Biostatistical Basics for Genetic Epidemiology

1
Biostatistical Basics for Genetic Epidemiology

• Interdisciplinary Genetic Research Course
• Shanghai
• October 6, 2008
• Kung-Yee Liang
• Department of Biostatistics
• Johns Hopkins School of Public Health

2
A Brief Outline

• Some basic concepts in epidemiology
• Designs
• Confounding effect modifications
• Some statistical tools
• Mantel-Haenszel method
• Logistic regression
• Interpretations
• Cautions on conventional inferences
• Matched analysis
• Polytomous regression
• Use in genetic epidemiology

3
Epidemiology

• A discipline to study the distribution of
  diseases
• (disorders) to provide the basics for developing
  and
• evaluating preventive procedures and public
  health
• practices
• Disease control and prevention through health
  education and intervention
• Health policy/expenditure implementations
• Clinical implications prognosis, treatment
  strategy

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Issues in Identifying Risk Factors

• Designs
• Measures of association
• Confounding
• Effect modification
• Data analysis

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Designs

• Prospective (cohort) exposed and unexposed
• subjects are followed up prospectively and
• events of interest are observed over time
• Study multiple endpoints
• Temporal and causal relationship
• Usually large scale time consuming and costly
• Loss to follow-up (survivorship bias)
• Breslow and Day (1987). The Design and Analysis
  of Cohort Studies, IARC

6
Designs (cont)

• Retrospective (case-control) affected (cases)
  and
• unaffected (controls) subjects are ascertained
  and
• exposure information collected retrospectively
• More efficient time-wise and budget-wise
• Subject to biases recall, detection, etc.
• More difficult to establish temporal and causal
  relationship
• Association
• Breslow and Day (1981). The Analysis of
  Case-Control Studies, IARC

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Measures of Association


Odds Ratio (OR) for disease

• RR ? 1 iff OR ? 1 no association
• RRgt1 iff ORgt1 positive association
• the larger RR(OR), the greater the association

8
Confounding

• The distortion of the true association between
• the disease and the risk factor due to the
• association of other factors with both disease
• and exposure, the latter association with the
• disease being causal.

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Confounding (cont)
350 200
150 300
550 450 1000
500 500
-
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Confounding (cont)
C E D
E C D

• For the latter, the intermediate variable is not
  a
• confounder, rather a mediated variable
• Smoking ? chronic cough ? lung cancer
• How to avoid this confusion
• Substantive knowledge

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Table 3.2 The relationships between outpatient
expenditure and BMI categories
in Taiwan (Tobit censored model)
plt0.05 plt0.01 plt0.001
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Table 4.2 The relationships between outpatient
expenditure and BMI categories
using Tobit censored model (control for chronic
disease)
plt0.01 plt0.001
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Confounding (cont)

• It appears that once adjusting for chronicle
  illnesses such as diabetes mellitus, hypertension
  and CVD, the effect of BMI on outpatient
  expenditures (OE) and physician visits (PV)
  disappears
• What is more likely is that the effect of BMI on
  OE and PE is indeed real as it is mediated
  through those illnesses

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How to Deal with Confounding?

• Stratification
• Sub-divide population into groups that are
• homogeneous with regard to confounding
• variables
• Post stratification
• Frequency matching
• Individual matching

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Stratification (cont)

• Post-stratification

Data are imbalanced
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Stratification (cont)

• Frequency matching
• Individual (one-to-one) matching

50 100
30 60
20 40
Control
27 29
3 4
Case
63
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Effect Modification

• The effect of risk factor on the disease (the
  association between risk factor and disease) is
  dependent on (modified by) the level of the
  confounding variable

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Effect Modification (cont)

• Also known as interaction between risk
• factor and confounder
• The confounder is called effect modifier
• Useful to identify high risk group
• It is model dependent
• Quantitative interaction same direction
• (2 versus 5)
• Qualitative interaction different direction
  (0.5 versus 5)
• More problematic

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Statistical Analysis

• Post-stratification / frequency matching
• Mantel-Haenszel (M-H) estimator
• Mantel-Haenszel test statistic

ni mi
ai bi
ci di
i 1,, K
ti Ni ni mi
Mantel-Haenszel (1959), JNCI Greenland, Breslow
Robbins (1986) Biometrics
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One-to-One Matching
Control
a b
c d
Case

• a,d concordant pairs
• b,c discordant pairs
• Mantel-Haenszel estimator b/c
• McNemar Test statistics

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Example Revisited

D Oesophageal cancer E ? 80g/day alcohol
consumption OR5.2 The odds (risk) of oesophageal
cancer for those who drink more than 80g/day is
about five times as high s those who drink less.
?
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Example Revisited (cont)
D Endometrial cancer E Estrogen usage OR 29/3
9.67 The odds (risk) of endometrial cancer is
elevated by ten folds if using estrogen
?
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Limitations of the Stratification / M-H Approach

• All the variables (confounder, risk factor) are
  required to be discrete
• One risk factor at time
• Should NOT use it with qualitative interaction
• Implications
• Cant establish dose response relationship
• The larger the exposure, the higher the risk
• Cant examine joint effects of several risk
  factors simultaneously

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An Alternative

• Logistic regression model
• Y 1(0) if affected (unaffected)
• Z1, , Zq confounding variables
• X1,, Xp risk factors of interest
• LogPr(Y1)/Pr(Y0) log odds
• All of the regression coefficients have the log
  odds ratio interpretations

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How to Interpret Logistic Regression Coefficients?

