Measurement error and misclassification
The two kinds
Error is NON-DIFFERENTIAL when it is unrelated to the other variables: a blood pressure cuff that is imprecise for everyone. It is DIFFERENTIAL when it depends on them: cases recalling exposures more thoroughly than controls, or an outcome assessor who knows the treatment allocation. Differential error can bias in either direction and by any amount.
Regression dilution
When a continuous exposure is measured with random error, the estimated slope is attenuated toward zero by roughly the reliability of the measurement. A single blood pressure reading contains substantial within-person variability, so the association between usual blood pressure and stroke estimated from one reading understates the real relationship considerably. Repeat measurements on a subsample allow the attenuation to be estimated and corrected.
What regression dilution looks like
Where the null-bias rule breaks
- Three or more exposure categories: misclassification can push an intermediate category's estimate away from the null.
- Errors correlated between exposure and outcome, or between exposure and confounder.
- A mismeasured CONFOUNDER, which leaves residual confounding whose direction follows the confounding, not the error.
- Any differential error at all, where the direction is whatever the differential mechanism produces.
- Even where the rule holds for the point estimate, it does not guarantee a conservative TEST: attenuation plus a wider effective variance changes the false-positive picture too.
What to do about it
Measure better where possible; take repeated measurements; build a validation substudy against a reference standard on a subsample; and use regression calibration, simulation-extrapolation or a Bayesian measurement model to correct. Where none of that is possible, conduct a quantitative bias analysis over plausible sensitivity and specificity rather than mentioning error in the limitations and moving on.
What to watch out for
The comforting rule that non-differential misclassification biases toward the null is true only in narrow circumstances, and it is routinely used to dismiss error in exactly the situations where it fails: with more than two exposure categories, with error correlated between variables, or when the mismeasured variable is a CONFOUNDER rather than the exposure, in which case adjustment is incomplete and the residual confounding can run in either direction. Attenuation also means a real effect can be missed entirely, so bias toward the null is not a reason to relax.
Clinical example
Self-reported dietary intake is compared between cases and controls. The error is substantial, plausibly differential because cases have been thinking about causes, and the exposure has several categories. None of the conditions for a safe bias-toward-the-null claim hold, and a bias analysis is the honest response.
- Random measurement error and regression dilution bias (opens in a new tab) · BMJ · doi 10.1136/bmj.c2289
- Effects of non-differential exposure misclassification on false conclusions in hypothesis-generating studies (opens in a new tab) · Int J Environ Res Public Health · doi 10.3390/ijerph111010951