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Essays on Bayesian Testing and Methods for Longitudinal Data.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Essays on Bayesian Testing and Methods for Longitudinal Data./
Author:	Suresh, Vikram.
Description:	1 online resource (98 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-03, Section: A.
Contained By:	Dissertations Abstracts International85-03A.
Subject:	Statistics. -
Online resource:	click for full text (PQDT)
ISBN:	9798380201063

Essays on Bayesian Testing and Methods for Longitudinal Data.
Suresh, Vikram.

Essays on Bayesian Testing and Methods for Longitudinal Data. - 1 online resource (98 pages)

Source: Dissertations Abstracts International, Volume: 85-03, Section: A.

Thesis (Ph.D.)--University of Cincinnati, 2023.

Includes bibliographical references

The three chapters presented in this work focus on improving statistical inference for time series models and clinical trial data. In the first chapter, a Bayesian approach is proposed for testing serial error independence in time series models, addressing the Lindley paradox and outperforming frequentist tests in AR1 models. The second chapter provides simulation evidence comparing conventional Mixed Models for Repeated Measures (MMRM) with Bayesian hierarchical models that explicitly specify dynamic correlation, showing improved predictive accuracy and reliable treatment effect estimation in small samples. The third chapter applies the best-performing model specifications from the previous chapter to clinical trial data, highlighting the importance of socioeconomic factors in treatment outcomes for major depressive disorder.The first chapter addresses the assumption of serial independence of model approximation errors in time series modeling, which is crucial for reliable inference. While frequentist methods like the Ljung-Box and Breusch-Godfrey tests have been widely used for hypothesis testing, the increasing popularity of Bayesian Inference demands comparable Bayesian testing procedures. However, Bayesian hypothesis testing has faced challenges in resolving the Lindley paradox, resulting in contradictory inference when compared to frequentist tests. To address this issue, we propose a Bayesian procedure for testing serial error independence in time series models, which enables paradox-free inference. The results demonstrate that the proposed Bayesian test outperforms frequentist tests in Autoregressive Order 1 (AR1) models in small to moderate-sized samples and performs comparably well in higher order autoregressive models. Clinical trials are often costly and have limited observations, making it crucial to achieve precise inference about treatment effects in small samples. The Mixed Models for Repeated Measures (MMRM) have been the standard tool for analyzing clinical trial evidence for several decades. However, the complicated covariance error structures used in prominent MMRM models may not adequately capture the dynamic correlations in the measured clinical variables. This chapter provides simulation evidence comparing MMRM covariance structure models with Bayesian hierarchical models (BHMs) that have an explicit dynamic structure. The results suggest that explicit specifications have better predictive accuracy both in- and out-of-sample. These models also reliably estimate treatment effects in small pseudo data samples generated from the estimates of two placebo-controlled clinical trials.The third chapter builds upon the results of the previous chapter by applying the best performing model specifications in a Bayesian hierarchical framework to clinical trials data. The Bayesian hierarchical models help estimate the degree of heterogeneity within a sample that enables precise inference. Treatment effect estimates and the impact of socioeconomic attributes are obtained from a sample of 665 adults with major depressive disorder from the Combined Medication to Enhance Depression Outcomes (CO-MED) study. We find that participants without a college education, those who are unemployed, and non-white individuals exhibited slower and less improvement in depressive symptoms. Moreover, being in the top 75\\% income percentile was associated with a 4.8\\% greater improvement in symptoms compared to being in the bottom 25\\% income percentile.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798380201063Subjects--Topical Terms:

556824
Statistics.
Subjects--Index Terms:

Bayesian inferenceIndex Terms--Genre/Form:

554714
Electronic books.

Essays on Bayesian Testing and Methods for Longitudinal Data.
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500 $a Source: Dissertations Abstracts International, Volume: 85-03, Section: A.
500 $a Advisor: Mills, Jeffrey A.
502 $a Thesis (Ph.D.)--University of Cincinnati, 2023.
504 $a Includes bibliographical references
520 $a The three chapters presented in this work focus on improving statistical inference for time series models and clinical trial data. In the first chapter, a Bayesian approach is proposed for testing serial error independence in time series models, addressing the Lindley paradox and outperforming frequentist tests in AR1 models. The second chapter provides simulation evidence comparing conventional Mixed Models for Repeated Measures (MMRM) with Bayesian hierarchical models that explicitly specify dynamic correlation, showing improved predictive accuracy and reliable treatment effect estimation in small samples. The third chapter applies the best-performing model specifications from the previous chapter to clinical trial data, highlighting the importance of socioeconomic factors in treatment outcomes for major depressive disorder.The first chapter addresses the assumption of serial independence of model approximation errors in time series modeling, which is crucial for reliable inference. While frequentist methods like the Ljung-Box and Breusch-Godfrey tests have been widely used for hypothesis testing, the increasing popularity of Bayesian Inference demands comparable Bayesian testing procedures. However, Bayesian hypothesis testing has faced challenges in resolving the Lindley paradox, resulting in contradictory inference when compared to frequentist tests. To address this issue, we propose a Bayesian procedure for testing serial error independence in time series models, which enables paradox-free inference. The results demonstrate that the proposed Bayesian test outperforms frequentist tests in Autoregressive Order 1 (AR1) models in small to moderate-sized samples and performs comparably well in higher order autoregressive models. Clinical trials are often costly and have limited observations, making it crucial to achieve precise inference about treatment effects in small samples. The Mixed Models for Repeated Measures (MMRM) have been the standard tool for analyzing clinical trial evidence for several decades. However, the complicated covariance error structures used in prominent MMRM models may not adequately capture the dynamic correlations in the measured clinical variables. This chapter provides simulation evidence comparing MMRM covariance structure models with Bayesian hierarchical models (BHMs) that have an explicit dynamic structure. The results suggest that explicit specifications have better predictive accuracy both in- and out-of-sample. These models also reliably estimate treatment effects in small pseudo data samples generated from the estimates of two placebo-controlled clinical trials.The third chapter builds upon the results of the previous chapter by applying the best performing model specifications in a Bayesian hierarchical framework to clinical trials data. The Bayesian hierarchical models help estimate the degree of heterogeneity within a sample that enables precise inference. Treatment effect estimates and the impact of socioeconomic attributes are obtained from a sample of 665 adults with major depressive disorder from the Combined Medication to Enhance Depression Outcomes (CO-MED) study. We find that participants without a college education, those who are unemployed, and non-white individuals exhibited slower and less improvement in depressive symptoms. Moreover, being in the top 75\\% income percentile was associated with a 4.8\\% greater improvement in symptoms compared to being in the bottom 25\\% income percentile.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Statistics. $3 556824
653 $a Bayesian inference
653 $a Hypothesis testing
653 $a Longitudinal data
653 $a Clinical trials
653 $a Socioeconomics
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710 2 $a University of Cincinnati. $b Business: Business Administration. $3 1468049
773 0 $t Dissertations Abstracts International $g 85-03A.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30725512 $z click for full text (PQDT)