Speaker: Maya Mathur, Associate Professor, Stanford Medicine
Abstract: Estimators assuming missingness at random (MAR) can fail under missingness not at random (MNAR). Introducing complete auxiliary variables sometimes restores MAR by breaking dependence between analysis variables and missingness. However, if the auxiliaries are themselves incomplete, MAR typically remains violated.
We first derive sufficient conditions weaker than MAR under which the MAR functional mu_MAR(x) for a conditional mean E[Y|X=x] is correct. These conditions are also necessary under the assumptions that all missingness patterns of the incomplete variables can occur and certain kinds of context-specific independence do not occur.
Second, we propose a new identifying functional for E[Y|X=x], called mu_MIA(x) for “Marginalization over Incomplete Auxiliaries''. Under the aforementioned assumptions, the weaker-than-MAR conditions indicate that, in two cases, mu_MIA(x) dominates mu_MAR(x): mu_MIA(x) is correct whenever mu_MAR(x) is, except in specific knife-edge configurations, and additionally mu_MIA(x) is correct across an important structural class of MNAR distributions under which mu_MAR(x) fails. The two domination cases are: (1) when all auxiliary variables are incomplete; or (2) when X is complete and Y is incomplete. In the latter case, barring knife-edge configurations, mu_MAR(x) is always incorrect.
Importantly, determining whether each case holds requires only identifying which variables are incomplete based on the study design or observed data, without additional untestable assumptions. Our R package miapack estimates mu_MIA(x). We illustrate with real data and provide simulations comparing estimators of mu_MIA(x) and mu_MAR(x).
This will be a free hybrid seminar. To register to attend remotely, please click here: https://cam-ac-uk.zoom.us/meeting/register/UyunRH3-TDGLWoOGjh_TdA