Page 80 - Contributed Paper Session (CPS) - Volume 7

CPS2033 Ronnie P.
3. Result
We show that differential one‐sided mis‐classification can lead to the
estimated causal effect being greater than or smaller than the true causal
effect. This is opposed to Ogburn and VanderWeele (2012), who show for non‐
differential misclassification that the estimated causal effect always lies
between the true and the crude causal effect.
For the case of linear regression, we derive an expression similar to well‐
known large‐sample omitted variable bias approximation in linear regression.
Thus, given some assumptions regarding the correlations between the
measurement error and the other variables in the model, this expression can
be used to say whether the effect is over‐estimated or under‐estimated.
Differential mis‐classificiation is also studied for a binary outcomes using
logistic and log‐linear models for the odds ratio and the relative risk. No
mathematical proofs are given for these models, but simulation studies show
that the bias in the log‐linear model for the relative risk, has the same pattern
as linear regression. However, for logistic model and odds‐ratio, the pattern is
not as clear, probability due to the non‐collapsibility property of the odds ratio.
Depending on the assumptions regarding the prevalence mental disorders,
the re‐analysis in this paper show that the surprising negative findings in in
Fowler, 2017, regarding the effect of vocational rehabilitation is potentially
explained by underreporting in Swedish registries.

4. Discussion and Conclusion
Measurement errors in the confounders is often neglected when adjusting
for confounders in observational studies. This study is a contribution in that
we study the case of non-differential mis-classification. For linear models an
expression is provided so that applied researcher can study whether the causal
effect is under-estimated or over-estimated. The results regarding the odds
ratio is less clear.
This research is funded by The Institute for Evaluation of Labour Market
and Education Policy, which is a research institute under the Swedish Ministry
of Employment, situated in Uppsala, Sweden. IFAU’s objective is to promote,
support and carry out scientific evaluations.

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