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Pseudomaximum Likelihood Inference for Latent Variable Regression Subject to Selection Bias

Qian-Li Xue, Johns Hopkins University Department of Biostatistics

This work was motivated by the need to combine outcome information from a reference population with risk factor information from a screened sub-population in a setting where the analytic goal was to study the association between risk factors and multiple binary outcomes. This talk consists of two parts: part I introduces a two-stage latent class procedure that first summarizes the commonalities among outcomes using a reference population sample, then analyzes the association between outcomes and risk factors while accounting for the fact that screening may alter the structure of item associations. It develops an approach to estimating model parameters that is similar to pseudo maximum likelihood. Part II presents an alternative approach by formulating the analysis as a missing covariates problem under the assumption of missing at random. The performance of the proposed methods are compared through a simulation study and in an illustrative analysis of data from the Women's Health and Aging Study, a recent investigation of the causes and course of disability in older women. Combining information in the proposed ways is found to improve both accuracy and precision in summarizing multiple categorical outcomes, which effectively diminishes ambiguity and bias in making risk factor inferences.

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