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Improving Estimation Efficiency by Integrating External Summary Information From Heterogeneous Populations
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Improving Estimation Efficiency by Integrating External Summary Information From Heterogeneous Populations
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Improving Estimation Efficiency by Integrating External Summary Information From Heterogeneous Populations
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Dissertation
Improving Estimation Efficiency by Integrating External Summary Information From Heterogeneous Populations
2023
Overview
This dissertation develops methodologies to incorporate summary information from external studies to improve estimation efficiency for an internal study that has individual-level data. I first propose a penalized constrained maximum likelihood (PCML) method that simultaneously selects the external studies whose target populations match the internal study's so that their information is useful for internal model fitting and incorporates the corresponding information into internal estimation. The PCML estimator has the same efficiency as an oracle estimator that knows which external information is useful and fully incorporates that information alone. I then extend the PCML method to a more general framework by allowing the number of external studies to increase with the sample size of the internal study and apply the method to study mental health of people with bipolar disorder during the COVID-19 pandemic. I further develop a doubly penalized constrained maximum likelihood (dPCML) method that also accounts for the uncertainty in external information with more flexibility on what external information can be integrated. The dPCML method covers some existing well-known data integration methods as special cases. For the proposed methods I carry out detailed theoretical investigations, provide algorithms for implementation, and conduct comprehensive simulation studies. Based on the simulation studies, the proposed methods have excellent numerical performance. For example, when using the dPCML method with external study sample sizes similar to the internal sample size, the reduction in empirical standard errors is more than 20% for the estimates of some model parameters compared to the maximum likelihood estimator (MLE) without using the external information, and more than 10% compared to some other existing methods, without introducing bias.
