Transcript data tea

Examples and SAS introduction:
-Violations of the rare disease assumption
-Use of Fisher’s exact test
January 14, 2004
1. When can the OR mislead?
When is the OR is a good
approximation of the RR?
General Rule of
Thumb:
“OR is a good
approximation as long
as the probability of the
outcome in the
unexposed is less than
10%”
February 25, 1999 Volume 340:618-626
From: “The Effect of Race and Sex on Physicians' Recommendations for Cardiac
Catheterization”




Study overview:
Researchers developed a computerized survey instrument
to assess physicians' recommendations for managing
chest pain.
Actors portrayed patients with particular characteristics
(race and sex) in scripted interviews about their symptoms.
720 Physicians at two national meetings viewed a recorded
interview and was given other data about a hypothetical
patient. He or she then made recommendations about that
patient's care.
February 25, 1999 Volume 340:618-626
From: “The Effect of Race and Sex on Physicians' Recommendations for Cardiac
Catheterization”
Their results…
The Media Reports: “Doctors
were only 60 percent as likely
to order cardiac
catheterization for women
and blacks as for men and
whites. For black women, the
doctors were only 40 percent
as likely to order
catheterization.”
Media headlines on Feb 25th,
1999…
Wall Street Journal: “Study suggests race, sex influence
physicians' care.”
New York Times: Doctor bias may affect heart care,
study finds.”
Los Angeles Times: “Heart study points to race, sex
bias.”
Washington Post: “Georgetown University study finds
disparity in heart care; doctors less likely to refer
blacks, women for cardiac test.”
USA Today: “Heart care reflects race and sex, not
symptoms.” ABC News: “Health care and race”
A closer look at the data…
The authors failed to report the
risk ratios:
RR for women: .847/.906=.93
RR for black race: .847/.906=.93
Correct conclusion: Only a 7%
decrease in chance of being
offered correct treatment.
Lessons learned:

90% outcome is not rare!
 OR is a poor approximation of the RR here,
magnifying the observed effect almost 6-fold.
 Beware! Even the New England Journal doesn’t
always get it right!

SAS automatically calculates both, so check how
different the two values are even if the RR is not
appropriate. If they are very different, you have to
be very cautious in how you interpret the OR.
SAS code and output
for generating OR/RR from
2x2 table
Cath
No Cath
Female
305
55
360
Male
326
34
360
data cath_data;
input IsFemale GotCath Freq;
datalines;
1 1 305
1 0 55
0 1 326
0 0 34
run;
data cath_data; *Fix quirky reversal of SAS 2x2 tables;
set cath_data;
IsFemale=1-IsFemale;
GotCath=1-GotCath;
run;
proc freq data=cath_data;
tables IsFemale*GotCath /measures;
weight freq; run;
SAS output
Statistics for Table of IsFemale by GotCath
Estimates of the Relative Risk (Row1/Row2)
Type of Study
Value
95% Confidence Limits
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Case-Control (Odds Ratio)
0.5784
0.3669
0.9118
Cohort (Col1 Risk)
0.9356
0.8854
0.9886
Cohort (Col2 Risk)
1.6176
1.0823
2.4177
Sample Size = 720
Furthermore…stratification
shows…
2. Example of Fisher’s Exact
Test
Fisher’s “Tea-tasting
experiment” (p. 40 Agresti)
Claim: Fisher’s colleague (call her “Cathy”) 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: Cathy’s 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
Fisher’s “Tea-tasting
experiment” (p. 40 Agresti)
Experimental Results:
Guess poured first
Milk
Tea
Milk
3
1
4
Tea
1
3
4
Poured First
Fisher’s 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.
Guess poured first
Milk
Tea
Poured First
Milk
3
1
4
Tea
1
3
4
Guess poured first
Milk
Tea
Milk
4
0
Tea
0
4
Poured First
4
4
Fisher’s Exact Test
Step 2: Calculate the probability of the tables (assuming fixed marginals)
Guess poured first
Milk
Tea
Milk
3
1
Tea
1
3
Poured First
4
4



P(3) 
 .229

4
3
4
1
8
4
Guess poured first
Milk
Tea
Milk
4
0
Tea
0
4
Poured First
4
4



P(4) 
 .014

4
4
4
0
8
4
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:



P(4) 
 .014




P(3) 
 .229




P(2) 
 .514




P (1) 
 .229

    .014
P(0) 

4
4
4
0
8
4
4
3
4
1
8
4
4
2
4
2
8
4
4
1
4
3
8
4
4
0
4
4
8
4
“right-hand
tail
probability”:
p=.243
“left-hand tail
probability”
(testing the null
hypothesis that
she’s
systematically
wrong): p=.986
SAS code and output
for generating Fisher’s Exact
statistics for 2x2 table
Milk
Tea
Milk
3
1
4
Tea
1
3
4
data tea;
input MilkFirst GuessedMilk Freq;
datalines;
1 1 3
1 0 1
0 1 1
0 0 3
run;
data tea; *Fix quirky reversal of SAS 2x2 tables;
set tea;
MilkFirst=1-MilkFirst;
GuessedMilk=1-GuessedMilk;run;
proc freq data=tea;
tables MilkFirst*GuessedMilk /exact;
weight freq;run;
SAS output
Statistics for Table of MilkFirst by GuessedMilk
Statistic
DF
Value
Prob
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Chi-Square
1
2.0000
0.1573
Likelihood Ratio Chi-Square
1
2.0930
0.1480
Continuity Adj. Chi-Square
1
0.5000
0.4795
Mantel-Haenszel Chi-Square
1
1.7500
0.1859
Phi Coefficient
0.5000
Contingency Coefficient
0.4472
Cramer's V
0.5000
WARNING: 100% of the cells have expected counts less
than 5. Chi-Square may not be a valid test.
Fisher's Exact Test
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Cell (1,1) Frequency (F)
3
Left-sided Pr <= F
0.9857
Right-sided Pr >= F
0.2429
Table Probability (P)
Two-sided Pr <= P
0.2286
0.4857
Sample Size = 8