# Graphical Examples of Misclassification Bias

*Lead Author(s):* Jeff Martin, MD

The effects of reduced sensitivity of the exposure measurement and/or reduced specificity of the exposure measurement on measurement bias can be seen in the following charts.

## Graphing Imperfect Sensitvity and Specifcity of Exposure

As show in the below figure from Copeland different scenarios for imperfect sensitivity and imperfect specificity have been worked out.

## Explanation of Graph

The graph assumes a case-control study where the true OR is 2.67,

- which is a decent size odds ratio today (Now that the many of the odds ratios of 10, like smoking and lung cancer, have already been found.)
- The prevalence of exposure in the controls is 0.2.
- On the y axis is the observed or apparent odds ratio and the line shows what happens as specificity is varied from 50% to 100% under 3 different scenarios of sensitivity.

Note especially how there are some pretty substantial hits on the apparent odds ratio as you move away from 100% specificity and that this is accentuated, noted by the steeper slopes, as sensitivity falls.

- Note how the slope is steeper in the sensitivity of 50% curve.

## Charting Decreasing OR

Again using

Copeland we look at the resulting scenarios for odds ratios under 2.0,

- which is often the smallest odds ratio that many of our studies can pick up.

If sensitivity is 90%, then specificity can be no less than about 87% before the OR drops below 2.

If sensitivity is 70%, then specificity can be no lower than about 94%.

If sensitivity is as low as 50%, then specificity can be no lower than about 98%.

## 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.