Using Regression Analysis to Assess Potential Effect Modifiers and Confounders

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Using Regression Analysis to Assess Potential
Effect Modifiers and Confounders

• Y (blood pressure reduction)

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Question

• Does the effect of the drug on Mean BPR depend on
  the gender of the patient?
• It turns out that we can build a model to address
  this question.

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Implications of this model

• By specializing the model to the females and then
  to the males we can see
• Measures the difference between the 2 drug
  effects
• i.e. whether gender is an effect modifier

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Sometimes a table can aid in understanding the
implications of a model



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Assess effect modification first

• If gender is a modifier, its assessment as a
  confounder is rarely relevant.
• If there is evidence that then one
  should present the gender specific estimates of
  the drug effect (together with their SEs and
  maybe CIs too)
• No further testing of the components of this
  model is typically required.
• Since we know that we then know that
  the drug has an effect and that the effect
  DEPENDS on the gender of the patient.

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What if gender is not an effect modifier?

• And we can then assess whether gender is a
  confounder by comparing
• With

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In other words

• By studying the context, using confidence
  intervals and other epidemiological ideas

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What if the potential modifier/confounder is
continuous? Say age

• Now look at
• As 2 straight lines in age
• And so the drug effect is the difference

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Age specific drug effect

• From the previous graph
• Compare the vertical difference between the red
  line and the blue line when ld 3 with the
  vertical difference when ld 7.
• For example, red minus blue (drug effect) is
  about -3 (when ld3) and a bit more than 2 (when
  ld7)
• The next graph shows the drug effect (de)
  versus ld demonstrating that ld is a modifier.

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The next graph shows

• A Drug effect adjusted for ld
• Notice that the 2 lines are parallel and that the
  drug effect (red line minus blue line) is the
  same for any value of ld
• This fixed difference is the adjusted drug
  effect

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Crude drug effect

• In the next graph, the 2 lines are horizontal (to
  emphasize that the effect is NOT adjusted for ld)
  
• In this illustration, the adjusted effect and
  crude effect are nearly the same and hence there
  is no evidence of confounding
• Remember, though, that if we had demonstrated
  modification, we would not even address the issue
  of confounding

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