Abstract
Misclassification of categorical variables is a common occurrence, resulting from the fallibility of diagnostic instruments (e.g., in measuring disease or genetic status or categorizing land use based on satellite imagery) or when categorizing a mismeasured quantitative variable (physical activity, dietary intake, etc.). Occasionally some misclassification is intentionally introduced for privacy reasons or in the use of randomized response methods for sensitive questions.
I'll begin with a short general expository overview of misclassification in two-way tables and lead into the more specific problem of the effects of misclassification on the performance of the Cochran-Armitage (CA) test. The CA test is often used (for better or worse) in both epidemiology and genetics to test for linear trend in two-way tables with a binary outcome. There has been increasing interest in the power and size of the test and in determination of sample size, especially when there is potential misclassification in the "exposure" category.
We provide a unified approach to determination of the power function over different sampling strategies (fixed overall sample size or fixed marginal sample sizes) and allowing for misclassification in one or both variables. The misclassification may be either differential or non-differential. We also discuss a modification of the CA test which is sometime used (based on a standard error obtained without invoking the null hypothesis). Numerical illustrations are presented for the more commonly studied problem of misclassification in the exposure category.