Using Logistic Regression In Case Control Studies

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Using Logistic Regression In Case Control Studies

• Department of Community Health Sciences
  September 27,2002

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No statistics should stand in the way of an
experimenter keeping his eyes open, his mind
flexible, and on the lookout for surprises.
(William Feller)
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Background

• Quan H., Arboleda-Florez J., Fick G.H., Stuart
  H.L., Love E.J. (2002) Association Between
  Physical Illness and Suicide Among The Elderly.
  Social Psychiatry and Psychiatric Epidemiology,
  37190-197
• David Adler, Nimira Kanji, Kiril Trpkov, Gordon
  Fick, Rhiannon M. Hughes HPC2/ELAC2 Gene Variants
  Associated with Prostate Cancer (in submission)
• The class of MDSC643.02 in the Winter Term 2002

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Case Control Studies

• Investigator selects cases and controls
• Investigator determines exposure
• Primary outcome measure Odds of exposure
  (yes/no)
• The Magic Odds Ratio (OR)

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Case Control Studies

• Two by Two tables
• Classical Stratified Analysis (SA)
• Stratum specific odds ratios
• Crude odds ratio
• Mantel Haentzel odds ratio
• EASY. Right?

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A Definition of the Chi-Square test A
procedure any fool can carry out and frequently
does.(SJ Penn)
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Logistic Regression

• 1) Model the log of the odds of exposure
• OR
• 2) Model the log of the odds of disease
• Does it matter? MOST of the time.
• Standard Likelihood theory gives us blessing for
  option 1)

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It does not matter -

• IF the model is equivalent to a stratified
  analysis,
• . then some of the coefficients from LR will the
  same as the log(OR) values from SA
• . not all the coefficients will be the same
  though

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Results will differ -

• In ALL other situations (at least a little)
• BUT there are those solid papers in the
  literature that appear to say its OKAY to
  model the odds of disease
• AND the textbooks and standard references appear
  to give a green light as well

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References

• Prentice RL and Pyke R (1979) Biometrika 663
  403-411
• after some impenetrable mathematics
• .is precisely the distributional statement that
  would arise if a model for the odds of disease
  were directly applied to the case-control data
• BUT BUT Arent we all frequentists?

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The books

• Kleinbaum, Kupper, Morgenstern
• Rothman and Greenland
• Rosner
• Matthews and Farewell
• They ALL note the estimates are OKAY
• They are ALL silent on the sampling distribution.
• BUT what about the standard errors? P-values?

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It does not follow that if quantitative methods
be indiscriminately applied to inexhaustible
quantities of data, scientific understanding will
necessarily emerge. (M.K. Hubbert)
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An exercise that makes no provision for the
definition and estimation of error cannot
properly be called an experiment. (D.B. DeLury)
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Exposures may not be dichotomous

• If exposure is measured, then the model for
  exposure could be linear regression
• There is no obvious magical odds ratio now
• BUT it is still SO SO tempting to just model the
  log of odds of disease with a continuous
  independent variable (exposure)

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The modelling process -

• Can lead us in very different ways to very
  different models and very different conclusions
• QUAN Hude et al
• et al and Rhiannon Hughes

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What about the Gate Keepers?

• Editors and Associate Editors
• Epidemiologists
• Biostatisticians

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Conclusions

• I am taking yet another poke at the much maligned
  case-control study
• Epidemiological issues still dominate the
  challenges of designing and using case-control
  studies
• It remains safe to model the exposure(s)
  individually as dependent variable(s) (if we
  trust the standard likelihood theory)

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SJ Penn again
A definition of Power A probability of a
possible outcome of a potential decision
conditional upon an imaginable circumstance given
a conceivable value of an algebraic embodiment of
an abstract mathematical idea and the strict
adherence to an extremely precise rule.