應用歷史相依模型於複雜醫療情境下最佳動態治療方案的穩健估計

Abstract

慢性病或反覆發作疾病的患者通常需要經歷一段長時間且多階段的治療過程。 動態治療方案 (DTRs) 為一系列的治療規則，強調在這類疾病的治療需要隨著個別病患本身的特徵與過去的治療動態改變，並根據這些資訊給予最佳的治療建議。最佳 DTR 即是使病患整體緩解時間的最大化的 DTR。然而傳統估計最佳 DTR 研究的模擬或分析通常在較為簡單的情境下，忽略實際上臨床資料的歷史 相依(history-dependent)。本研究提出多種歷史相依模型，反映階段與共變數歷史對於最佳 DTR 的影響，並在與治療有交互作用的連續共變數中加入轉換點 (change points)，以期能夠更符合臨床情境。另外，過去研究在評估模型表現時，僅透過比較真值與最佳 DTR 的點估計，計算模型判斷正確的比例，然而此方式未將參數估計的標準誤納入考慮。因此，本研究進一步提出了兩個考量區間 估計的評估指標:第一個是區間估計正確的比例，第二個是排除無法確定最佳 DTR 的信賴區間(即統計上不顯著)後計算出來的正確比例。在模擬中，本研究考慮三階段治療過程與兩種治療的情境，在七個不同的模型下生成事件發生時間; 這七個模型中，有三個僅使用該階段的治療與共變數，稱為歷史獨立模型，其餘四個包含所有過去與現階段的治療與共變數，即為本研究提出的歷史相依模型。在每個真值模型下，使用這七個模型來配適資料，並計算傳統和本研究提出的評估指標，以比較配適模型的表現。模擬結果顯示，整體而言，配適這四種歷史相依模型皆可以得到與配適真值模型相似的校正區間估計之正確比例，得到穩健的估計。

Patients with chronic or recurrent diseases often undergo prolonged, multi-stage treatment processes. Dynamic Treatment Regimes (DTRs) represent sequences of treatment rules that emphasize the need for treatments to dynamically adapt to individual patients' characteristics and treatment histories, ultimately guiding the recommendation of the treatment. Optimizing DTRs for time-to-event outcomes aims to maximize overall remission time in certain diseases. However, traditional optimal DTR estimation research settings are typically under simple conditions and overlook the complexities of clinical reality such as stage and history dependency. In this study, we provide various history-dependent models to reflect the influences of covariate and treatment histories on the optimal DTRs, aiming to better align with the complex realities of medical situations. For example, models with change-points in continuous covariate which interact with treatment are introduced. The traditional evaluation index of the model performance in estimation of optimal DTRs is the correct proportion of individuals with the optimal treatments correctly predicted for the proposed model based on the point estimates of optimal DTRs. However, such point-estimation evaluation index disregards the standard errors of the estimators. On this basis, we further propose two interval-estimation evaluation indices regarding correct proportion. One is the interval-estimation correct proportion of the individuals’ confidence intervals of optimal DTRs for the proposed model contain the true values with statistical significance. The second one is a modified version of the first interval-estimation evaluation index by excluding the confidence intervals without statistical significance which cannot decide optimal treatments. In the simulation study, consider binary treatments at three stages and generate time to event under seven different models. Among the seven models, three models only including the treatment and covariate at the current stage are called history-independent models. The remaining four models that include both the treatment and covariate at the current stage and those at previous stage are called history-dependent models. Under each true model scenario, all of seven these models are used to fit the data and provide the traditional and proposed evaluation indices to compare the performance of the fitted models. The simulation results show that, overall, fitting these four history-dependent models and fitting the true model can achieve similar modified correct proportions based on interval estimation, leading to robust estimates.