
• Representativeness Kruskal and Mosteller
  papers Slippery concept Large sample vs small
  sample

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2. Selection in the face of variation

• State question
• Define measurement(s)
• Define population of inference
• Specify selection mechanism
• Random selection is gold standard
• Random sample is representative sample

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3. Controlling variation

• Clearest examples in sports Divisions,
  junior,
• Societal examplesMin, max speed
  limitsOccupational (noise limits, flying
  hours)Vergunningen, vergunningen,
• Blocking in statistics

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4. Inducing variation

• Antitrust laws Increase competition, i.e.
  variability
• Draft system in sports Teams more equal, P(win)
  near 1/2
• Societal Admission to medical school in
  Holland Representativeness (slippery concept)
  Key to clinical trials

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5. Working with variation

• Statisticians are expert at working with
  variation
• Example from Dorfman (1943)
• Situation Assay for syphillis in 1000s of army
  recruits relatively few of whom had syphillis.
• Pool n samples, if negative, stop. If positive
  test all n samples.

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Dorfman sampling efficiency

Assume pool of n Probability subject positive
p X number of assays needed
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Dorfman sampling efficiency, Eff

Efficiency of pooling relative to no pooling by
size of pool (n) and prevalence of occurrence of
event (p)
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6. Missing data

• Serious problem, obviously
• Spitfire example
• Impacts population of inference
• Anatomy of missingness
• Normal (e.g. pediatrician chart)
• Transcription error
• Just not there (Murphy was here)
• Deliberately missing (e.g. extended testing on
  subset of patients)

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Another anatomy of missingness

• as we know,
• there are known knowns
• there are things we know we know.
• We also know there are known unknowns
• that is to say,
• we know there are some things
• we do not know.
• But there are also unknown unknowns
• the ones we dont know we dont know.
• Donald Rumsfeld

(set to music, see NPR website)
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Translation into modern statistics

• as we know,
• there are known knowns
• there are things we know we know.
• We also know there are known unknowns
• that is to say,
• we know there are some things
• we do not know.
• But there are also unknown unknowns
• the ones we dont know we dont know.
• Donald Rumsfeld

Non-missing MCAR/MAR Non-ignorable
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Now its your turn
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B. Working with causation

• Hard-wired to look for causes
• Aristotles four causes
• Usual state of nature
• Establishing cause-effect in science
• Observational and experimental data

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1. Hard-wired to look for causes

• Yesterday, the building is shaking
• Peter Jennings story
• Accident reports

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A few accident reports

• 1. Coming home I drove into the wrong house and
  collided with a tree I dont have.
• 2. A truck backed through my windshield into my
  wifes face.
• 3. I saw a slow moving, sad-faced old gentle-man
  as he bounced off the roof of my car.
• 4. I had been driving for forty years when I
  fell asleep at the wheel and had an accident.

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2. Aristotles four causes

• Material cause (table made of wood)
• Formal cause (four legs and flat top make this
  a table)
• Efficient cause (carpenter makes a table)
• Final cause (surface for eating or writing
  makes this a table) (From S.M. Cohen, U
  Washington)

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3. Usual state of nature
Explanations after accident Crime in search of
criminal Sickness in search of cause Childs
behavior and parent responsibility .
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4. Establishing cause-effect in science

• Causation requires longitudinal data
• Randomized expts intrinsically so
• Cohort study closest non-experimental analogue
• Usually a higher standard than law(law more
  likely than not, pgt0.50)(statistics
  significance level, pgt0.95)

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5. Observational vs experimental studies

• Characteristic Observational Experiment
• Ethical issues Fewer More
• Researcher control Less More
• Orientation Retrospective Prospective
• Selection bias Big problem Less
• Confounding Present Absent
• Realism More Less
• Causal plausibility Weaker Stronger
• Analysis More complicated Less

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5. Causation and non-experimental data

• Selection bias
• Where did you get the data?
• Confounding
• What do you think the data are telling you?

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Causal assertion. Is it measurable?
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Basic Biostatistics Applied to NYT

• What is the question?
• Is it measurable?
• Where will you get the data?
• What do you think the data are telling you?

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Basics of StatisticsBasics of Life

• Variation
• Causation