Lecture 6: Case control studies

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Lecture 6 Case control studies

• 513-668 Statistical models in Epidemiology

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Outline

• Retrospective and Prospective probability models
• Conditional likelihood
• Matching
• Conditional logistic regression

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Case control design

• Goal estimation of Assoc(E,D)
• no follow-up required
• poor definition of controls in early studies lead
  to criticism

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Probability model within study base

• cc study can be seen within the context of an
  underlying cohort (base)
• 8 possible groups result from
• exposure outcome selection
• important assumption probability of selection
  indpendent of exposure
• Assoc(E,D) may be derived from either a
  retrospective or prospective conditional argument

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Two probability models

• Retrospective Model of conditional probabilities
  of P(ED)
• Prospective Model of conditional probabilities
  of P(DE)
• Likelihoods can be estimated using profile
  likelihood. Misleading if number of nuisance
  parameters (e.g. strata in matched study)
  increase.

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Notes on case control studies

• Most convincing when study base is closely
  defined, as in nested case control study
• Matching decreases selection bias, increases
  efficiency
• Prevalent cases may be used to study
  Assoc(E,Prevalence). More biases possible

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11 matched case-control studies

• Each matched pair is in a separate stratum
• Mantel-Haenszel estimate works here though
  profile likelihood does not
• Hypergeometric likelihood is another alternative.
  Results from conditioning on number of exposed
  subjects.
• Conditional odds that the case is exposed odds
  ratio (constant across strata)

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1 casem controls

• Relation between conditional odds and odds ratio
  depends on number of exposed subjects
• Conditional odds (N exposed in stratum/N
  unexposed in stratum) OR
• Extending this to multiple controls involves
  permutations