HSS4303B

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HSS4303B Intro to Epidemiology

• Mar 8, 2010 Matched Studies

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Summary from Last Time

• Case control study design
• Sources of cases and controls
• Problems in selection of controls
• Practical and conceptual problems
• Matching
• Recall problems
• Limitation in recall
• Recall bias
• Multiple controls
• Type of case control studies
• Nested case control study
• Prevalence study

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Summary of related studies
Table 10-10. Finding Your Way in the Terminology Jungle
Case-control study     Retrospective study
Cohort study Longitudinal study Prospective study
Prospective cohort study Concurrent cohort study Concurrent prospective study
Retrospective cohort study Historical cohort study Nonconcurrent prospective study
Randomized trial     Experimental study
Cross-sectional study     Prevalence survey
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Review of Cohort studies
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Design of cohort study (1)
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Design of cohort study (2)
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Prospective vs Retrospective Cohort

• Prospective study
• Identify a population and follow them
  prospectively until events develop
• Concurrent cohort
• Longitudinal study

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Cohort study prospective design
Pitfalls of the study Loss of subjects Loss of
investigators Lifestyle changes in the subjects
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Prospective vs Retrospective Cohort

• Retrospective study
• Identify a population and observe the events as
  they occur and retrospectively determine their
  exposure status from historical records
• Non-current prospective study
• Historical cohort study

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Cohort study retrospective study
Pitfalls of the study Availability of
records Quality of records Recall bias
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Prospective and retrospective studies

• The designs of both prospective and retrospective
  study are similar
• Exposed and unexposed population are compared for
  the events
• Difference in time frame
• Prospective study forward time frame
• Retrospective study historical records for
  similar period of time as prospective study

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Prospective and retrospective studies
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Potential biases in cohort studies

• Bias in assessment of the outcome
• Information on exposure status biases outcome
  status
• Information bias
• Difference in available information for the
  exposed and unexposed
• Biases from non-response and losses to follow-up
• Attrition rate creates study power problems
• Analytic biases
• Subjectivity at the time of analyses

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Table 82. Comparison of the Attributes of Retrospective and Prospective Cohort Studies.
Attribute Retrospective Approach Prospective Approach
Information Less complete and accurate More complete and accurate
Discontinued exposures Useful Not useful
Emerging new exposures Not useful Useful
Expense Less costly More costly
Completion time Shorter Longer
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Advantages and Disadvantages of Cohort Studies.
Advantages Disadvantages
Direct calculation of risk ratio (relative risk) Time consuming
May yield information on the incidence of disease Often requires a large sample size
Clear temporal relationship between exposure and disease Expensive
Particularly efficient for study of rare exposures Not efficient for the study of rare diseases
Can yield information on multiple exposures Losses to follow-up may diminish validity
Can yield information on multiple outcomes of a particular exposure Changes over time in diagnostic methods may lead to biased results
Minimizes bias  
Strongest observational design for establishing cause and effect relationship  
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Review of Odds Ratios (Case-Control Study)
  Cases Controls
Exposed 6 3
Nonexposed 4 7
  10 10
Compute odds ratio of this dataset
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Case control study of 10 unmatched subjects
summary
Figure 11-8 A case-control study of 10 cases and 10 unmatched controls.
  Cases Controls
Exposed 6 3
Nonexposed 4 7
  10 10
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But What if Data is Matched?

• Why do we match again?

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Matched case control study

• Cases are matched with the controls on specific
  variables
• Cases and controls are analyzed in pairs rather
  than individual subjects

