On Inverse Probability Weighting for Nonmonotone Missing at Random Data

Abstract

The development of coherent missing data models to account for nonmonotone missing at random (MAR) data by inverse probability weighting (IPW) remains to date largely unresolved. As a consequence, IPW has essentially been restricted for use only in monotone missing data settings. We propose a class of models for nonmonotone missing data mechanisms that spans the MAR model, while allowing the underlying full data law to remain unrestricted. For parametric specifications within the proposed class, we introduce an unconstrained maximum likelihood estimator for estimating the missing data probabilities which can be easily implemented using existing software. To circumvent potential convergence issues with this procedure, we also introduce a Bayesian constrained approach to estimate the missing data process which is guaranteed to yield inferences that respect all model restrictions. The efficiency of the standard IPW estimator is improved by incorporating information from incomplete cases through an augmented estimating equation which is optimal within a large class of estimating equations. We investigate the finite-sample properties of the proposed estimators in a simulation study and illustrate the new methodology in an application evaluating key correlates of preterm delivery for infants born to HIV infected mothers in Botswana, Africa.

Discrete Choice Models for Nonmonotone Nonignorable Missing Data: Identification and Inference

“…Specifically, it is well known that when the nonresponse process and the full data distribution depend on separate parameters, the MAR assumption implies that the part of the observed data likelihood which depends on the full data parameter factorizes from the nonresponse process. The missing data mechanism is then said to be "ignorable" (Little and Rubin, 2002) because it is possible to learn about the full data law without necessarily estimating the missing data process, or equivalently, it is possible to learn about the missing data process without modeling the full data law (Sun and Tchetgen Tchetgen, 2016). No such factorization is in general available under CCMV as the missing data process is nonignorable.…”

“…While IPW estimation avoids specification of a full-data likelihood, the approach does require a model for the nonresponse process. However, the development of general coherent models for nonmonotone nonresponse has proved to be particularly challenging, even under the MAR assumption; see Robins and Gill (1997) and Sun and Tchetgen Tchetgen (2016) for two concrete proposals and further discussion.…”

Efficient Nonparametric Causal Inference with Missing Exposure Information

“…This would also be useful for continuous instrumental variable problems [Kennedy et al, 2019b] with instrument missingness. Further, identification, efficiency theory, and estimation are all more complicated in settings where there is simultaneous missingness in covariates, treatment, and outcome [Sun and Tchetgen Tchetgen, 2018]; however, this also occurs often in practice and deserves deeper investigation. Lastly, we assumed exchangeability in the sense of the missing indicator R being conditionally independent of the underlying exposure Z given both covariates X and outcome Y; it would be of interest to consider the case where we only assume R ⊥ ⊥ Z | X.…”

Quantifying an Adherence Path-Specific Effect of Antiretroviral Therapy in the Nigeria PEPFAR Program

“…A caveat is that these do not take into account the variability induced by multiple imputation that was necessary in the PEPFAR analysis due to the presence of missing data, so in fact we anticipate more variability in the PEPFAR analysis. (Tsiatis, 2007;Sun and Tchetgen Tchetgen, 2014). We present results using complete-cases in the appendix to show the impact of imputing this volume of data.…”