  Missing data is a common challenge in biomedical research. This fact, along
with growing dataset volumes of the modern era, make the issue of
computationally-efficient analysis with missing data of crucial practical
importance. A general computationally-efficient estimation framework for
dealing with missing data is the pseudo-expected estimating equations (PEEE)
approach. The method is applicable with any parametric model for which
estimation involves the solution of a set of estimating equations, such as
likelihood score equations. A key limitation of the PEEE approach is that there
is currently no closed-form variance estimator, and variance estimation
requires the computationally burdensome bootstrap method. In this work, we
address the gap and provide a closed-form variance estimator whose computation
can be significantly faster than a bootstrap approach. Our variance estimator
is shown to be consistent even with auxiliary variables and under misspecified
models for the incomplete variables. Simulation studies show that our variance
estimator performs well and that its computation can be over 50 times faster
than the bootstrap. The computational efficiency gain from our proposed
variance estimator is crucial with large datasets or when the main analysis
method is computationally intensive. Finally, the PEEE approach along with our
variance estimator are used to analyze incomplete electronic health record data
of patients with traumatic brain injury.
