針對縱向資料分析比較多種強健變異數估計量

Comparison of Various Robust Variance Estimators for Analysis of Longitudinal Data

蘇郁雅(Yu-Ya Su)

指導教授 ： 張淑惠

國立臺灣大學/公共衛生學院/流行病學與預防醫學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.10903

摘要

在道德與成本的考量之下，多數臨床試驗傾向只抽取相對有限的個體再進行大量重測以獲得足夠的樣本數，使廣義估計方程式之強健變異數估計量失去一致性並導致迴歸係數估計量不服從漸近常態分布；至2011年為止，所有強健變異數估計量之校正方法的研究皆僅止於在有限樣本之叢集資料下，比較各校正估計量的有效性，模擬與實證結果得到在叢集數受限於(5,40)時，各校正強健變異數估計量仍能有效的提高一致性並使迴歸係數估計量服從漸近常態分布。
本論文聚焦於相關結構因具時序性而更為複雜的縱向資料，在個體數有限時，設定實作相關矩陣結構為縱向資料特有的一階自迴歸結構並引入已有的六種強健變異數估計量校正方法，重新以迴歸係數估計量的t信賴區間長度與上下界、各變異數估計量的均方誤差、與迴歸係數真值的t信賴區間覆蓋率等三種統計標準，綜合比較各估計量的一致性、精準性與準確性、和有效性。
經由模擬結果顯示在個體數受限至(10,20)之連續與離散縱向資料下，可分別考慮以Wang與Long (2011)，以及Kauermann與Carroll (2001)、Fay與Graubard (2001) 提出之校正強健變異數估計量做為迴歸係數變異的候選估計量，然而當個體數小於10時，即需另以重複模擬抽樣方能獲得迴歸係數估計量之分布後，再用以檢定推論結果。

關鍵字

廣義估計方程式 ； 強健變異數估計量 ； 縱向資料 ； 一階自迴歸結構 ； 有限樣本

並列摘要

From the aspects of ethic and cost-effective principles, many clinical trials and longitudinal social science studies usually involve in relatively small number of study subjects with a moderate to large number of observations per subject during follow-up. When the number of subjects or the cluster size is finite, the robust variance estimator for generalized estimating equations parameter estimates of regression models for marginal means proposed by Liang and Zeger (1986) exhibits considerable bias and may result in inflated type 1 error. Various modifications of the robust variance estimator for analysis of clustered data have been proposed in literature. However, little work has been done for longitudinal data.
In this paper, we adopt the existing robust variance estimators, proposed for analyzing the clustered data, in the analysis of longitudinal data. In our simulation study, not only exchangeable correlation structure but also a time-related correlation matrix such as first-order autoregressive structure are considered as the working correlation structures for the longitudinal data. Our numerical results suggest that when the number of subjects is larger than 10, the robust variance estimator proposed by Wang & Long (2011) for continuous responses, and estimators proposed by Kauermann & Carroll (2001) or Fay & Graubard (2001) for binary responses perform relatively well in terms of mean squared error and coverage rate of resulting t confidence interval. When the number of subjects is smaller than 10, we need to use jackknife or bootstrap estimators instead of robust variance estimators in order to infer more information about the population characteristics by taking resamples.

並列關鍵字

Generalized estimating equation ； Robust variance estimator ； Longitudinal data ； First-order autoregressive structure ； Finite-sample

參考文獻

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