臺灣博碩士論文加值系統

網絡統合分析（Network meta-analysis）能夠結合直接與間接證據，以比較多種治療的相對效益或危害。結構方程模式（Structural equation modeling）則是一種探討多個觀察變數和潛在變數的統計方法。先前的研究顯示網絡統合分析中的Lu-Ades模型可應用於結構方程模式。然而，Lu-Ades模型乃以治療之間的差異（contrast）作為分析單位的差異參數化模型（contrast-parameterized model），因此不僅會引入差異之間的相關性，也帶來資料輸入和模型建構的麻煩。

在本篇博士論文中，我們提出了如何在結構方程模式中，直接以各治療的結果為分析單位，即臂參數化模型（arm-parameterized model），來進行網絡統合分析。其中我們發現臂參數化模型會引入過多固定效應參數而造成附帶參數問題（incidental parameter problem），因此使用積分的方式將參數消除。我們說明了如何將採用受試者內設計（within person design）的研究納入臂參數化模型分析。另外，在臂參數化模型的架構下，傳統統合分析的新估計方法「無限制加權最小平方法（unrestricted weighted least squares）」可以輕易地推廣到網絡統合分析。

而後，我們利用發展的模型佐以結構方程模式的多群組分析（multiple group analysis）來探討網絡統合分析的不一致性（inconsistency），包括全域不一致性（global inconsistency）以及直接-間接證據不一致性（direct-indirect evidence inconsistency）。全域不一致性可在結構方程模式中以設計不一致性模型（design inconsistency model）評估。直接-間接證據不一致性則再被細分為設計導向及資訊導向兩種分析方式。為了瞭解設計導向直接-間接證據不一致性的結構，我們定義了證據網絡圖及證據比較圖，並根據這兩種圖提出臂基準不一致模型（arm-parameterized inconsistency model）。該模型能夠統合當前所有評估直接-間接證據不一致性的模型。在資訊導向直接-間接證據不一致性方面，我們提出了證據裂解模型（evidence-splitting model），並證明該模型是當前唯一能夠正確反映「直接比較證據」與「網絡統合分析中的其他證據」差異的模型。其中，證據裂解模型的參數關係較特殊，因此只有在結構方程模式才能正確估計。

最後，我們試圖了解當今網絡統合分析的估計方法在稀少資料下的表現。此處稀少資料指事件發生機率低的二元結果資料。經模擬發現，頻率學派常用的經驗勝算比（empirical odds ratio）在事件發生機率低時會出現嚴重偏誤。綜合偏誤、型一錯誤及檢力表現，階層廣義線性模型（hierarchical generalized linear model）是最佳的稀少資料估計法。而就我們提出的臂參數化模型而言，只要各治療效果差異不大，可使用我們自傳統統合分析Peto勝算比延伸出的多變量Peto勝算比來分析。另外，為解決Peto勝算比估計值受到各治療組別人數比例的問題，我們進一步提出中心化Peto勝算比，並發現該估計法可在各治療組別人數比例不均等的狀況下降低一部份偏誤。

利用結構方程模式估計臂參數化模型的彈性甚高。除了可以適應各種模型假設，亦可評估網絡統合分析的重要面向，例如不一致性。綜上所述，結構方程模式具有成為網絡統合分析標準評估工具的潛力。

Network meta-analysis is a crucial tool to combine direct and indirect evidence to compare the efficacy and harm between several treatments. Structural equation modeling is a statistical method that investigates relations among observed and latent variables. Previous studies have shown that the contrast-based Lu-Ades model for network meta-analysis can be implemented in the structural equation modeling framework. However, the Lu-Ades model uses the difference between treatments as the unit of analysis, thereby introducing correlations between observations and rendering data entry and model building a complex task.

In this PhD thesis, we first demonstrated how to undertake network meta-analysis in structural equation modeling using the outcome of treatment arms as the unit of analysis (arm-parameterized model). As arm-parameterized model may introduce too many fixed effect parameters, leading to the incidental parameter problem, which could be resolved using parameter elimination via integration. We also showed that our models can include trials of within-person designs without the need for complex data manipulation. In addition, a novel approach to meta-analysis, the unrestricted weighted least squares, can be readily extended to network meta-analysis under our statistical framework.

Based on the structural equation model we developed, we used multiple group analysis to evaluate inconsistency within network meta-analysis. We assessed two types of inconsistency: global inconsistency and direct-indirect evidence inconsistency. Global inconsistency was evaluated using the design inconsistency model, which can be constructed elegantly in structural equation modeling. Direct-indirect evidence inconsistency was further categorized into two approaches: design-oriented and information-oriented. For the design-oriented direct-indirect evidence inconsistency, we proposed two graphs, evidence network graphs and evidence comparison graph, to explore its structure. Based on the graph, we proposed an arm-parameterized inconsistency model that unifies current approaches to inconsistency evaluation. For the information-oriented direct-indirect evidence inconsistency, we proposed a series of evidence splitting models and showed that our model was the only model to truly reflect the difference between the direct information for the contrast of interest and the rest of the evidence network. These evidence splitting models requires flexible parameterizations and are estimable only in structural equation modeling.

