PseudoLikelihood Estimation for Incomplete Data
Molenberghs, G; Kenward, MG; Verbeke, G; Teshome, B; (2011) PseudoLikelihood Estimation for Incomplete Data. Statistica Sinica, 21 (1). pp. 187206. ISSN 10170405

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Abstract
In statistical practice, incomplete measurement sequences are the rule rather than the exception. Fortunately, in a large variety of settings, the stochastic mechanism governing the incompleteness can be ignored without hampering inferences about the measurement process. While ignorability only requires the relatively general missing at random assumption for likelihood and Bayesian inferences, this result cannot be invoked when nonlikelihood methods are used. A direct consequence of this is that a popular nonlikelihoodbased method, such as generalized estimating equations, needs to be adapted towards a weighted version or doublyrobust version when a missing at random process operates. So far, no such modification has been devised for pseudolikelihood based strategies. We propose a suite of corrections to the standard form of pseudolikelihood to ensure its validity under missingness at random. Our corrections follow both single and double robustness ideas, and is relatively simple to apply. When missingness is in the form of dropout in longitudinal data or incomplete clusters, such a structure can be exploited toward further corrections. The proposed method is applied to data from a clinical trial in onychomycosis and a developmental toxicity study.
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