存活分析中， Cox 比例風險模型(Cox proportional hazards model) 最常被用來描述變數與存活資訊間的關係。然而，我們需進一步地評估模型的正當性，也就是必須符合比例風險假設(proportional hazards assumption)，方能利用 Cox 比例風險模型來配適資料。一個令人感興趣的問題是檢定比例風險假設是否有足夠的證據說明 Cox 比例風險模型可以配適資料配適的很好。另一方面，當比例風險假設不成立時，使用 Cox 比例風險模型是不合理的，因此，加速失敗時間 (accelerated failure time) 模型是另一個選擇，可以使用此模型來代替 Cox 模型。然而，在有時間相依(time-dependent) 共變數 (covariates) 之下的加速失敗時間模型，沒有一個簡單的方法可以檢驗加速失敗時間模型是否可以合理的配適資料。在此我們將介紹一個更廣義的模型，稱為擴充風險模型 (extended hazard model)，此模型包含了 Cox 比例風險模型及加速失敗時間模型，可以用來解決上述的問題。因為 Cox 比例風險模型及加速失敗時間模型是擴充風險模型的特例，藉由此特性可以將此模型視為完整模型 (full model) ，而 Cox 比例風險模型及加速失敗時間模型視為簡約模型 (reduced model) 做概似比檢定(likelihood ratio test) 來決定用何種模型來配適存活資料。最後，以台灣愛滋病 (HIV/AIDS) 病患的資料證明可以使用擴充風險模型做模型的檢定, 選擇適當的模型。

The Cox proportional hazards model has been widely used to describe the relationship between survival information and covariates. The validity to apply the Cox model for data is usually based on checking the proportional hazards assumption. It’s an interesting problem to investigate whether checking this assumption is sufficient as an evidence to fit data with the Cox model. On the other hand, when proportional hazards assumption fails, the Accelerated Failure Time (AFT) model is a popular alternative to the Cox model. However, when data include time-dependent covariates there are no convenient tools to check if AFT is appropriate for the data. An general class model termed “extended hazard model”, which contains the Cox and AFT models as its special case may be helpful to study the above problems. Because under the nested structure, we may test the fit of Cox and AFT models for data. Finally, we demonstrate the new model through a case study of Taiwanese HIV/AIDS cohort data.

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