Quantitative ambiguities in matched versus unmatched analyses of the 2x2 table for a case-control study

When controls are individually matched to the cases in a case-control study, the subsequent data can be analysed in a matched or unmatched format. If done with careful attention to clinical variables that can produce important bias or confounding, the matching would have a scientific basis that warrants preservation of a matched analysis. If done, however, in the more common manner, as an act of demographic convenience, the matching is not based on a cogent 'correlation'; and an unmatched analysis may be preferred because it uses all the data and it is easier to understand. Regardless of the merits of the arguments, investigators can choose (and can often justify) either a matched or unmatched analysis. If the matched table is structured in the customary format of (a b/c d), the results for the odds ratio and chi-square test in the matched and unmatched analyses will be relatively similar if ad congruent to bc, but be strikingly disparate if ad is substantially higher or lower than bc. The same distinction can be noted by comparing a (or any value observed in the four cells) with the corresponding value that would be expected for that cell as calculated from the marginal totals. If the observed and expected values sharply disagree, the values of the odds ratio and chi-square will sharply disagree in the matched and unmatched formats. To avoid invidious choices when disparate results emerge from the matched and unmatched methods, investigators can routinely apply and routinely report what is found with both methods. Readers can then see both sets of results and can take their choice.