二元有序間隔時間具共變數相依交叉比半參數估計

Abstract

在長期追蹤研究中，個體自起始事件至研究結束前可能會經歷二元有序事件。舉例而言，慢性病患之出院與再住院即是二元有序事件。以常數和隨時間改變之交叉比分析二元有序事件中的第一與第二間隔時間之相依性蘊含慢性病人疾病歷程資訊。此相依性可能會受病患特質，例如性別與基因效應或其他有關之因子等影響。因此，我們針對二元有序間隔時間之交叉比提出參數化之對數線性模型。此參數化之交叉比模型可以用針對第二間隔時間給定共變數與第一間隔時間條件風險之分層比例風險模型其風險比來表示，且此比例風險模型不須額外假設第一與第二間隔時間之邊際分布形式。此具共變數相依交叉比之半參數估計可由最大化分層加權部份概似函數方法來得到，其中以倒數機率設限權重來處理第二間隔時間之誘導相依設限。我們同時證明此具共變數相依交叉比估計具有一致性與漸進常態分布性質，並以模擬分析檢驗所提出估計式之有限樣本表現量。提出之方法也應用於結腸癌資料，以自進入研究至發生結腸癌復發與發生結腸癌復發至死亡之二元有序間隔時間，估計其與共變數相關之相依交叉比。

In longitudinal follow-up studies, individual may experience ordered bivariate events before the end of the study. For instance, discharge and rehospitalization are ordered bivariate events for patients having a chronic disease. Association analysis between the first and second gap times between ordered bivariate events in terms of timeinvariant and time-varying cross ratios may provide predictive information on the course of chronic disease. Such association may be affected by patient’s characteristics, such as gender, genome type and other related factors. Therefore, we introduce parametric loglinear models for cross ratio between ordered bivariate gap times. These parametric cross ratio models can be expressed in terms of hazard ratios from stratified proportional hazards models via conditional hazards for the second gap times given the first gap time and covariates without specifying the marginal distributions of the first and second gap times. Then, semiparametric estimates of the covariate-dependent cross ratios can be obtained by maximizing the stratified weighted partial likelihood in which the inverse probability of censoring weights is used to tackle the induced dependent censoring of the second gap time. We have shown the consistency and asymptotic normality of the estimated covariate-dependent cross ratios. The finite-sample performance of the proposed methods is examined by simulation studies. The proposed method is also applied to the colon data for the estimation of the covariate-dependent cross ratios for the first gap time from entry study to recurrent colon cancer and the second gap time from recurrent colon cancer to death.