Causal mediation analyses with rank preserving models

We present a linear rank preserving model (RPM) approach for analyzing mediation of a randomized baseline intervention's effect on a univariate follow-up outcome. Unlike standard mediation analyses, our approach does not assume that the mediating factor is also randomly assigned to individuals in addition to the randomized baseline intervention (i.e., sequential ignorability), but does make several structural interaction assumptions that currently are untestable. The G-estimation procedure for the proposed RPM represents an extension of the work on direct effects of randomized intervention effects for survival outcomes by Robins and Greenland (1994, Journal of the American Statistical Association 89, 737-749) and on intervention non-adherence by Ten Have et al. (2004, Journal of the American Statistical Association 99, 8-16). Simulations show good estimation and confidence interval performance by the proposed RPM approach under unmeasured confounding relative to the standard mediation approach, but poor performance under departures from the structural interaction assumptions. The trade-off between these assumptions is evaluated in the context of two suicide/depression intervention studies.