1. Pairs in which both the case and the
controls were exposed 2. Pairs in which neither
the case nor the control was exposed 3. Pairs
in which the case was exposed but not the
control 4. Pairs in which the control was exposed
and not the case
Concordant pairs Discordant pairs
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Data
Pair Outcome Yes (cases) Outcome No (controls)
1 2 3 4 Exposed Not exposed Not exposed Exposed Exposed Exposed Exposed Not exposed
Eg, outcome getting the runs (the cases) vs
not getting the runs (controls) exposure
did you attend the picnic and eat the egg salad?
confounder lactose intolerance (?)
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Data
Pair Outcome Yes (cases) Outcome No (controls)
1 2 3 4 Exposed Not exposed Not exposed Exposed Exposed Exposed Exposed Not exposed
Assume this is an unmatched study. How does the
contingency table look?
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Data
Pair Outcome Yes (cases) Outcome No (controls)
1 2 3 4 Exposed Not exposed Not exposed Exposed Exposed Exposed Exposed Not exposed
Outcome (cases) No outcome (controls) Totals
Exposed (picnic) 2 3 5
Not exposed (no picnic) 2 1 3
Totals 4 4 8
Odds ratio?
(2x1)/(3x2) 0.33
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Data
Pair Outcome Yes (cases) Outcome No (controls)
1 2 3 4 Exposed Not exposed Not exposed Exposed Exposed Exposed Exposed Not exposed
Now lets organize the data considering that its
a matched study
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Data
Pair Outcome Yes (cases) Outcome No (controls)
1 2 3 4 Exposed Not exposed Not exposed Exposed Exposed Exposed Exposed Not exposed
  Controls Controls
    Exposed Not Exposed
Cases Exposed
Cases Not Exposed
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Data
Pair Outcome Yes (cases) Outcome No (controls)
1 2 3 4 Exposed Not exposed Not exposed Exposed Exposed Exposed Exposed Not exposed
  Controls Controls
    Exposed Not Exposed
Cases Exposed 1 1
Cases Not Exposed 2 0
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Concordant and discordant pairs
  Control Control
    Exposed Not Exposed
Case Exposed a b
Case Not Exposed c d
a pairs both case and the control were
exposed b pairs case was exposed but not the
control c pairs case was not exposed but the
control is exposed d pairs neither case nor
control was exposed a and d pairs are concordant
pairs b and c pairs are discordant pairs
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Data
Pair Outcome Yes (cases) Outcome No (controls)
1 2 3 4 Exposed Not exposed Not exposed Exposed Exposed Exposed Exposed Not exposed
  Controls Controls
    Exposed Not Exposed
Cases Exposed 1 1
Cases Not Exposed 2 0
concordant
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Data
Pair Outcome Yes (cases) Outcome No (controls)
1 2 3 4 Exposed Not exposed Not exposed Exposed Exposed Exposed Exposed Not exposed
  Controls Controls
    Exposed Not Exposed
Cases Exposed 1 1
Cases Not Exposed 2 0
concordant
discordant
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Individual matching (11)

• Echovirus meningitis outbreak, Germany, 2001
• Was swimming in pond A risk factor?
• Case control study with each case matched to one
  control

Concordant pairs
Source A Hauri, RKI Berlin
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Odds ratio for matched pairs

• Odds ratio for matched pairs is
• The ratio of the ratio of the discordant pairs
• The ratio of the number of pairs in which the
  case was exposed and the control was not, to the
  number of pairs in which the control was exposed
  and the case was not exposed
• b / c
• The ratio of the number of pairs that support the
  hypothesis of an association to the number of
  pairs that negate the hypothesis of an association

?
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Matched cases and controls 2 x 2 table
  Control Control
    Exposed Not Exposed
Case Exposed 2 4
Case Not Exposed 1 3
Concordant pairs 2 pairs (exposed and exposed)
and 3 pairs (not exposed and not
exposed) Discordant pairs 4 pairs (exposed and
not exposed and 1 pair (not exposed and
exposed) Odds ratio b / c 4 / 1 4
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Picnic Data
Pair Outcome Yes (cases) Outcome No (controls)
1 2 3 4 Exposed Not exposed Not exposed Exposed Exposed Exposed Exposed Not exposed
Matched odds ratio
b/c 1/2 0.5
  Controls Controls
    Exposed Not Exposed
Cases Exposed 1 1
Cases Not Exposed 2 0
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Remember this example?
Concordant pairs
Source A Hauri, RKI Berlin
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Individual matching (11) Analysis
Echovirus meningitis outbreak, Germany, 2001 Was
swimming in pond A risk factor? Case control
study with each case matched to one control
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What Else Can We Do With These Data?

• Remember the Chi-Square test?

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Chi-square

• Chi square is a non-parametric test of
  statistical significance for bivariate tabular
  analysis
• It lets you know the degree of confidence you can
  have in accepting or rejecting an hypothesis
• It provides information on whether or not two
  different samples are different enough in some
  characteristic or aspect of their behaviour

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Chi Square

• There are actually all sorts of chi-square tests
  out there
• Pearsons
• Yates
• Mantel-Haenszel
• Portmanteau
• Fishers Exact

lt- Well be using this one
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Also need to compute something called degrees of
freedom
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Chi-square calculation
Variable 1
 Variable 2  Data type 1  Data type 2  Totals
 Category 1  a b a b
 Category 2  c d c d
 Total a c b d a b c d N
Chi square N(ad-bc)2 / (ab) (cd) (bd) (ac)
The degrees of freedom (number of columns minus
one) x (number of rows minus one) not counting
the totals for rows or columns. For our data
this gives (2-1) x (2-1) 1.

