病患自控式止痛的統計模型分析

Abstract

研究背景: 雖然對於疼痛的了解一直在進步，如何有效的管理手術引起的急性疼痛一直是醫護人員所關注的議題。經過調查大部分手術後的病患沒有得到適當的止痛，大約只有四分之一的病患得到適當的止痛。如何改善手術的止痛服務，因為病人和病人本身在不同時間點上，對於止痛藥物劑量需求存在著巨大的異質性，如何精準的使用止痛藥物劑量，正面臨一個巨大的挑戰。本研究利用一個常見且廣泛被臨床人員使用多年的止痛機器 – 靜脈病患自控式止痛器收集且分析病患在三天內的重複測量止痛藥物劑量，利用複雜的統計模型和隨機過程的分析病患動態的藥物使用劑量，改善手術後止痛的管理。 研究目標: 本論文第一階段的目標是使用隨機混和模型和動態追蹤資料模型分析，這兩個模型同時考慮了重複測量的特性以及加入影響因子的分析，可以根據不同手術與不同時間，發展客製化止痛藥物劑量。接下來利用多階段馬可夫模型討論止痛藥物劑量在不同階段的轉移使否被危險因子所影響。最後，使用了隱馬可夫模型發展出個人化的止痛藥物監測系統，期望在不同時間點監測並且預測不同的麻醉需求階段。期望能精準的使用止痛藥物劑量，並且能提高病患止痛的品質，減少副作用的產生。 材料與方法: 本研究為回溯性觀察實驗，在通過人體試驗後( IRB: 2011-03-037IC)，收集了2005年到2010年共六年的資料，完整連續觀察三天止痛藥物劑量的變化加以分析。統計模型分為四個部分，首先利用貝式隨機截距項模型(Bayesian random intercept model)分析不同手術對於使用止痛藥物劑量的差異，發展針對不同手術使用不同使用劑量的止痛策略。其次拓展分析在不同時間的止痛藥劑量，利用貝式動態追蹤資料模型(Bayesian dynamic panel model)加入滯後變數(lagged variable)找出連續止痛藥劑量間的關係。第三部分，利用三階段馬可夫模型分析動態劑量階段(低、中、高劑量)間的轉移狀況，最後利用隱馬可夫(hidden Markov model)分析最佳的劑量階段數量，並且依據觀察個人的連續止痛劑量下找出最可能的隱藏劑量分類階段，達成個人化的醫療的目標。 結果: 手術間止痛藥物劑量的變異性極大，經過此模型估計不同手術間對於止痛藥物劑量的影響，已經可以發展出針對不同手術的止痛策略，在此模式下可以依據病患年齡、性別、體重、是否有癌症以及不同的手術達到客製化估計總止痛藥物的劑量。其次在動態追蹤資料模型中，分析了連續止痛藥物劑量之間的關係(0.477)，利用此變數可以估計不同時間點的止痛藥物劑量。第三部分利用三階段馬可夫模型分析的三個劑量狀態的轉移速率。低到中、中到高的轉移機率分別是0.252和0.335，另外，高到中、中到低的轉移機率分別是0.600和0.359。結果顯示整體的力量是往低劑量移動，符合臨床的觀察。最後平衡的機率，分別是在低、中、高狀態依次為47.8% ,33.5% ,18.7%。在三階段隱馬可夫模型並且加入因子分析，發現三個族群的劑量(高、中、低需求階段下平均分別為12.36 、5.48、2.11mg的止痛劑量)，經過手術後第72個小時結束後，低需求共有83.6%；高需求則在一開始很高，之後急速減少，最後在手術後第72小時，高和中度需求只剩2.0%和14.4%。最後根據隱馬可夫模型，我們可以藉由觀察連續的止痛藥物劑量偵測到隱藏狀態的最可能路徑。 討論: 利用統計模型分析可以提供麻醉從業人員有用的資訊，並且改善使用靜脈病患自控式止痛服務，根據不同的手術以及不同的麻醉藥物需求，提共更精確地止痛藥物劑量。在這些統計分析中，隱馬可夫模型提供了最強大的人工智慧學習，依據麻醉劑量分類出不同的止痛藥物需求階段，並且發展出客製化的動態止痛藥物規劃。同時隱馬可夫模型可以預測止痛藥物需求階段，找出最佳止痛藥物需求階段，以此為基礎發展出個人化的監測止痛藥物需求系統。

