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Penn State University

1. Midya, Vishal. Frequentist and Bayesian hypothesis testing focusing on meaningful effect sizes.

Degree: 2020, Penn State University

Several fields of science including biomedical science, psychology and social sciences are facing severe challenges from ``replication crisis''. Studies with lower power, preference for statistically significant results and erroneous inference of no effect after failing to reject a point null hypothesis are one of the major contributing factors to this ongoing crisis. The use of point null hypothesis or Null Hypothesis Significance Testing (NHST) without properly justifying ``effect size'' has worsened the situations. This thesis is a collection of three articles which attack such malpractices by exploring the systematic biases these methods cause. It then proposes alternative measures or in some cases modifies the current procedures to ward off false results. Both Bayesian and Frequestist procedures for hypothesis testing have been studied. In the first Chapter ``Bayes Factor and Region of Practical Equivalence in Interval Null Hypothesis Testing'', we have studied testing of interval null hypotheses for improved scientific inference. For example, Lakens et al (2018) and Lakens and Harms (2017) use this approach to study if there is a pre-specified meaningful treatment effect in gerontology and clinical trials, instead of a point null hypothesis of any effect. Two popular Bayesian approaches are available for interval null hypothesis testing. One is the standard Bayes factor and the other is the Region of Practical Equivalence (ROPE) procedure championed by Kruschke and others over many years. This paper connects key quantities in the two approaches, which in turn allow us to contrast two major differences between the approaches with substantial practical implications. The first is that the Bayes factor depends heavily on the prior specification while a modified ROPE procedure is very robust. The second difference is concerned with the statistical property when data is generated under a neutral parameter value on the common boundary of competing hypotheses. In this case the Bayes factors can be severely biased whereas the modified ROPE approach gives a reasonable result. Finally, the connection leads to a simple and effective algorithm for computing Bayes factors using draws from posterior distributions generated by standard Bayesian programs such as BUGS, JAGS and Stan. Usual Frequetist hypothesis testing using point null hypothesis and vague alternative only leads to rejection or inability to reject the null. Even when a decision in favour of or against the null is made, it remains unclear whether the decision makes sense under a practically meaningful effect size. Often time, model selection procedures like BIC are used in place of hypothesis testing to choose between the null or the alternative. But such tools have very desperate Type 1 and Type 2 errors which sometimes lead to unreliable inference. This paper revolves around specifying a certain effect size under the alternative hypothesis instead of blindly leaving it unspecified and simultaneously resolving the imbalance between Type 1 and Type 2… Advisors/Committee Members: Jiangang Liao, Dissertation Advisor/Co-Advisor, Jiangang Liao, Committee Chair/Co-Chair, Vonn Andrew Walter, Committee Member, Pritish Mondal, Special Member, Arun Kumar Sharma, Outside Member, Arthur Steven Berg, Program Head/Chair, Arthur Steven Berg, Committee Chair/Co-Chair, Arthur Steven Berg, Dissertation Advisor/Co-Advisor.

Subjects/Keywords: Testing of Hypothesis; Bayes Factor; Bayesian Information Criterion; Effect Size; Type 2 Error; Interval Null Hypothesis; Type 1 Error; ROPE

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APA (6th Edition):

Midya, V. (2020). Frequentist and Bayesian hypothesis testing focusing on meaningful effect sizes. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/18036vum41

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Midya, Vishal. “Frequentist and Bayesian hypothesis testing focusing on meaningful effect sizes.” 2020. Thesis, Penn State University. Accessed April 15, 2021. https://submit-etda.libraries.psu.edu/catalog/18036vum41.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Midya, Vishal. “Frequentist and Bayesian hypothesis testing focusing on meaningful effect sizes.” 2020. Web. 15 Apr 2021.

