According to scientists, too much coffee may cause...

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• Coffee Chronicles
• BY MELISSA AUGUST, ANN MARIE BONARDI, VAL
  CASTRONOVO, MATTHEW
• JOE'S BLOWS Last week researchers reported that
  coffee might help prevent Parkinson's disease. So
  is the caffeine bean good for you or not? Over
  the years, studies haven't exactly been clear

• According to scientists, too much coffee may
  cause...
• 1986 --phobias, --panic attacks
• 1990 --heart attacks, --stress, --osteoporosis
• 1991 -underweight babies, --hypertension
• 1992 --higher cholesterol
• 1993, 08 --miscarriages
• 1994 --intensified stress
• 1995 --delayed conception
• But scientists say coffee also may help
  prevent...
• 1988 --asthma
• 1990 --colon and rectal cancer,...
• 2004Type II Diabetes (6 cups per day!)
• 2006alcohol-induced liver damage
• 2007skin cancer

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Medical Studies
The General Idea
Evaluate whether a risk factor (or preventative
factor) increases (or decreases) your risk for an
outcome (usually disease, death or intermediary
to disease).
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• Association test between categorical variables
  

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General 2x2 Table
N
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Risk Ratio ( Relative Risk)
Risk ratio is used to compare the risk for two
groups An risk of 1 means there is no
difference between the groups.
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Coronary calcification is a process in which the
interior lining of the coronary arteries develops
a layer of hard substance known as plaque.
Excessive amounts of cholesterol, fat, and waste
material become calcified in arteries that have
been weakened or damaged due to smoking, high
blood pressure, diabetes, or a generally
unhealthy diet. Coronary calcification restricts
blood flow, presenting the risk of chronic chest
pain, heart attacks, and eventual heart
failure.Is depression and coronary
calcification is associated
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Difference of proportions Z-test
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Or, use relative risk (risk ratio) Compare the
risk for each groups
See how to get this in R
Interpretation those with coronary calcification
are 35 more likely to have depression (not
significant).
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Or, use chi-square test
Observed
Expected
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Chi-square test
Note 1.77 1.332
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Chi-square test also works for bigger contingency
tables (RxC)
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Chi-square test also works for bigger contingency
tables (RxC)
Coronary calcification No depression Sub-threshhold depressive symptoms Clinical depressive disorder
0-100 865 20 9
101-500 463 13 11
gt500 511 12 16
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Observed
Expected
Coronary calcification No depression Sub-threshhold depressive symptoms Clinical depressive disorder
0-100 865 20 9 894
101-500 463 13 11 487
gt500 511 12 16 539
1839 45 36 1920
Coronary calcification No depression Sub-threshhold depressive symptoms Clinical depressive disorder
0-100 8941839/1920 856.3 84945/1920 21 894-(21856.3)16.7
101-500 4871839/1920 466.5 48745/1920 11.4 487-(466.511.4)9.1
gt500 1839-(856.3466.5) 516.2 45-(2111.4) 12.6 36-(16.79.1) 10.2
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Chi-square test
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Cause and effect?
depression in elderly
atherosclerosis
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Confounding?
depression in elderly
atherosclerosis
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Cross-Sectional Studies

• Advantages
• cheap and easy
• generalizable
• good for characteristics that (generally) dont
  change like genes or gender
• Disadvantages
• difficult to determine cause and effect
• problematic for rare diseases and exposures

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2. Cohort studies

• Sample on exposure status and track disease
  development (for rare exposures)
• Marginal probabilities (and rates) of developing
  disease for exposure groups are valid.

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Example The Framingham Heart Study

• The Framingham Heart Study was established in
  1948, when 5209 residents of Framingham, Mass,
  aged 28 to 62 years, were enrolled in a
  prospective epidemiologic cohort study.
• Health and lifestyle factors were measured (blood
  pressure, weight, exercise, etc.).
• Interim cardiovascular events were ascertained
  from medical histories, physical examinations,
  ECGs, and review of interim medical record.

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Example 2 Johns Hopkins Precursors
Study(medical students 1948 through 1964)
http//www.jhu.edu/jhumag/0601web/study.html
From the John Hopkins Magazine website (URL
above).
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Cohort Studies
Disease
Disease-free
Target population
Disease
Disease-free
TIME
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The Risk Ratio, or Relative Risk (RR)
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Hypothetical Data

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Case-Control Studies

• Sample on disease status and ask retrospectively
  about exposures (for rare diseases)
• Marginal probabilities of exposure for cases and
  controls are valid.
• Doesnt require knowledge of the absolute risks
  of disease
• For rare diseases, can approximate relative risk

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Case-Control Studies
Exposed in past

• Disease
• (Cases)

Not exposed
Target population
Exposed
No Disease (Controls)
Not Exposed
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Example the AIDS epidemic in the early 1980s

• Early, case-control studies among AIDS cases and
  matched controls indicated that AIDS was
  transmitted by sexual contact or blood products.
• In 1982, an early case-control study matched AIDS
  cases to controls and found a positive
  association between amyl nitrites (poppers) and
  AIDS odds ratio of 8.6 (Marmor et al. 1982).
  This is an example of confounding.

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Case-Control Studies Examples

• Case-control studies identified associations
  between lip cancer and pipe smoking (Broders
  1920), breast cancer and reproductive history
  (Lane-Claypon 1926) and between oral cancer and
  pipe smoking (Lombard and Doering 1928). All
  rare diseases.
• Case-control studies identified an association
  between smoking and lung cancer in the 1950s.

