On Inverse Probability Weighting for Nonmonotone Missing at Random Data

TL;DR

This paper develops new models and estimation methods for inverse probability weighting in nonmonotone missing at random data, enabling more flexible and reliable analysis beyond traditional monotone missingness assumptions.

Contribution

It introduces a class of models for nonmonotone MAR data, along with unconstrained maximum likelihood and Bayesian constrained estimators, improving inference and implementation.

Findings

Proposed estimators perform well in finite samples.

Method applied to study preterm delivery in HIV-infected mothers.

Augmented estimator enhances efficiency over standard IPW.

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.