Generalized multiple indicators, multiple causes measurement error models
Tekwe, Carmen D.
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Multiple Indicators, Multiple Causes (MIMIC) models are often employed by researchers studying the effects of an unobservable latent variable on a set of outcomes, when causes of the latent variable are observed. There are times however when the causes of the latent variable are not observed because measurements of the causal variable are contaminated by measurement error. The objectives of this dissertation are: (1) to extend the classical linear MIMIC model to allow both Berkson and classical measurement errors, defining the MIMIC measurement error (MIMIC ME) model, (2) to extend the classical linear MIMIC models to allow both Berkson and classical measurement errors where the distributions of the manifest variables belong in the exponential family, defining the generalized linear MIMIC ME (G-MIMIC ME) model, (3) to develop likelihood based estimation methods using the EM algorithm with Monte Carlo approximation to the integral in the E-step for both the MIMIC ME and G-MIMIC ME models, and (4) to obtain data driven estimates of the variance of the classical measurement error associated with log(DS02), an estimate of the amount of radiation dose received by atomic bomb survivors at the time of their exposure. Participants of the Adult Health Study (AHS) cohort of the atomic bomb data who were exposed to radiation emitted from the detonation of the bombs with complete data were studied. The defined MIMIC ME model was applied to study the effects of dyslipidemia, a latent construct and the effect of true radiation dose on the physical manifestations of dyslipidemia (triglycerides, bad cholesterol and HDL cholesterol). The G-MIMIC ME model is also applied to study the effect of genetic damage (a latent construct based on exposure to atomic bomb radiation) and the effect of true radiation dose on the physical manifestations of genetic damage (chromosome aberrations (CA) and the amount of hemizygous mutant fractions at the glycopherin A locus in red mature blood cells (GPA)). We find that radiation dose was positively related to triglycerides (p-value<0.0001), negatively associated with HDL cholesterol (p-value=0.001), while no statistical significant relationship was found between radiation dose and bad cholesterol (p-value=0.14). Triglycerides were most strongly associated with dyslipidemia with 85% of the dose adjusted variation in triglycerides explained by dyslipidemia. Dyslipidemia explained 14% and 15% of the adjusted variation in bad and HDL cholesterol, respectively. Our application of the G-MIMIC ME model to the atomic bomb data allowed us to conclude that CA was positively related to genetic damage (p-value<0.0001) while log(GPA) was not (p-value=0.44). The classical measurement error variance was estimated to be 0.092 (CV=0.31) and 0.109 (CV=0.34) based on our applications of the MIMIC ME and G-MIMIC ME models, respectively.