Classic Statistics Lectures      Copyright Robert Wolfe
Confounding Examples                     KKM Chapter 13

 A. Confounding and effect modification

    A factor, Z, is said to be an effect modifier of a
    relationship between a risk factor, X, and an outcome
    measure, Y, if the strength of the relationship between the
    risk factor, X, and the outcome, Y, varies among the levels of Z.

    A factor, Z, is said to confound a relationship between a
    risk factor, X, and an outcome, Y, if it is not an effect
    modifier and the unadjusted strength of the relationship
    between X and Y differs from the common strength of the
    relationship between X and Y for each level of Z.

    More complicated definitions allow for a factor to be both
    an effect modifier and a counfounder.

    If Z is an effect modifier, then it is important to report
    the strength of the X-Y relationship for specific values of Z.

    If the strength of the X-Y relationship does not vary
    greatly among the levels of Z, it may not be important to
    account for the effect modification.

    If Z is a confounder, then it is common to report both the
    strength of the unadjusted X-Y relationship and the strength
    of the adjusted X-Y relationship.  If the adjusted and
    unadjusted strengths do not differ greatly, then it may not
    be important to report both.

 B. Examples:

    1. Effect modification:  Renal transplant.  The effect of
       High dose cyclosporin (cs) on transplant failure is modified by type
       of transplant.

       Source                Cadaver            Related
       Cyclosporin High      No    Yes          No   Yes
       Failed                20     80           5    30
       Success               30    320          45   170
       Total                 50    400          50   200
       Risk                 0.4    0.2         0.1  0.15
       Risk ratio              2.0               0.7

       Cyclosporin high dose appears beneficial among cadaver transplants but
       harmful among related transplants.  The direction of the high cs
       effect depends upon the type of transplant.  Transplant type
       is an effect modifier of the cyclosporin-failure
       relationship.  We speculate that this may be due to a mild
       nephrotoxic effect of cs in conjunction with a reduction of
       rejection rates that is large among cadaver transplants but
       small among related transplants.

    2. Confounding: The effect of treatment on patient survival is
       confounded by age.

       Age            20-49          50+          All

       Treatment    Trans Hemo   Trans Hemo   Trans Hemo

       Deaths         50   150     100 2400     150  2550
       Years        5000  5000    1000 8000    6000 13000
       Rate         0.01  0.03    0.10 0.30   0.025 0.196
       Ratio           0.333         0.333       0.128

       The death rate among transplant patients is one third that
       of hemodialysis patients for both young and old patients.
       Overall, the death rate among transplant patients is only 13
       percent that among dialysis patients, but that is partly due
       to the fact that younger patients have lower death rates
       than do older patients and are preferentially given
       transplants.

 C. Testing for confounding (don't do it):

    When attempting to document the effect of a specific risk
    factor on an outcome, confounding factors should be
    controlled for even if they are not significantly related to
    the outcome in the analysis.  In this case, the objective of
    the analysis is to estimate the strength of the relationship
    between the risk factor and the outcome not explainable by
    confounding factors, and the strength of the relationship
    between the confounding factors and the outcome is not as
    important.

    When searching for a parsimonious model for predicting the
    outcome, it is useful to exclude unimportant factors from
    the model.  Some data analysts use statistical significance
    as a criterion for importance.  This approach may miss confounders.

 D. Confounders and intervening variables:  Often a quandary.

    Data from cancer patients (with a specific stage) treated at
    two hospitals are given below.  Five year survival outcomes
    are reported.

    Treatment      Chemo        Surgery         All
                   only         + Chemo
    Hospital      A    B       A     B        A    B
    Dead        160    40    100    400      260   440
    Survive     640   160    100    400      740   200
    Total       800   200    200    800     1000  1000
    Risk        0.2   0.2    0.5    0.5     0.26  0.44

    Ratio          1.0          1.0            

    The death rate at hospital B is substantially higher than at
    hospital A.

    The research unit at Hospital B explains this as due to the
    fact that its patients have more aggressive cancer that
    requires surgery and whose prognosis is thus worse.  When
    controlled for type of treatment, the two hospitals appear
    to have similar death rates.

    An inexperienced consumer advocate abrasively points out
    that that is nonsense and that hospital B isn't managing its
    chemotherapy well enough to prevent the progression of
    cancer and that the medical profession is ripping off the
    public just like the nuclear industry and it might even be a
    conspiracy.

    Expert physicians from hospital B point to many articles in
    the medical literature that they have published to prove that 
    they know what they are talking about.

    Should treatment patterns be adjusted for?  NO, adjust for grade of cancer!

 E. More confounding examples:  See Table 13.1 page 246 KKM