廣義半參數化重複事件模型之統計推論

Statistical Inferences for General Semiparametric Recurrent Event Models with Informative Censoring

何弘棋(Hung-Chi Ho)

指導教授 ： 江金倉

國立臺灣大學/理學院/應用數學科學研究所/博士(2017年)

https://doi.org/10.6342/NTU201703804

摘要

這份研究的目的是要藉由更廣義的半參數化模型探討含訊息右設限的重複事 件隨機過程. 當個體特異之潛在變數與右設限時間的分配不被指定時, 與形狀參 數 (shape parameter) 相關的重複事件時間之分配行為必須被仔細考慮, 因其攸 關參數估計與模型檢查. 鑑於此特質, 我們發展了不同的方法以便估計形狀依賴 (shape-dependent) 與形狀獨立 (shape-independent) 之發生率回歸模型. 特別的 是, 我們提議的估計準則也有助於模型之檢查且不需付出指定顯著水準的代價. 同時, 在輕微的條件下, 估計式與模型檢查統計量即有良好的大樣本性質. 我們 利用電腦模擬以評估估計式與檢查統計量之有限樣本表現. 此外, 我們將提議的 方法應用在兩個實際的資料上.

關鍵字

漸近常態性 ； 帶寬 ； 高斯過程 ； 具訊息的設限 ； 強度函數 ； 潛在變數 ； 模型選擇一致性 ； 重複事件過程

並列摘要

This research aims to investigate a recurrent event process with informative censoring through more general semiparametric latent intensity regression models. When the distributions of a subject-specific latent variable and censoring times are left unspecified, the distinct distribution behaviors, which are related to the shape parameter, of recurrent event times should be fully considered in constructing estimation and testing procedures. In light of this feature, different approaches are developed to estimate shape- dependent and independent occurrence rate regression models. Es-pecially, the presented estimation criteria are useful in building test rules for variant competing occurrence rate regression models without specifying the significance level. Meanwhile, the large-sample properties of estimators and the model selection consistency of test statistics are established under very mild conditions. The finite-sample performance of the proposed estimators and test statistics is further assessed through comprehensive simulations. Moreover, the applicability of our methodology is illustrated by recurrent event samples of intravenous drug users for inpatient care and chronic granulomatous disease patients.

並列關鍵字

asymptotic normality ； bandwidth ； Gaussian process ； informative censoring ； intensity function ； latent variable ； model selection consistency ； non-stationary Poisson process ； occurrence rate function ； pseudo estimation ； qth-order kernel function ； recurrent events ； shape parameter ； single-index ； size parameter.

參考文獻

Chiang, C. T. and Huang, M. Y. (2012). New estimation and inference procedures for a single-index conditional distribution model. Journal of Multivariate Analysis. 111, 271–285.

Chiang, C. T., James. L. F., and Wang, M. C. (2005). Random weighted bootstrap method for recurrent events with informative censoring. Lifetime Data Analysis. 11, 489–509.

Chiang, C. T., Wang, S. H., and Huang, M. Y. (2017). Versatile estimation in censored single-index hazards regression. Annals of the Institute of Statisti-cal Mathematics. DOI: 10.1007/s10463 – 017 – 0600 – 6.

Fleming, T. R. and Harrington, D. V. (1998). Counting processes and survival analysis. Wiley, New York.

Gong, G. and Samaniego, F. J. (1981). Pseudo maximum likelihood estimation: