Much controversy exists regarding proper methods for the selection of variables in confounder control. Many authors condemn any use of significance testing, some encourage such testing, and other propose a mixed approach. This paper presents the results of a Monte Carlo simulation of several confounder selection criteria, including change-in-estimate and collapsibility test criteria. The methods are compared with respect to their impact on inferences regarding the study factor's effect, as measured by test size and power, bias, mean-squared error, and confidence interval coverage rates. In situations in which the best decision (of whether or not to adjust) is not always obvious, the change-in-estimate criterion tends to be superior, though significance testing methods can perform acceptably if their significance levels are set much higher than conventional levels (to values of 0.20 or more).
Greenland et al. (1989) studied this question.