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A bias may arise, when unmatched analysis is done to get an asymptotic maximum likelihood estimate from an 1-to-2 matched data set in a case-control study. Quantification of the bias showed that it could be in either direction of underestimation or overestimation of matched odds ratio. It depends on four different components : matched odds ratio, ratio of exposure/unexposure among cases, difference of the concordants among the case-exposures, and difference of the concordants among the case-unexposures. The direction of the bias was discussed in a simple univariate setting with actual examoles. It suggests that results of this study can be applied to the analysis of matched data in order to predict potential estimation bias in the analytic stage.