Q&A Homework 4, Problem 6

QUESTION: On homework #4, problem 6, how are we supposed to examine 
confounding? Do you want statistical tests?

ANSWER:

First, we have not yet covered statistical tests at all, so I definitely do not 
want any hypothesis tests, even if you know how to do them.

But even if we had covered testing, I would still not rely too heavily on 
hypothesis tests to answer this question. I look primarily at descriptive 
statistics to assess confounding.

In problem 6b you are asked to provide descriptive statistics that might 
be used to assess a possible association between hepatomegaly and 
survival. An association exists if the distribution of time to death 
differs among those who have hepatomegaly and those who don't. To that 
end, you might look at the 75th, 50th, and 25th percentiles (when they can 
be estimated) for the hepatomegaly and no hepatomegaly groups and see if 
they differ very much. Alternatively, you can look at the estimated 
probability of surviving 3, 6, or 9 years, and again look to see whether 
those probabilities differ between the groups. Of course, because the data 
on time to death is right censored for some individuals, you must use the 
Kaplan-Meier curves to estimate these quantities. And plotting the KM 
curves gives a graphical comparison of all of them.

Now, in problem 6c, you are to assess whether edema might confound the 
above analysis. For a variable to be a confounder, it must

1) be associated with the response (time to death) in a causal fashion 
independent of the POI. You can look for an association between survival and 
edema by much the same methods you used above. In order to ensure that any such 
association is independent of the predictor of interest (hepatomegaly in this 
case), you could consider looking in each hepatomegaly group separately.

AND

2) be associated with the predictor of interest (hepatomegaly) in the sample. 
Edema and hepatomegaly would be associated if the prevalence of edema differed 
between subjects who had hepatomegaly and those who did not.

If there is no confounding by edema, then the association between hepatomegaly 
and survival is clearly not affected. If there could be confounding, then you 
could look to see that there was an association between hepatomegaly and 
survival in patients who have edema and
an association between hepatomegaly and survival in patients who do not have 
edema. (That is, repeat problem 6a in the two subgroups defined by edema or no 
edema.)

For future reference: an "adjusted" analysis would be some sort of average of 
the estimated association in the two subgroups. If markedly different estimates 
of the association are observed in the two subgroups, then that would be 
suggestive of effect modification.

Scott

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Scott S. Emerson, M.D., Ph.D.            Biost Dept: (O) 206-543-1044
Professor of Biostatistics                           (F) 206-543-3286
Department of Biostatistics  Box 357232         ROC: (O) 206-221-4185
University of Washington                             (F) 206-543-0131
Seattle, Washington 98195                   semerson@u.washington.edu
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