Joint assessment of modifiers and/confounders

1
Joint assessment of modifiers and/confounders

• Maybe one-at-time assessment is not enough
• The merits of regression analysis start to kick
  in!

2
Joint effect modification

• Now consider a model like
• (Yikes!)
• but this is just 4 lines E(Y) versus age
• For the 4 groups
• Females receiving placebo
• Males receiving placebo
• Females receiving active

3
and lastly

• Males receiving active
• How do we interpret this ..er mess?
• Look at the drug effect for each gender as a
  function of age

4
Drug effect is active - placebo

• For females
• For males
• How does drug effect depend on gender?
• Take the difference again
• So we can see that measures the extent to
  which gender as an effect modifier depends on age

5
But also measures

• The extent to which age as an effect modifier
  depends on gender
• You can spin the interpretation in either way
  here (as is the case with most interaction
  measures)

6
Now lets look at the 3 factor example from
Rabe-Hesketh

• Define indicator variables for each of the 3 drug
  groups x, y and z
• Decide on a baseline drug group say x.
• The models estimates/predcitions do not depend
  on this choice but do provide interpretations for
  the coefficients
• Since there are 3 groups, we need 2 coefficients
  to display the 2 degrees of freedom associated
  with the differences among the 3 groups

7
Then we can build a saturated model

• This model will give estimates that reproduce the
  12 cell averages
• The model separates into a number of 2 df sets

8
Notice that this last set of 2 df

• Can be expressed in 3 ways (each way means the
  same thing!)
• How does the diet/biofeed interaction depend on
  drug group?
• How does the drug/diet interaction depend on
  biofeed group?
• How does the drug/biofeed interaction depend on
  diet group?

9
The decision to whether to (and how to) separate
up the 2 df sets should be made in advance

• Individual one df tests can be made using the
  usual t-tests. It is always to good idea to check
  out what such tests mean (what a concept!)
• Of course, it may be that 2(or more) df tests
  cover the issues at hand. In such cases, one
  should offer the appropriate F test.
• For example, if one fits
• regr sbp x y d b db dx dy bx by dbx dby
• and then tries
• test dbxdby0
• One receives the 2 df F test for whether or not
  the db interaction depends on drug group