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Daniel Heitjan, Ph.D.
Professor and Department Chair, Department of Statistical Sciences
Southern Methodist University
Professor, Population & Data Sciences
UT Southwestern Medical Center

Statisticians have long recognized the potential biasing effects of nonignorable missing‑data mechanisms.  For example, if, say, larger observations are more likely to be missing or censored, then standard estimates such as the sample mean of the observed data (when some subjects are missing) or the Kaplan-Meier curve (when some subjects are censored) are invalid.  Unfortunately, methods that attempt to estimate or test the degree of nonignorability are unsatisfactory, thanks to conceptual and numerical difficulties associated with nonignorable modeling.  How then shall we handle such data sets?

My idea is to embed the reference ignorable model (under which the standard analysis is valid) in a nonignorable model (under which the standard analysis is potentially invalid) in which I define a nonignorability parameter to represent the degree of departure from missing at random.  I then conduct a sensitivity analysis to evaluate the dependence of the MLE of the parameter of interest (as a function of the nonignorability parameter) varies with the degree of nonignorability.  If it takes a large value of the nonignorability parameter to substantially affect the estimated parameter of interest, we judge the standard analysis to be insensitive.

In this talk, I describe an approach to such a sensitivity analysis based on the index of local sensitivity to nonignorability (ISNI) statistic.  An R package is available to conduct this analysis for the univariate GLM and a range of models for clustered or longitudinal data.  I will demonstrate applications in live-data examples.