Background: Although the understanding of pain has progressed, managing postoperative pain remains a significant problem worldwide. Inadequate pain relief is common in postoperative patients, and only about one in four surgical patients have their pain adequately controlled. Unfortunately, to improve pain management for postoperative patients recorded by the popular and well-accepted pain management modality, intravenous patient controlled analgesia (IVPCA) is faced with the issue of heterogeneity (large between- and within-individual variations) and repeated measurements during the postoperative pain management that cannot be handled without using complex statistical models and stochastic processes. Objectives: My thesis first aimed to use random-effect and dynamic panel model, both taking into account the measured covariates and correlated data within patient, to develop client-oriented procedure-specific and dynamic regimen on analgesic consumption. And then to elucidate the kinetic movement between three different levels of analgesic consumption by using multi-state Markov model and finally to identify the underlying hidden state of analgesic need and their kinetic transitions to yield the observed analgesic consumption with hidden Markov model (HMM) in order to develop a surveillance system to detect the classified states governing analgesic consumption. Material and methods: This was a retrospective observational study approved by the Institutional Review Board of the Taipei Veterans General Hospital (IRB: 2011-03-037IC). The study subjects were collected between January 2005 and December 2010. The surgical patients using IVPCA immediately after operation and all equally observed for postoperative three days. Bayesian random intercept model was first used to estimate the influence of surgical effects on analgesic consumption and Bayesian dynamic panel model was then used to model the relationship between two consecutive observations with the incorporation of time lag variable. Three-state Markov model was used to analyse the dynamic process of analgesic consumptions. The hidden Markov model was further applied to identifying the optimal classified states (relaxing the assumption of three states) and to find the most likely hidden state path in the postoperative period given the observed time series data on analgesic consumptions. Results: The variation of analgesic consumption between surgeries was substantial. The IVPCA regimen formulation for surgical procedure was then developed from the random intercept model. The effect of lagged response variable was 0.477 between two consecutive observations by dynamic panel model. The further application was to predict the next analgesic consumption by the lagged observation. The estimated regression coefficients from Bayesian random-intercept model was used to predicting client-specific total morphine consumption with age, gender, cancer, weight, and surgical types. In three-state Markov model, the estimated transition rates for low to medium and medium to high were 0.252 and 0.335 respectively, while transition rates for high to medium and medium to low were 0.600 and 0.359 respectively. The results showing the overall force toward the low analgesic consumption states match the clinical finding of downslope trend of analgesic consumption over time. The stationary distribution for low, medium and high states were 48.7%, 33.5% and 18.7%, respectively. The three-state (“High”, “Medium”, and “Low” analgesic need with the mean value 12.36, 5.48, 2.11 mg) hidden Markov model with the covariates indicated above was the parsimonious model. There were 50.6% of “High” analgesic need and 12.2 % of “Low” analgesic need in the first six-hour timeframe after operation. Low analgesic need state increases with time and accounted for 83.6% after postoperative 72 hours. “High” and “Medium” analgesic need state and decreases sharply after first six-hour and becomes 2.0% and 14.4% at the end of three days usage. Age, gender, cancer, weight, and surgery were identified as a set of significant predictors for various transitions using HMM. Through hidden Markov model, we are able to decode the best pathway of hidden states with Viterbi algorithm given a sequence of analgesic consumptions. Conclusions: The better use of statistical models enables anesthesiology to improve the IVPCA regimens to adapt various surgeries into patient-specific analgesic need in different postoperative periods. Among these statistical models, the hidden Markov model is the most powerful learning algorithm in classifying three distinct states on the consumption of analgesic consumption and developing client-oriented dynamic process of the analgesic consumption. The results of forecasting analgesic need, decoding the optimal pathways of the classified state, and predicting the evolution of the classified from the hidden Markov model used can be used as a surveillance system to detect the unusual states on analgesic consumption postoperatively.