Homoskedastic adjustment inflation factors in model selection

Insufficient confounder adjustment is viewed as a common source of "false discoveries", especially in the epidemiology sector. However, adjustment for "confounders" that are correlated with the exposure, but which do not independently predict the outcome, may cause loss of power to detect the exposure effect. On the other hand, choosing confounders based on "stepwise" methods is subject to many hazards, which imply that the confidence interval eventually published is likely not to have the advertized coverage probability for the effect that we wanted to know. We would like to be able to find a model in the data on exposures and confounders, and then to estimate the parameters of that model from the conditional distribution of the outcome, given the exposures and confounders. The haif package, downloadable from SSC, calculates the homoskedastic adjustment inflation factors (HAIFs), by which the variances and standard errors of coeffcients for a matrix of X-variables are scaled (or inflated), if a matrix of unnecessary confounders A is also included in a regression model, assuming equal variances (homoskedasticity). These can be calculated from the A- and X-variables alone, and can be used to inform the choice of a set of models eventually fitted to the outcome data, together with the usual criteria involving causality and prior opinion. Examples are given of the use of HAIFs and their ratios.