# Nondifferential misclassification for polychotomous exposure in case control studies

Non-differential misclassification of dichotomous exposure is known to bias the odds ratio towards the null. Unfortunately this rule does not apply for polytomous exposure as well. The aim of the current work is to study the effect of non-differential misclassification of polytomous exposure on the association between exposure and disease. Three levels of parameters are chosen for evaluation. These are the proportion in a given exposure category, the case-control ratio and the odds ratio. The effect on these parameters was found to depend mainly on the misclassification matrix. Two extreme patterns were identified. The first one called the truly non-differential pattern, where the probability of misclassification in any exposure category is independent of the source category. The second pattern is called the adjacent only pattern, where misclassification is allowed only among adjacent categories. In reality these two patterns represent the two ends of a spectrum where most misclassification matrices lies somewhere in-between. The truly non-differential is the pattern where the odds ratios were found to be biased towards the null. On the other hand the adjacent-only pattern is the least predictable regarding the direction of the bias. An important distinction between the issues of the direction of the bias and the magnitude of the bias should be considered. Although the adjacent-only pattern may lead to a bias less in magnitude than truly non-differential pattern, the direction of the bias is unpredictable. It is also found that for a trend in the association to be reversed there should be a combination of low proportion in a given group and high rate of misclassification into that group. A discussion of the extension of the finding to more than one variable was presented