• log
• X1 log Odds
• 1
  ? ?1
• 0
  ?
• ß1 log Odds Ratio
• log

? ?1X1
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How to Interpret Logistic Regression
Coefficients? (cont)

• Log
• (X1, X2) log Odds
• 1 0
• 0 1
• 0 0

? ?1X1 ß2X2
? ?1
? ?2
?
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How to Interpret Logistic Regression
Coefficients? (cont)

• log
• (Z1, X1) log Odds
• 1 1
• 1 0
• 0 1
• 0 0

? ?1Z1 ß1X1
? ?1 ?1
? ?1
? ?1
?
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How to Interpret Logistic Regression
Coefficients? (cont)

• (Z1, X1) log Odds
• 1 1
• 1 0
• 0 1
• 0 0

log ? ?1Z1 ß1X1 dZ1?X1
? ?1 ?1 ?
? ?1
? ?1
?
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How to Interpret Logistic Regression
Coefficients? (cont)

• log
• X1 log Odds
• 5
• 4
• 31
• 30

? ß1X1 X1 continuous
? 5?1
? 4?1
? 31?1
? 30?1
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How to Interpret Logistic Regression
Coefficients? (cont)

• log
• X1 continuous Z 1(0)
• log
• X1 continuous Z 1(0)
  

? ?1Z1 ß1X1
? ?1Z1 ß1X1 dZ1?X1
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In General

• X (X1,., Xp) , 0 (0,., 0)
• OR(X 0)
• Multiplicative
  (log-linear) models

Pr(Y1X, Z) / Pr (Y0X, Z)
Pr(Y10, Z) / Pr (Y00, Z)
e ?1X1 ? e?2X2 ? ?e?PXP
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In General (cont)

• X (x11, x2,., xp), X? (x1, x2,., xP)
• OR(X X?) OR (X 0) / OR (X? 0)
• e?1

?1(x11) ?2x2,?PxP
e
?1x1?2x2,?PxP
e
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For Matched Case-Control Studies

• The conventional logistic regression method (e.g.
  SAS PROC LOGISTIC) is NOT adequate

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For Matched Case-Control Studies

• Matching variables can be used to examine their
  interactions with risk factors (effect
  modification)
• 
  Model
• Variable 1
  2 3
• Estrogen use 2.074
  1.431 2.074
• (EST) (0.421)
  (0.826) (0.421)
• ESTAGE1
  0.847
• 
  (1.034)
• ESTAGE2
  0.780
• 
  (1.154)
• ESTAGE?
  0.385
• 
  (0.616)
  
  

? AGE 0, 1 or 2
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For Matched Case-Control Studies

• 3. How many matching variables to consider?
• Many confounding variables
• May not find matched controls if all confounders
  are considered for matching
• May run into over-matching problem
• Recommendations
• No more than two or three strong confounders
• The rest are adjusted through regression

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For Matched Case-Control Studies

• 4. How many controls to match per case?
• As a rule of thumb 4 matched controls per case
• Efficiency of one controls versus R control
• R/(R 1)
• More controls maybe needed if
• The risk factor considered is rare
• The underlying degree of association is high
• Breslow et al. (1983) JASA

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Polytomous Logistic Regression

• It is common that the response variable has three
  or more categories
• Cell types in lung cancer
• Severity of injury
• Subtypes in oral cleft
• Cleft lip w/o palate (CLP)
• Cleft palate only (CP)

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Polytomous Logistic Regression (cont)
Oral Cleft Oral Cleft Oral Cleft Oral Cleft
C2 CP CLP control
Present 27 32 24
Absent 97 177 142
OR 1.65 1.07 1.0
?

• C2 target allele for the candidate gene
  transforming
• factor alpha (TGFA)

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Polytomous Logistic Regression (cont)

• Polytomous logistic regression model
• Y 0, 1, 2,, C
• log aj ß x, j 1, 2,, C
• ßj change in log odds (Y j versus Y 0) per
  unit change in x.
• ßj -ßk change in log odds (Y j versus Y K)
  per unit change in x.

t j
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Polytomous Logistic Regression (cont)
Variable CP/control CLP/control
Intercept (?) 2.756 (0.753) 3.388 (0.679)
TGFA 0.045 (0.406) -0.025 (0.580)
MS 0.821 (0.370) 1.071 (0.329)
TGFA MS 0.580 (0.746) -0.279 (0.714)
MA 0.108 (0.024) -0.112 (0.022)
MS Maternal smoking MA Maternal age
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Summary

• We have discussed
• Some basic concepts in epidemiology
• Designs
• Cohort vs case-control
• Confounding effect modifications
• Some statistical tools
• Mantel-Haenszel procedure
• Logistic regression
• Matching vs not
• Dichotomous vs polytomous

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Summary (cont)

• These designs and methods are useful for genetic
  epidemiological research
• Detection of familial aggregation
• Identification of genetic subtypes
• Test for genetic association
• Examination of gene-environment interaction
• Liang Beaty (2000) Stat Meth in Med Res