Walter-Stitt及Cox時間相依模式應用於具潛在前導期及截切性質偏差篩檢資料

Abstract

背景 在一個篩檢計畫之中，欲透過比較篩檢偵測(臨床症前期的早期偵測)及臨床偵測(由於臨床症狀及徵兆而被診斷)兩種模式個案的存活狀況來評估篩檢效益時，往往會因為沒有考慮潛在前導期(不可觀察)、滯留期(在臨床症前期的時間)及截切性質(篩檢過度抽樣滯留期長的個案)而高估其效益。雖然Walter及Stitt (1987)已有提出一母數方法處理潛在前導期，但截至目前為止仍很少有運用母數及半母數的存活模式來同時處理潛在前導期及不可觀察的截切性質。 方法 本論文延伸Walter及Stitt母數方法使模型得以同時處理篩檢資料中的潛在前導期及左截切性質。由於乳癌死亡風險比為主要的評估指標，本論文亦提出Cox半母數等比例風險模型來處理這兩個性質。此外，本論文利用SAS發展不同估計方法的程式，包括動差法、最大概似估計法及貝氏蒙地卡羅馬可夫鏈。無論母數或是半母數的方法皆應用在乳癌篩檢資料上，包括Health Insurance Project (HIP)試驗及瑞典W郡試驗。 結果 結果顯示若未校正前導期偏差及由於病程差異的偏差可能會高估篩檢偵測比臨床偵測之存活效益。此結果可由以下的篩檢偵測之乳癌死亡風險及篩檢偵測比上臨床偵測之風險比來支持， 1. 校正潛在前導期及截切性質後之風險速率 (1) 校正潛在前導期後之風險速率 以W郡試驗為例，未校正之風險速率(0.0107)比校正潛在前導期後低，使用非線性混合方法及貝氏蒙地卡羅馬可夫鏈估計結果分別為0.0182 (0.0111-0.0251)及0.0188 (0.0126-0.0252)，類似的結果也可以在HIP試驗中看到。值得注意的是，滯留期基於較弱訊息Gamma先驗分佈之估計值會較強訊息Gamma先驗分佈或定值的結果較為穩健。 (2) 校正潛在前導期及截切性質後之風險速率 使用W郡試驗，在使用非線性混合方法及貝氏蒙地卡羅馬可夫鏈校正兩項偏誤後，風險速率分別為0.0205 (0.0134-0.0276) 及 0.0211 (0.0145-0.0284)。基於(2)的結果，校正潛在前導期及截切性質之十年存活為80.98%，相較於未校正前之十年存活率89.85%，降低8.87%。 2. 不同偵測模式對於乳癌死亡風險比 (1) 母數方法：使用瑞典W郡試驗，篩檢組比對照組之未校正風險比為0.26 (0.18-0.36)，在考慮潛在前導期後會膨脹至0.38 (0.25-0.55)，更進一步考慮截切性質後會膨脹至0.43 (0.27-0.60)。 (2) 半母數方法：使用瑞典W郡試驗，首次篩檢及後續篩檢對於對照組之風險比在考慮潛在前導期後，分為0.59 (0.49-0.70)及0.50 (0.47-0.52)。在多考慮由於腫瘤特質(大小、淋巴結轉移及組織學分級)之早期偵測後，首次篩檢及後續篩檢對於對照組之風險比分別會膨脹至0.86 (0.71-1.04) 及 0.86 (0.82-0.91)。 結論 本論文成功延伸潛在前導期Walter-Stitt統計模式，開發時間相依Cox模式，並開發多種估計方法(包含貝氏及非貝氏)，以處理在面對由於篩檢個案之潛在前導期及截切性質而高估的篩檢效益。

Background The benefit of cancer screening with the comparison of survival between screen-detected (early detection of pre-clinical screen-detectable phase (PCDP)) and clinically-detected (diagnosis due to the presence of clinical symptoms and signs defined as clinical phase (CP)) mode is often overestimated due to the failure of considering latent (unobserved) lead-time, the derivation from sojourn time (time spent in the PCDP), and truncation (oversampling cases with long sojourn time at screen). Both correlated issues, latent lead-time and also unobservable truncation, have been barely addressed by using parametric and semi-parametric approaches of survival models although the Walter and Stitt model, a parametric approach, has already considered lead-time bias. Methods We extended the Walter and Stitt parametric method to render their model amenable to dealing with screening data with both lead-time and left truncation. The semi-parametric Cox proportional hazards regression model is also proposed to tackle these two issues while the hazard ratio for the risk of breast cancer death is of great interest. Feasible computer algorithms with non-Bayesian and Bayesian approaches for the estimation of parameters with different methods including moment methods, maximum likelihood estimation (MLE), and Bayesian Markov Chain Monte Carlo (MCMC) method were programmed by using SAS software. Both parametric and semi-parametric models and computer algorithms were applied to breast cancer screening data including the HIP trial and the Swedish W-County trial. Results The failure of adjusting latent lead time and truncation biases may result in overestimation of the survival benefit for screen-detected breast cancer in opposite to clinically-detected breast cancer. This can be supported by the following findings expressed by hazard rate of breast cancer death among screen-detected breast cancer and also hazard ratio for the risk of breast cancer between screen-detected breast cancer and clinically-detected breast cancer. 1. Hazard rate of post lead-time and truncation survival (1) Hazard rates with adjustment for lead-time bias Using the W-county trial, the unadjusted hazard rate (0.0107) was lower than those with adjustment for lead-time, 0.0182 (0.0111-0.0251) and 0.0188 (0.0126-0.0252) using non-linear mixed method and Bayesian MCMC method, respectively. Similar results of the HIP trial were noted. Note that the estimates based on the weak information prior of sojourn time with gamma distribution were more robust than the larger information prior or fixed values of sojourn time. (2) Hazard rates with adjustment for lead-time and truncation biases Using the W-county trial, the hazard rates after adjustment for both biases were 0.0205 (0.0134-0.0276) and 0.0211 (0.0145-0.0284) using non-linear mixed method and Bayesian MCMC method, respectively. Based on the finding of (2), 10-year post lead-time and truncation survival was calibrated as 80.98%, which was lower than the unadjusted survival of 89.85% by 8.87%. 2. Hazard ratio (HR) for the risk of breast cancer death by detection mode The failure of adjusting for latent lead time and truncation biases may result in overestimation of hazard ratio for the screen-detected cases in opposite to clinically-detected breast cancer (control group). (1) Parametric approach: Using the data from the W-county trial, the hazard ratio of screen-detected case compared to the control group was 0.26 (0.18-0.36) without adjusting for lead-time, was inflated to 0.38 (0.25-0.55) after lead-time adjustment and to 0.43 (0.27-0.60) with further consideration of truncation bias. (2) Semi-parametric approach: Using the data from the W-county trial, the hazard ratios after adjustment for lead-time and truncation biases were 0.59 (0.49-0.70) and 0.50 (0.47-0.52) for prevalent screen and subsequent screen, respectively. After taking early detection through the incorporation of three tumour attributes (size, nodes, and histological grade), the corresponding hazard ratios were inflated to 0.86 (0.71-1.04) and 0.86 (0.82-0.91) for prevalent screen and subsequent screen, respectively. Conclusion The Walter-Stitt and time-dependent Cox model was successfully extended, developed, and programmed with different estimation method (including non-Bayesian and Bayesian approach) using available software to deal with the overestimation of the survival benefit of screen-detected cases attributable to lead-time and truncation biases.