If estimates of the effect of a treatment variable on an outcome of interest are to be adjusted for a set of possible confounding factors, it is necessary to rely on the assumption of experimental treatment assignment (ETA) according to which each experimental unit has positive probability of being observed at any of the possible levels of the treatment variable regardless of the values the confounding factors may take on. Even if this assumption is only practically violated in the sense that certain values of the confounding factors cause some treatment levels to become not impossible, but at least highly unlikely, the adjusted variable importance parameter often becomes poorly identified in finite samples.
We introduce an algorithm that is intended to make variable importance estimation more robust with respect to violations of the ETA assumption. Two different identifiability criteria are proposed for deciding when an adjusted variable importance parameter cannot be reliably estimated from the data. These criteria are then used to identify a maximal set of adjustment variables for which the ETA assumption appears reasonably well satisfied. A more efficient estimator of the parameter corresponding to the selected adjustment set is then sought by selecting from among estimators making use of even smaller adjustment sets by minimizing an estimate of the mean squared error for the selected parameter.
A simulation study aimed at evaluating the benefits of this latter step suggests that it can lead to efficiency gains on the order of 100% if the ETA assumption is violated to some extent and to efficiency gains on the order of 35% if the ETA assumption is well approximated. The proposed algorithm is applied to the problem of identifying mutations in the protease enzyme of HIV that have an effect on virologic response to the commonly used antiretroviral drug lopinavir. While both unadjusted and fully adjusted analyses yield unsatisfactory results, the subset of significant mutations identified by the algorithm introduced here includes eight of the 12 known major lopinavir resistance mutations as well as two mutations that are thought to increase susceptibility to lopinavir. Two of the four major mutations not identified in our analysis occurred very rarely in our data set, giving the algorithm low power to detect any impact on virologic response. Recent in vitro experiments suggest that the other two major mutations not identified here may in fact be less important in determining lopinavir resistance than previously thought. The excellent agreement of the results reported here with current understanding of lopinavir resistance suggest that variable importance estimation based on data-adaptive selection of the adjustment set represents a promising new approach for studying the effects of HIV mutations on clinical virologic response to antiretroviral therapy as well as for biomarker discovery in general.
Bembom, Oliver; Fessel, Jeffrey W.; Shafer, Robert W.; and van der Laan, Mark J., "Data-adaptive Selection Of The Adjustment Set In Variable Importance Estimation" (March 2008). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 231.