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Chi-square calculations
Number of animals that survived the treatment
   Dead  Alive Total
 Treated  36  14  50
 Not treated  30  25  55
 Total  66  39  105
(36x25)/(14x30) 2.14
Odds ratio
Chi square
105(36)(25) - (14)(30)2 / (50)(55)(39)(66)
3.418
(2-1)x(2-1) 1
DOF
Now what do we do with this?
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Degrees of freedom and chi square table
Df 0.5 0.10 0.05 0.02 0.01 0.001
1 0.455 2.706 3.841 5.412 6.635 10.827
2 1.386 4.605 5.991 7.824 9.210 13.815
3 2.366 6.251 7.815 9.837 11.345 16.268
4 3.357 7.779 9.488 11.668 13.277 18.465
5 4.351 9.236 11.070 13.388 15.086 20.517
Using the Chi square table The corresponding
probability is 0.10ltPlt0.05. This is below the
conventionally accepted significance level of
0.05 or 5, so the null hypothesis that the two
distributions are the same is verified. In other
words, when the computed x2 statistic exceeds the
critical value in the table for a 0.05
probability level, then we can reject the null
hypothesis of equal distributions. Since our x2
statistic (3.418) did not exceed the critical
value for 0.05 probability level (3.841) we can
accept the null hypothesis that the survival of
the animals is independent of drug treatment
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p-value

• The p-value is the probability that your sample
  could have been drawn from the population being
  tested given the assumption that the null
  hypothesis is true.
• A p-value of .05, for example, indicates that you
  would have only a 5 chance of drawing the sample
  being tested if the null hypothesis was actually
  true.
• A p-value close to zero signals that your null
  hypothesis is false, and typically that a
  difference is very likely to exist.
• Large p-values closer to 1 imply that there is no
  detectable difference for the sample size used.
• A p-value of 0.05 is a typical threshold used to
  evaluate the null hypothesis.

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p-value

• So what does a p-value of 0.10 mean?
• We fail to reject the null hypothesis

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What is the null hyp that we are testing?

• In cohort studies, the chi-square test tells us
  whether to accept or reject the null hypothesis
  that RR1
• In case-control studies, the chi-square test
  tells us whether or accept or reject the null
  hypothesis that OR1
• Piersons chi-square is NOT appropriate to test
  the null hypothesis of whether the matched study
  pairs are related
• For that we use something called McNemars test,
  which we will not cover in this class

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Remember the Picnic Data
Pair Outcome Yes (cases) Outcome No (controls)
1 2 3 4 Exposed Not exposed Not exposed Exposed Exposed Exposed Exposed Not exposed
Matched odds ratio
b/c 1/2 0.5
  Controls Controls
    Exposed Not Exposed
Cases Exposed 1 1
Cases Not Exposed 2 0
Pretend its unmatched and construct the
contingency table
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Data
Can you compute a chi-square for this?
Pair Outcome Yes (cases) Outcome No (controls)
1 2 3 4 Exposed Not exposed Not exposed Exposed Exposed Exposed Exposed Not exposed
Outcome (cases) No outcome (controls) Totals
Exposed (picnic) 2 3 5
Not exposed (no picnic) 2 1 3
Totals 4 4 8
Odds ratio?
(2x1)/(3x2) 0.33
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Caveat to Piersons Chi Square

• Typically, does not work well if any cell has a
  count of lt5
• If it does, better off using Fishers Exact Test
  or some other similar test
• We will not be doing that in this class

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Summary
Chi square (ad-bc)2 (abcd) / (ab) (cd)
(bd) (ac)
The degrees of freedom equal (number of columns
minus one) x (number of rows minus one) not
counting the totals for rows or columns.
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If youre lazy

• Lots of online OR, RR and chi-square calculators
• Eg,
• http//faculty.vassar.edu/lowry/odds2x2.html

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Homework
12 women with uterine cancer and 12 without were
asked if theyd ever used supplemental estrogen.
Each woman with cancer was matched by race,
weight and parity to a woman without cancer
pair Women with cancer Women without cancel
1 2 3 4 5 6 7 8 9 10 11 12 Estrogen user Estrogen nonuser Estrogen user Estrogen user Estrogen user Estrogen nonuser Estrogen user Estrogen user Estrogen nonuser Estrogen nonuser Estrogen user Estrogen user Estrogen nonuser Estrogen nonuser Estrogen user Estrogen user Estrogen nonuser Estrogen nonuser Estrogen nonuser Estrogen nonuser Estrogen user Estrogen user Estrogen nonuser Estrogen nonuser
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Homework

1. What is the estimated relative risk of cancer
   when analyzing this study as a matched-pairs
   study?
2. What is the estimated relative risk of cancer
   when analyzing this study as an unmatched study?
3. What is the chi square statistic of the
   (unmatched) relationship between cancer and
   estrogen intake?
4. What is the null hypothesis being tested by the
   chi-square test?
5. What does the p-value of the statistic tell you
   about whether to reject or accept the null
   hypothesis?