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Case-control example

• A study of the relation between body mass index
  and the incidence of age-related macular
  degeneration (Moeini et al. Br. J. Ophthalmol,
  2005).
• Methods Researchers compared 50 Iranian patients
  with confirmed age-related macular degeneration
  and 80 control subjects with respect to BMI,
  smoking habits, hypertension, and diabetes. The
  researchers were specifically interested in the
  relationship of BMI to age-related macular
  degeneration.

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Corresponding 2x2 Table
50
80
What is the risk ratio here? Tricky There is no
risk ratio, because we cannot calculate the risk
of disease!!
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The odds ratio

• We cannot calculate a risk ratio from a
  case-control study.
• BUT, we can calculate a measure called the odds
  ratio

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Odds vs. Risk
If the risk is Then the odds are
½ (50)
¾ (75)
1/10 (10)
1/100 (1)
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199
Note An odds is always higher than its
corresponding probability, unless the probability
is 100.
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The Odds Ratio (OR)
abcases
cdcontrols
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The Odds Ratio (OR)
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Proof via Bayes Rule (optional)


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The Odds Ratio (OR)
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The Odds Ratio (OR)
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The Odds Ratio (OR)
Can be interpreted as Overweight people have a
43 decrease in their ODDS of age-related macular
degeneration. (not statistically significant
here)
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The odds ratio is a good approximation of the
risk ratio if the disease is rare.
If the disease is rare (affecting lt10 of the
population), then
WHY? If the disease is rare, the probability of
it NOT happening is close to 1, and the odds is
close to the risk. Eg
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Summary of statistical tests for contingency
tables
Table Size Test or measures of association
2x2 risk ratio (cohort or cross-sectional studies) odds ratio (case-control studies) Chi-square difference in proportions Fishers Exact test (cell size less than 5)
RxC Chi-square Fishers Exact test (expected cell size lt5)
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Fishers Exact Test
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Who is Fisher

• Ronald Aylmer Fisher (17 February 1890  29 July
  1962) was an English statistician, evolutionary
  biologist, geneticist, and eugenicist. Fisher is
  known as one of the chief architects of the
  neo-Darwinian synthesis, for his important
  contributions to statistics, including the
  analysis of variance (ANOVA), method of maximum
  likelihood, fiducial inference, and the
  derivation of various sampling distributions, and
  for being one of the three principal founders of
  population genetics. Anders Hald called him "a
  genius who almost single-handedly created the
  foundations for modern statistical science",
  while Richard Dawkins named him "the greatest
  biologist since Darwin".

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Fishers Tea-tasting experiment
Claim Fishers colleague (call Dr. Muriel
Bristol) claimed that, when drinking tea, she
could distinguish whether milk or tea was added
to the cup first. To test her claim, Fisher
designed an experiment in which she tasted 8 cups
of tea (4 cups had milk poured first, 4 had tea
poured first). Null hypothesis Cathys guessing
abilities are no better than chance. Alternatives
hypotheses Right-tail She guesses right more
than expected by chance. Left-tail She guesses
wrong more than expected by chance
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Fishers Tea-tasting experiment
Experimental Results
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Fishers Exact Test
Step 1 Identify tables that are as extreme or
more extreme than what actually happened Here
she identified 3 out of 4 of the
milk-poured-first teas correctly. Is that good
luck or real talent? The only way she could have
done better is if she identified 4 of 4 correct.
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Fishers Exact Test
Step 2 Calculate the probability of the tables
(assuming fixed marginals)
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Step 3 to get the left tail and right-tail
p-values, consider the probability mass
function Probability mass function of X, where
X the number of correct identifications of the
cups with milk-poured-first
R also gives a two-sided p-value which is
calculated by adding up all probabilities in the
distribution that are less than or equal to the
probability of the observed table (equal or more
extreme). Here 0.229.014.0.229.014 .4857
See R code in file 2by2table.R on my website
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Summary of statistical tests for contingency
tables
Table Size Test or measures of association
2x2 risk ratio (cohort or cross-sectional study) odds ratio (case-control study) Chi-square difference in proportions Fishers Exact test (cell size less than 5)
RxC Chi-square Fishers Exact test (expected cell size lt5)
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The rare disease assumption
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The odds ratio vs. the risk ratio
Rare Outcome
1.0 (null)
Common Outcome
1.0 (null)
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When is the OR is a good approximation of the RR?
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Advantages/LimitationsCase-control studies

• Advantages
• Cheap and fast
• Efficient for rare diseases
• Disadvantages
• Getting comparable controls is often tricky
• Temporality is a problem (did risk factor cause
  disease or disease cause risk factor?
• Recall bias

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Inferences about the odds ratio
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Properties of the OR (simulation)
(50 cases/50 controls/20 exposed)
If the Odds Ratio1.0 then with 50 cases and 50
controls, of whom 20 are exposed, this is the
expected variability of the sample OR?note the
right skew
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Properties of the lnOR
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Hypothetical Data
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30
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When can the OR mislead?
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ExampleDoes dementia predict death?

• Dementia The leading predictor of death in a
  defined elderly population. Neurology 2004 62
  1156-1162
• Among patients with dementia 291/355 (82) died
• Among patients without dementia 947/4328 (22)
  died

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Dementia study

• Authors report OR 16.23 (12.27, 21.48)
• But the RR 3.72
• Fortunately, they do not dwell on the OR, but it
  could mislead if not interpreted correctly

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Better to give OR or RR?
From an RCT (prospective!) of a new diet drug,
the authors showed the following table
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Better to give OR or RR?