In the analysis of data from case-control studies, quantitative exposure variables are frequently categorized into qualitative exposure variables, such as quarters. The qualitative exposure variables may be scalar variables that take the median values of each quantile interval, or they may be vectors of indicator variables that represent each quantile interval. In a qualitative analysis, the scalar variables may be used to test the dose-response relation, while the indicator variables may be used to estimate odds ratios for each higher quantile interval versus the lowest. Qualitative analysis, implicitly and explicitly documented by many epidemiologists and biostatisticians, has several desirable advantages (including simple interpretation and robustness in the presence of a misspecified model or outlier values). In a quantitative analysis, the quantitative exposure variables may be directly regressed to test the dose-response relation, as well as to estimate odds ratios of interest. As this paper demonstrates, quantitative analysis is generally more efficient than qualitative analysis. Through a Monte Carlo simulation study, the authors estimated the loss of efficiency that results from categorizing a quantitative exposure variable by quartiles in case-control studies with a total of 200 cases and 200 controls. In the analysis of the dose-response relation, this loss is about 30% or more; the percentage may reach about 50% when the odds ratio for the fourth quartile interval versus the lowest is around 4. In estimating odds ratios, the loss of efficiency for the second, third, and fourth quartile intervals versus the lowest is around 90%, 75%, and 40%, respectively. The authors consider the pros and cons of each analytic approach, and they recommend that 1) qualitative analysis be used initially to estimate the odds ratios for each higher quantile interval versus the lowest to examine the dose-response relation and determine the appropriateness of the assumed underlying model; and 2) quantitative analysis be used to test the dose-response relation under a plausible log odds ratio model.
