In regression analysis, random errors in an explanatory variable cause the
usual estimates of its regression coefficient to be biased. Although this problem has
been studied for many years, routine methods have not emerged. This thesis
investigates some aspects of this problem in the setting of analysis of epidemiological
data.
A major premise is that methods to cope with this problem must account for
the shape of the frequency distribution of the true covariable, e.g., exposure. This is
not widely recognized, and many existing methods focus only on the variability of the
true covariable, rather than on the shape of its distribution. Confusion about this
issue is exacerbated by the existence of two classical models, one in which the
covariable is a sample from a distribution and the other in which it is a collection of
fixed values. A unified approach is taken here, in which for the latter of these models
more attention than usual is given to the frequency distribution of the fixed values.
In epidemiology the distribution of exposures is often very skewed, making
these issues particularly important. In addition, the data sets can be very large, and
another premise is that differences in the performance of methods are much greater
when the samples are very large.
Traditionally, methods have largely been evaluated by their ability to remove
bias from the regression estimates. A third premise is that in large samples there may
be various methods that will adequately remove the bias, but they may differ widely in
how nearly they approximate the estimates that would be obtained using the
unobserved true values.
A collection of old and new methods is considered, representing a variety of
basic rationales and approaches. Some comparisons among them are made on
theoretical grounds provided by the unified model. Simulation results are given which
tend to confirm the major premises of this thesis. In particular, it is shown that the
performance of one of the most standard approaches, the "correction for attenuation"
method, is poor relative to other methods when the sample size is large and the
distribution of covariables is skewed. / Graduation date: 1993
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/36494 |
| Date | 18 February 1993 |
| Creators | Delongchamp, Robert |
| Contributors | Pierce, Donald A. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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