Transcript Statistical Reasoning and Analysis

Statistical Reasoning and Analysis
Tony Panzarella
Department of Biostatistics
Princess Margaret Cancer Center
[email protected]
September 2014
“Lies, damned lies, and statistics”
(British Prime Minister Benjamin Disraeli,1804–1881)
“Talked politics, scandal, and the three
classes of witnesses—liars, d—d liars,
and experts.” (The Life and Letters of Thomas
Henry Huxley by L. Huxley, 1900)
https://en.wikipedia.org/wiki/Lies,_damned_lies,_and_statistics
Statistics – the new Sexy!?
 Hal Varian, Google's chief economist, says statistician
will be 'the sexy job in the next 10 years.' Chad Schafer
explains why. (August 4, 2013, Daniel Marsula/Post-Gazette)
http://www.post-gazette.com/opinion/Op-Ed/2013/08/04/The-Next-PageData-Driven-Why-statistics-is-sexy/stories/201308040172#ixzz3CFcEr9IV
 Google’s prediction: What will be the "sexy" job in the next ten years?
Here’s a strange prediction
from Google’s Chief Economist:
“I keep saying that the sexy job
in the next 10 years will be
statisticians. And I’m not kidding.”
Some Keywords
Study Designs, Confounding
Pitfalls of Data Analysis
 Bias (representative sampling, statistical
assumptions)
 Errors in methodology (statistical power,
multiple comparisons, measurement error)
 Interpretation (precision and accuracy,
causality, graphical representation)
Era of Big Data
Prelude: Design and Analysis
Objective: Design the ultimate Intro to
PHS talk… and the worst one that I can
still get away with…
Methods: Identify topic(s), and delivery
with visuals
Examples; No formula
Take-home messages
Correlations, Cluster analysis
Source: Sebastian Wernicke, 2010, TedTalks
Nonparametric methods using ranks,
Discriminant analysis
Source: Sebastian Wernicke, 2010, TedTalks
Confidence Intervals, Associations,
Time-to-event analysis
Source: Sebastian Wernicke, 2010, TedTalks
Data Mining, Pattern Recognitions
Source: Sebastian Wernicke, 2010, TedTalks
Pattern Recognitions
(Evidence….Hans Rolling)
Source: Sebastian Wernicke, 2010, TedTalks
Hans Rolling “The best stats you’ve ever seen, New insights on poverty)
Motivating Example: Smoking & Survival
20-year follow-up study, Wickham in UK
(Tunbridge et al. 1977)
1972-1974, one-in-six survey of the electoral
roll, largely concerned with thyroid disease and
heart disease
For simplicity, consider women aged 45 to 75 at
the start of the study
 Smoking status: current smoker (Y/N)
 20-year survival info: determined for all women in
the study
Smoking & Survival (Cont’d)
Protective effect of smoking?
(data adapted from Appleton et al. 1996, Am. Stat.)
Smoking & Survival (Con’t)
 Consider 10-year ranges: 45-54,55-64,65-75
 Non-smoking group does better in each case!
Gender Bias, or Not?
1973, UC Berkeley
was sued for
discrimination
against women in
graduate school
admissions
Percent acceptance:
Male vs Female,
44% vs. 35%
Gender Bias, or Not? (cont’d)
P. J. Bickel, E. A. Hammel, J. W. O'Connell.
(1975). Sex Bias in Graduate Admissions: Data
from Berkeley. Science 187, (4175). pp. 398-404
Message #1
Be aware of the dangers of ignoring a
covariate that is correlated to an outcome
variable and an explanatory one.
 Simpson, E.H. (1951). “The interpretation of
Interaction in Contingency Tables”, Journal of the
Royal Statistical Society, B, 13, 238-241.
 Simpson’s Paradox; many other examples
Guard Against Biases
Biases due to …
Selection of subjects: web surveys
Responses: e.g. question on income
Contamination in controls: non-blind study
Recall: food-intake
Attrition: drop out
Reporting: negative findings
Publication: meta-analysis
Over thirty kinds of biases
Guard Against Biases
[BACKUP REFERENCE] Bias in design
 Concato et al (2001). A nested case–control study of the
effectiveness of screening for prostate cancer: research design


Concato et al. (2001) reports another type of bias in designs for prostate cancer detection when
groups were asymptomatic men who received digital rectal examination, screening by prostate
specific antigen and transrectal ultrasound, but there was no ‘control’ group with ‘no screening’.
Thus the effectiveness of screening could not be evaluated.
Although prostate-specific antigen (PSA) and digital rectal examination (DRE) are commonly used
to screen for prostate cancer, available data do not confirm that either test improves survival. This
report describes the methodological aspects of a nested case–control study addressing the
question of whether PSA screening, with or without DRE, is effective in increasing survival.
Potential sources of bias are discussed, as well as corresponding strategies used to avoid them
Possible steps to minimize bias
 Assess the validity of the identified target population, and the groups to
be included in the study in the context of objectives and the methodology.
 Evaluate the reliability & validity of the measurements required to assess
the antecedents and outcomes, also other tools you plan to deploy.
 Carry out a pilot study and pretest the tools. Make changes as needed.
 Identify possible confounding factors and other sources of bias; develop
an appropriate design that can take care of most of these biases.
 Use matching, blinding, masking, and random allocation as needed.
 Analyze the data with proper statistical methods. Use standardized or
adjusted rates where needed, do the stratified analysis, or use
mathematical models such as regression to take care of biases that
could not be ruled out by design.
 Report only the evidence based the results – enthusiastically but
dispassionately
Multiple Testing (Large p & small n)
Data Dredging
“Deming, data and observational studies: a
process out of control and needing fixing”
Young and Karr (2011) Significance, p116-120.
“Deming, data and observational studies: a
process out of control and needing fixing”
Deming, data and
observational studies: a
process out of control
and needing fixing”
Young and Karr (2011).
Significance, p116-120
•
Young, S. S. and Yu, M. (2009) To
the Editor. Journal of the
American Medical Association,
301, 720–721.
Visual Display of Quantitative Information
• Effectiveness of traffic enforcement in 1955-6, Before vs. After
Source (Tufte, 1983)
In the Age of BIG Data
Does Big Data make Statistics obsolete?
NO!
BIG data, Big mistake? (Google Flu)

http://www.ft.com/cms/s/2/21a6e7d8-b479-11e3-a09a-00144feabdc0.html#axzz3CHWGduc7
Statistical Truisms
 Correlation does not imply Causation
In fact, causal relationships are among the most
significant discoveries from big data that analytics
practitioners seek. Finding causes to observed effects
would truly be a gold mine of value for any business,
science, government, healthcare, or security group that
is analyzing big data.
 Sample variance does not go to zero,
even with Big Data
Statistical Truisms (cont’d)
Sample bias does not necessarily go to
zero, even with Big Data
Sample bias can lead to models with biased results,
slanted against the wonderful diversity of the original
population
 Absence of Evidence is not the same as
Evidence of Absence
 Reference: http://www.amstat.org/publications/jse/v10n3/chance.html
Acknowledgements
Prof. Wendy Lou
Q&A