Year of Award
Doctor of Philosophy (PhD)
Department of Mathematics
As one of the most recommended strategies in decision making of contemporary medicine, evidence-based medicine (EBM) is attracting more and more attention. For EBM, the scientific evidences are obtained mainly from the randomized controlled trials (RCTs), systematic review and meta-analysis. In particular, meta-analysis can help researchers statistically combine several independent studies for a same clinical problem. In meta-analysis, Cohen's d and Hedges' g are among the most commonly used effect size measurements for continuous data. To compute these mean difference criteria, the sample mean and standard deviation are two conventional statistics reported in the literature. However, some other clinical studies may instead report the median, minimum and maximum values, and/or sample quartiles. Such a situation requires researchers to estimate the sample mean and standard deviation from these reported summary statistics. We note, however, that most existing estimators in the literature have some serious limitations. For this, we propose to improve the existing methods and extend them to three frequently encountered scenarios. In this thesis, we developed the optimal sample mean estimators, the normality test statistics and the updated Cohen's d mean difference criterion for three commonly encountered scenarios in meta-analysis. In Chapter 1, we gave a brief introduction on evidence-based medicine, meta-analysis and the summary data. In Chapter 2, we introduced our optimal estimators of the sample mean under the three scenarios, respectively. In Chapter 3, we proposed several methods for testing the normality of the underlying data. And in Chapter 4, we proposed to improve the famous Cohen's d and its relevant parameters. To assess the practical performance of our newly proposed methods, we also chose a few real data at the end of each chapter as illustrating examples. Numerical results of those studies indicated that our proposed methods have satisfactory performance both in theory and in practice. Following our new methodology, we also recommended an improved procedure for medical researchers to conduct meta-analysis. For illustration, we chose a meta-analysis in Chapter 5 on the effect of phytosterols to plasma CRP level (Rocha et al., 2016) to compare the results obtained from our recommended procedure and from the original methods. The results showed that our recommended procedure may lead to distinctly different results for a same clinical problem. To conclude the thesis, we expect that our newly proposed methods can be regarded as "rules of thumb" and will soon be widely applied in meta-analysis and evidence-based medicine.
Includes bibliographical references (pages 137-150).
Luo, Dehui, "Statistical learning of median in meta-analysis" (2017). Open Access Theses and Dissertations. 469.