Finally, we set out to evaluate the performance of various estimation approaches for network meta-analysis under the sparse data scenario, i.e. when the event probability was low for binary data. Simulations revealed that the conventional empirical odds ratio, which is commonly used frequentist packages for network meta-analysis, suffered from severe bias toward the null under low event probability. Of all the current estimation methods, hierarchical generalized linear model was the most robust approach in terms of bias, control of type I error rate and power. For our structural equation modeling framework, the multivariate Peto odds ratio, which is an extension of Peto odds ratio in conventional meta-analysis, performed well when the effect size was not too large. We also proposed a centered multivariate Peto odds ratio whose estimates does not depend on the relative sample size of each treatment and can partly alleviate the bias under the scenario of unequal patient allocation across treatment arms.

In conclusion, arm-parameterized model in structural equation modeling provides an extremely flexible framework for network meta-analysis, which can adapt to various model assumptions and assess their adequacy in network meta-analysis, such as inconsistency. Therefore, structural equation modeling has the potential to become a standard tool for network meta-analysis.

口試委員審定書 i
誌謝 iii
摘要 v
Abstract vii
Contents xi
Contents of Figures xiv
Contents of Tables xviii
Chapter 1 Introduction 1
1.1 Meta-analyses 1
1.2 Network meta-analyses 3
1.3 Structural equation modeling 6
1.4 Inconsistency in network meta-analyses 8
1.5 Aim 9
Chapter 2 Literature Review 11
2.1 General backbone model of network meta-analyses 11
2.2 Implementation of network meta-analysis in structural equation modeling 15
2.3 Current inconsistency evaluation methods 20
2.3.1 Evaluation methods for global inconsistency 21
2.3.2 Evaluation methods for direct-indirect evidence inconsistency 30
2.4 Current estimation methods for network meta-analyses 41
2.4.1 Bayesian inference 41
2.4.2 Frequentist inference 43
2.4.3 Frequentist inference for linear mixed models 44
2.4.4 Frequentist inference for generalized linear mixed models 48
2.5 Estimation methods for sparse data in pairwise and network meta-analyses 57
2.5.1 Sparse data methods in pairwise meta-analysis 57
2.5.2 Sparse data methods in network meta-analysis 63
Chapter 3 Methods 65
3.1 Implementation of arm-parameterized network meta-analysis model in structural equation modeling 65
3.1.1 The backbone arm-parameterized model 65
3.1.2 The recognition of incidental parameter problem 67
3.1.3 Parameter elimination via integration 72
3.1.4 Incorporating studies adopting within-person designs 74
3.1.5 Arm-parameterized unrestricted weighted least squares (UWLS) model 77
3.1.6 Demonstration of the structural equation modeling framework 82
3.2 Evaluation of inconsistency in network meta-analysis with structural equation modeling 84
3.2.1 Global inconsistency evaluation 84
3.2.2 The information structure of direct-indirect evidence inconsistency 86
3.2.3 Design-oriented direct-indirect evidence inconsistency and its visualization using evidence graphs 88
3.2.4 A novel evidence-splitting method for information-oriented direct-indirect inconsistency assessment 108
3.2.5 Assessing inconsistency in real data under the SEM framework 125
3.3 Extension and evaluation of sparse data network meta-analysis estimation methods 130
3.3.1 Extension to the empirical correction 130
3.3.2 A novel multivariate extension to Peto odds ratios 131
3.3.3 Simulation and evaluation of the estimation methods 137
Chapter 4 Results 143
4.1 Demonstration of various arm-parameterized network meta-analysis models using structural equation modeling real data 143
4.1.1 Demonstration of arm-parameterized random effect model 143
4.1.2 Demonstration of the arm-parameterized unrestricted weighted least squares model 144
4.1.3 Demonstration of arm-parameterized random effect model with within-person designs 145
4.2 Demonstration of evidence comparison graph and various inconsistency models using structural equation modeling with real data 148
4.2.1 Demonstration of the design inconsistency model 148
4.2.2 Demonstration of the design-oriented direct-indirect evidence inconsistency models 148
4.2.3 Demonstration of the information-oriented direct-indirect evidence inconsistency models 152
4.3 Simulation results for sparse data evaluation 156
4.3.1 Simulation results with small but equal sample size for each arm 163
4.3.2 Simulation results with large but equal sample size for each arm 192
4.3.3 Simulation results with unequal sample size for each arm 199
Chapter 5 Conclusions 207
5.1 Summary and discussion of main findings of this thesis 207
5.1.1 A novel framework of structural equation modeling on network meta-analysis 207
5.1.2 Evaluation of inconsistency using multiple group analysis under the structural equation modeling framework 208
5.1.3 Development and evaluation of sparse data evaluation methods for NMA 211
5.2 Future work arising from this thesis 213
5.3 Final remarks 217
References 219
Appendix 225

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