臺灣博碩士論文加值系統

在分析長期追蹤資料與群集資料時，常使用的方法之一為Liang and Zeger(1986) 所提出的廣義估計方程式。在群集資料中，群集大小不同是很常見的情況，因此群集大小是否有資訊就變成研究者感興趣的一個問題。而因為在群集大小有資訊時，廣義估計方程式會有偏差。所以Hoffman et al.(2001) 提出群內重複抽樣解決這個問題。但需要大量時間運算，因此 Williamson et al. 提出群加權廣義估計方程式，並證明群加權廣義估計方程式與群內重複抽樣是一致的，且需要的時間更短。

選模指標一直以來是個重要的議題。在群集大小沒有資訊時，常用的有Shen and Chen(2012) 提出的 MLIC (missing longitudinal information criterion)和 Pan(2001) 所提出的 QIC， 然而在群集大小有資訊時，並沒有一個好的選模指標。因此在本文中，我們將利用群內重複抽樣，與誤差平方和的概念來建構新的選模指標 Resampling Longitudinal lnformation Criterion (RLIC)。並且利用模擬研究來佐證RLIC不管在群集大小有沒有資訊都能有不錯的結果，最後利用新的選模指標RLIC對實際資料作分析。

The generalized estimating equation (GEE) has been a popular tool for marginal regression analysis with longitudinal data, and its extension, the Cluster weighted GEE approach (CWGEE, Williamson et al., 2003), can further accommodate data when cluster size is informative. The model selection issue in the GEE framework has been discussed in previous literature when cluster size is non-informative. However, it is still unknown how to perform model selection in GEE analysis when the cluster size is informative.

In this work, we have proposed a resampling model selection criterion RLIC for selection of the mean model in the GEE model. The proposed method is shown to perform well when cluster size is non-informative/informative. We also examine the performance of a naive procedure namely to apply the QIC method (Pan, 2001) with informative cluster size treated as non-informative. We find that such a naive application of QIC do not perform as well as the RLIC method. The proposed method is further applied to data from the Taiwan longitudinal study on aging to assess the marginal relationship of frailty status with health and social status in the elderly, when cluster size is informative.

第一章 緒論 ......................................... 1

第二章 文獻回顧 ........................................3
2.0.1 符號定義..................................3
2.1 廣義估計.........................................3
2.2 群集大小有資訊的估計方法...........................5
2.2.1 群內重複抽樣...............................5
2.2.2 群加權廣義估計式............................6
2.3 群集大小沒有資訊時常用選模指標......................7
2.3.1 QIC........................................7
2.3.2 MLIC.......................................8

第三章 Resampling Longitudinal Information Criterion.....9
3.1 WCR 下的選模指標....................................9
3.2 CWGEE 下的選模指標.................................12
3.3 群集大小沒有資訊時的 RLIC...........................16

第四章 模擬研究...........................................18
4.1 群集大小有資訊時的情況...............................18
4.1.1 反應變數為相關連續型資料.......................18
4.1.2 反應變數為有相關二元資料.......................20
4.2 群集大小沒有資訊時的情況.............................22
4.2.1 反應變數為相關連續型資料.......................22
4.2.2 反應變數為有相關二元資料.......................23
4.3 群集大小 N=10 的情況................................24
4.4 模擬結論............................................25

第五章 實例分析...........................................27

第六章 結論...............................................31

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Chan, D.-C. D.,H.H. Tsou, C.-Y. Chen, and C.-Y. Chen (2010). Validation of the chinese-canadian study of health and aging clinical frailty scale (csha-cfs) telephone version. Archives of gerontology and geriatrucs 50(3), e74-e80.

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