Stratified Analysis

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Stratified Analysis

• Tuesday 1/29/02
• PH 2711
• Jan Risser

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30 of Type A die shortly after MI and wont be
prevalent cases
90 die
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Selection of Controls
BASE Population
The assumption that cases and controls originate
from the same hypothetical source cohort is a
critical issue affecting the validity of
case-control studies. (Szklo)
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Data Analysis Purpose

• Control for confounding
• How is the primary association of interest
  affected when adjusted for potential confounding
  variables?
• Provide precision of point estimates
• Discover interaction
• Interpret findings
• in relation to the literature and limitations of
  your study

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Confounding

• A distortion of an association between and
  exposure and disease brought about by an
  extraneous factor or factors.
• Occurs when the exposure is associated with the
  confounding factor and with the disease.

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Strategies for control of confounding

• 1. Random allocation of exposure
• Ideal (adjusts for known as well as unknown
  confounders
• Rarely possible in observational studies of risk
  factors ethical constraints, time, and cost

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Strategies for control of confounding

• 2. Restriction
• The effects of know or potential confounders can
  be eliminated by restriction of study subjects
• Should be considered for strong by uncommon risk
  factors
• Can simplify the analysis (fewer variables)
• Reduces the number of potential subject but
  increases precision of estimates number of
  subjects
• Loss of generalization of restricted factors

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Strategies for control of confounding

• 3. Matching - Partial restriction
• Match on disease status
• Matching gains efficiency in case control studies
• Matching in design must be retained in the
  analysis
• Compare matched vs. unmatched estimates

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Strategies for control of confounding

• 4. Stratification
• Use stratified analysis to evaluate interaction
  and control for confounding
• No assumptions and straightforward computational
  procedures
• Stratum specific estimates become imprecise with
  numbers in cells becomes small
• ALWAYS look at stratification before jumping into
  models (logistic, etc)

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Strategies for control of confounding

• 5. Modeling
• After stratification - modeling may be employed
  to control confounding and test for interaction
• Modeling is attractive when number of variables
  is large or when continuous variables can not be
  / should not be categorized
• Disadvantage assumptions

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Analysis of etiologic studies

• Determine crude point estimate and CI for each
  strata
• Calculate univariate OR first
• How does this compare to what we know
• Form Strata
• Look for confounding
• Look for interaction
• Decide if summary measures of association are
  appropriate
• Determine summary measure

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Univariate Odds Ratio
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Odds Ratio
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Statistical Significance
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(No Transcript)
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95 CI around OR

• Exact Unbeatable
• based on Fisher limits
• time consuming, with iterations
• Test Based Transformation of the statistical
  test (Chi square)
• Cornfeld, Woolf approximation
• more accurately represent Exact with greater
  deviation from the null

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Test based confidence interval
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Woolf approximation
Using a Taylor series expansion
Woolf Ann Human Gen 195519251-253.
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Cornfeld

• Requires iterations
• Is theoretically preferable since it involves
  recalculating the standard error using fitted
  cell frequencies that correspond to the value of
  the confidence interval

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95 CI around OR
a and c cells 4 Total N 1644
A and C cells 40 Total N 16440
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Comparison of CIs from Stata

• http//www.sph.uth.tmc.edu/courses/epi/Jrisser/PH2
  711_spr02/Projects/ci.htm

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Form Strata

• Look for confounding
• Look for interaction
• Decide if summary measures of association are
  appropriate
• Determine summary measures
• For case control studies Mantel Haenszel
  weighted odds ratio.

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Interaction

• The interdependent operation of two or more
  factors to produce an unanticipated effect.
• Statistical interactions statistical model does
  not explain the joint effect of two or more
  independent variables. Model dependent.
• Biological interactions Synergy. There is a
  difference in biologic effect of exposure
  according to the presence/absence cofactor.

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Simpsons Paradox

• Data show one thing when aggregated and something
  different when disaggregated.

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Interaction or Simpsons bias
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Weighted averages

• Precision-based Taylor series variance
• Mantel-Haenszel for use in case control
  studies.
• Direct mathematical connection between this and
  the MH Chi square test (following)
• Standardized weights standard pop.
• Provide unconfounded summary comparisons with a
  known standard population, and for SMR.

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Mantel-Haenszel Odds Ratio
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Mantel-Haenszel Relative Risk
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MD Odds Ratio
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MH Chi Square (multiple strata)
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Ischemic Heart Disease Exercise

• Cases initial diagnosis of IHD - angina,
  myocardial infarction, sudden death.
• Restricted to females under 60
• Diagnosis 1960-1974
• Rochester Minnesota residents

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Ischemic Heart Disease Exercise

• Controls two individually matched controls for
  each case
• No prior IHD dx
• Resident
• Year of Dx
• Age /- 3 years

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Ischemic Heart Disease Exercise

• Risk factor information derived from records
  prior to IHD Dx in cases and controls
• Matched also on length of prior medical record
  (in an attempt to make any information bias
  non-differentia)
• ORs with and without matching similar - therefore
  no confounding introduced by matching.

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Ischemic Heart Disease Exercise

• Determine crude point estimates and CI for each
  factor (smoking and OC use)

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Ischemic Heart Disease Exercise

• How does this compare to what we know
• Previous studies
• RR of 2-4 for hypertension, smoking, high
  cholesterol
• RR 4-5 for diabetes
• Shapiro suggests OC use increases risk and there
  is a strong interaction between OC use and smoking

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Ischemic Heart Disease Exercise

• Form strata and look for interaction

Crude OR 2.8
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Ischemic Heart Disease Example
Calculate the adjusted odds ratio using the
Mantel-Haenszel test.
Crude OR 2.8, adjusted OR 2.8
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Ischemic Heart Disease Exercise

• Test for interaction
• mhodds or cc case exposure, by(factor)
• You get a Test of homogeneity
• This is the MH chi square test, testing the
  hypotheses OR1OR2ORx
• If the results are significant - then you have
  interaction
• chi2(1) 0.41 Prgtchi2 0.524

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Mantel-Haenszel Odds Ratio

• Easy to compute
• Results are same as MH Chi Square
• (if OR 1, Chi square0)
• Can be used when there are 0 cells which permits
  adjustment for many categories
• Can be used for summary risk ratios, rate ratios,
  and odds ratios (see KKM, p345).