# Example of Misclassification Bias

## Outcome Variable - Cohort Study

*Lead Author(s):* Jeff Martin, MD
Misclassification bias of the outcome variable does not reduce the measure of association.
### Diagram

As you can see in the diagram below the risk ratio is 2.0 in the true scenario.

If specificity of the outcome measurement is 100%
- but there is only 70% sensitivity of the classification of the outcome,
- the risk ratio is unaltered at 2.0.

This is because all that you have done is to decrease both this cell and this cell by the same percentage.
- Therefore, the ratio between exposed and unexposed will not be affected.

This little trick is worth knowing about when you are using cutoffs for continuous variables using ROC curves - it is a recommendation to choose cutoffs which provide very high specificity.
## Specificity of Outcome 100%

As noted in this figure from Copeland (1977) when specificity is 100%,
- you can actually get an unbiased risk ratio regardless of the sensitivity of the outcome measurement.
- Here the true risk ratio is 2.0 and when specificity is 100% you can get a risk ratio of 2.0 regardless of the sensitivity.

## ROC Curve with Specificity of Outcome 100%

As shown in the figure below 100% specificity in the outcome measurement preserves unbiased risk ratios even in the face of less than perfect sensitivity.
- This is worth knowing when you are considering which outcomes to use or where to make cutoffs for certain diagnostic tests that are measured in their most raw form with a continuous variable.

## Choosing the Cutoff

**Choosing the most specific cutoff or the cutoff associated with 100% specificity** will lead to least biased ratio measures of effect.
- In the ROC curve you can see that you have many choices in terms of where you can make your cutoff for positivity to remind.
- This is important, for example, when you have a diagnostic test for outcome, say an antibody test for an infectious disease, you have many choices in terms of where you can make your cutoff for positivity.

## References

Copeland, K. T., Checkoway, H., McMichael, A. J., & Holbrook, R. H. (1977). Bias due to misclassification in the estimation of relative risk. *Am J Epidemiol, 105* (5), 488-495.