A Formal Treatment of Sequential Ignorability

Taking a rigorous formal approach, we consider sequential decision problems involving observable variables, unobservable variables, and action variables. We can typically assume the property of extended stability, which allows identification (by means of G-computation) of the consequence of a specified treatment strategy if the unobserved variables are, in fact, observed - but not generally otherwise. However, under certain additional special conditions we can infer simple stability (or sequential ignorability), which supports G-computation based on the observed variables alone. One such additional condition is sequential randomization, where the unobserved variables essentially behave as random noise in their effects on the actions. Another is sequential irrelevance, where the unobserved variables do not influence future observed variables. In the latter case, to deduce sequential ignorability in full generality requires additional positivity conditions. We show here that these positivity conditions are not required when all variables are discrete.Comment: 25 pages, 5 figures, 1 tabl

Missing at random, likelihood ignorability and model completeness

This paper provides further insight into the key concept of missing at random (MAR) in incomplete data analysis. Following the usual selection modelling approach we envisage two models with separable parameters: a model for the response of interest and a model for the missing data mechanism (MDM). If the response model is given by a complete density family, then frequentist inference from the likelihood function ignoring the MDM is valid if and only if the MDM is MAR. This necessary and sufficient condition also holds more generally for models for coarse data, such as censoring. Examples are given to show the necessity of the completeness of the underlying model for this equivalence to hold