Factoring vs linear modeling in rate estimation: A simulation study of relative accuracy

A common strategy for modeling dose-response in epidemiology is to transform ordered exposures and covariates into sets of dichotomous indicator variables (that is, to factor the variables). Factoring tends to increase estimation variance, but it also tends to decrease bias and thus may increase or decrease total accuracy. We conducted a simulation study to examine the impact of factoring on the accuracy of rate estimation. Factored and unfactored Poisson regression models were fit to follow-up study datasets that were randomly generated from 37,500 population model forms that ranged from subadditive to supramultiplicative. In the situations we examined, factoring sometimes substantially improved accuracy relative to fitting the corresponding unfactored model, sometimes substantially decreased accuracy, and sometimes made little difference. The difference in accuracy between factored and unfactored models depended in a complicated fashion on the difference between the true and fitted model forms, the strength of exposure and covariate effects in the population, and the study size. It may be difficult in practice to predict when factoring is increasing or decreasing accuracy. We recommend, therefore, that the strategy of factoring variables be supplemented with other strategies for modeling dose-response.