Vancouver:

Midya V. Frequentist and Bayesian hypothesis testing focusing on meaningful effect sizes. [Internet] [Thesis]. Penn State University; 2020. [cited 2021 Apr 15]. Available from: https://submit-etda.libraries.psu.edu/catalog/18036vum41.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Midya V. Frequentist and Bayesian hypothesis testing focusing on meaningful effect sizes. [Thesis]. Penn State University; 2020. Available from: https://submit-etda.libraries.psu.edu/catalog/18036vum41

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation


Vanderbilt University

2. -3660-4570. Coping With Complexities in High Dimensional Data: PheWAS in EMR and Statistical Inference in fMRI Data.

Degree: PhD, Biostatistics, 2020, Vanderbilt University

When conducting analyses on high dimensional data, one could face statistical difficulties due to large dimensionality and the noisy nature of the data. In this dissertation, we specifically look into potential complexities one might encounter when analyzing electronic medical record (EMR) and functional magnetic resonance imaging (fMRI) data. Phenome-Wide Association study (PheWAS) is a newly proposed method that scans through phenotypes (Phecodes) with a specific genotype of interest using logistic regression. Since the clinical diagnoses in EMR are often inaccurate which can lead to biases in the odds ratio estimates, much effort has been put to accurately define the cases and controls to ensure an accurate analysis. Specifically in order to correctly classifying controls in the population, an exclusion criteria list for each Phecode was manually compiled to obtain unbiased estimates. However, this method could be inefficient and the accuracy of the lists cannot be guaranteed. We propose to estimate relative risk (RR) instead. With simulation and real data application, we show that RR is unbiased without compiling exclusion criteria lists. With RR as estimates, we are able to extend PheWAS to larger-scale phenotypes which preserve more disease-related clinical information than Phecodes. The main purpose of task-induced fMRI is to measure neuronal activities related to specific task. fMRI data usually require several preprocessing steps before analysis. Among all, spatial smoothing is a necessary step known to increase signal-to-noise ratios but the choice of degree of smoothing is often arbitrary. One critical statistical issue in fMRI analysis is the balance between Type I and II error rates. We first demonstrate the influence of the degree of smoothing and experimental factors on the trade-off between Type I and II error rates. Next, we propose to use second-generation p-values (SGPV) as an inference tool instead of the traditional p-values for hypothesis testing. By allowing the interval null hypothesis, we have shown that SGPV is able to alleviate the critical statistical issue by controlling Type I error rate more steadily while obtaining enough power. Advisors/Committee Members: Johnson, Robert (advisor), Kang, Hakmook (advisor).

Subjects/Keywords: EMR; PheWAS; fMRI; Statistical analysis; study design; Type I error rate; Type II error rate; p-value; Multiple comparison; Second-generation p-values; SGPV; Interval null; Hypothesis testing

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

-3660-4570. (2020). Coping With Complexities in High Dimensional Data: PheWAS in EMR and Statistical Inference in fMRI Data. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://hdl.handle.net/1803/15924

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16th Edition):

-3660-4570. “Coping With Complexities in High Dimensional Data: PheWAS in EMR and Statistical Inference in fMRI Data.” 2020. Doctoral Dissertation, Vanderbilt University. Accessed April 15, 2021. http://hdl.handle.net/1803/15924.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7th Edition):

-3660-4570. “Coping With Complexities in High Dimensional Data: PheWAS in EMR and Statistical Inference in fMRI Data.” 2020. Web. 15 Apr 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-3660-4570. Coping With Complexities in High Dimensional Data: PheWAS in EMR and Statistical Inference in fMRI Data. [Internet] [Doctoral dissertation]. Vanderbilt University; 2020. [cited 2021 Apr 15]. Available from: http://hdl.handle.net/1803/15924.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-3660-4570. Coping With Complexities in High Dimensional Data: PheWAS in EMR and Statistical Inference in fMRI Data. [Doctoral Dissertation]. Vanderbilt University; 2020. Available from: http://hdl.handle.net/1803/15924

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

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