#### Transcript Slides for February 3

```Joint assessment of modifiers
and/confounders
Maybe one-at-time assessment is not
enough
The merits of regression analysis start
to kick in!
Joint effect modification
• Now consider a model like:
E (Y )   0  1D   2G  3 A   4 DG  5 DA  6GA   7 DGA
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•
•
•
•
•
(Yikes!)
…but this is just 4 lines: E(Y) versus age;
For the 4 groups:
Females receiving placebo: E (Y )  0  3 A
Males receiving placebo: E (Y )  0   2  (3  6 ) A
Females receiving active: E(Y )  0  1  (3  5 ) A
…and lastly
• Males receiving active:
E (Y )  (  0  1   2   4 )  ( 3  5   6   7 ) A
• How do we interpret this ..er mess?
• Look at the drug effect for each gender as
a function of age
Drug effect is: active - placebo
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For females: 1   5 A
For males: ( 1   4 )  ( 5   7 ) A
How does drug effect depend on gender?
Take the difference again:  4   7 A
So we can see that  7 measures the
extent to which gender as an effect
modifier depends on age
But  7 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)
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 model’s 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
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:
E (Y )   0
 1 y   2 z {2 df for drug effects (in the absence of d and b)}
  3 d   4b   5 db
  6 dy   7 dz {2 df for drug/diet int (in the absence of b)}
  8by   9bz {2 df for drug/biofe ed int (in the absence of d)
 10dby  11dbz{2 df for db int dependency on drug )}
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?
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 dbx=dby=0
• One receives the 2 df F test for ‘whether or not the db interaction
depends on drug group’
```