Individually-matched etiologic studies: classical estimators made new again

Abstract

With greater access to regression-based methods for confounder control, the etiologic study with individual matching, analyzed by classical (calculator) methods, lost favor in recent decades. This design was costly, and the data sometimes mis-analyzed. Now, with Big Data, individual matching becomes an economical option. To many, however, conditional logistic regression, commonly used to estimate the incidence density ratio parameter, is somewhat of a black box whose output is not easily checked. An epidemiologist-statistician pair recently proposed a new estimator that is easily applied to data from individually-matched series with a 2:1 ratio (and no other confounding variables) using just a hand calculator or spreadsheet. Surprisingly—or possibly not—they overlooked classical estimators developed in earlier decades. This prompts me to re-introduce some of these, to highlight their considerable flexibility and ease of use, and to update them. Nowadays, for any matching ratio (M:1), the Maximum Likelihood result can be easily computed from data gathered under the matched design in two different ways, each using just the summary data. One is via any binomial regression program that allows offsets, applied to just M 'rows' of data. The other is by hand! The aim of this note is not to save on computation; instead, it is to make connections between classical and regression-based methods, to promote terminology that reflects the concepts and structure of the etiologic study, and to focus attention on what parameter is being estimated.

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