Page 78 - Contributed Paper Session (CPS) - Volume 7

CPS2033 Ronnie P.
In this study we focus on binary confounding variables. Usually,
measurement error of binary variables is called misclassification, which can be
divided into different types of misclassification. It is common to distinguish
between non-differential misclassification, i.e. misclassification that is random,
and differential misclassification, that is misclassification that varies between
groups.
There are some results in the literature covering the case of non-
differential misclassification of a confounder, e.g. Greenland (1980) argued
that non-differential classification of a binary confounder leads to attenuation
bias. However, even though this was further studied by e.g. Ahlbohm (1992),
Fox (2005), Greenland (1996), Savitz (1989), Fung (1984) no formal proofs were
given. Moreover, none of these studies related the bias to causal quantities,
instead the bias was related to parameters in statistical models.
Formal proofs for non-differential classification of a binary confounder
were eventually provided by Ogburn and Vanderweele (2012). They showed
that under a monotonicity assumption, i.e. the direction of causal effect is
same across levels of the confounder, there is in fact an attenuation bias. Their
result is an important contribution and they also relate the bias to parameters
within the causal inference framework.
However, Ogburn and Vanderweele (2012) do not study misclassification
in the differential case. Although Di Martino et al. (2014) discover that
differential misclassified confounder can lead to unpredictable consequences
and misleading results for logistic regression models when studying treatment
quality of caesarean sections in different hospitals, they only study
misclassification using empirical data and no theory.
The focus of this study is a certain type of misclassification denoted one-
sided misclassification that is differential. It occurs when the classification is
always correct for individuals coded as belonging to a certain category, but
not necessarily for those not belonging to the category.
One-sided misclassification may occur due to under-reporting and it
would be the case when all individuals being registered having a characteristic
really have it, however, among those individuals not registered as having the
characteristic some still have it. A typical confounder could be "dementia",
where it would be rather safe to assume that all individuals registered as
having dementia really has impaired cognitive ability, but there are individuals
in the register having dementia but are misclassified as having "no dementia".
Another example would be diabetes.
Further, and more generally, this study fits into the broader category of
sensitivity analyses, that is, to assess the robustness of empirical evidence by
examining how one’s estimate varies when a key assumption is relaxed
(Rosenbaum, 2002).

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