以事件存活分析、儲列模型及多階段模型探討急診病患滯留時間、處理流程、及影響因子分析

Abstract

研究背景 在過去的四十年間，急診醫學快速發展，各式檢驗與檢查的推陳出新、各種急診的緊急處理標準流程、各樣治療選擇的不斷進步，現今的急診室已可以處理絕大部份急性與慢性的疑難雜症了。但伴隨著服務的提昇，是急診就診人數的不斷上昇，停留時間的不斷延長，也造就了急診壅塞這個全世界皆然的困境。急診壅塞對於病患而言，在許多方面如併發症發生率、住院死亡率等指標中，均已被證實有不利的影響，也因此成為急診相關研究的重點之一。在急診壅塞原因與解決之道的相關研究中，很大的部份集中於急診留滯時間與處理流程的檢討上。此因來診量的多少牽涉到整體醫療大環境的變化，比較不是單一醫療機構可以掌控的，而急診病患住院沒有病房的後端堵塞問題也與急診本身處置較無相關。回顧相關文獻，幾乎都是國外的研究，本土急診壅塞的相關資料確實十分稀少。僅有的少數研究也多是敘述性的描述，以相關統計方式如存活分析、多階段模型來深入探討急診各項指標與處理流程的研究更是尚未出現。但另一方面，由於國內就醫便利、緊急醫療費用相對便宜、以及台灣普遍重自身權益輕醫療專業判斷的特殊民情，均使得台灣的急診壅塞情形比國外有過之而無不及。因而探討本土關於急診病患就醫滯留時間與處置流程的相關研究也就顯得更刻不容緩了。 研究目的 (1) 以存活分析方法描述及分析急診病患總滯留時間及影響因子; (2) 以儲列理論分析急診來診人數及處理能量之模型; (3) 以多階段馬可夫模型分析急診病患於各階段的處理流程動態發展及影響因子。 研究資料 本研究使用林口長庚急診2013年全年急診就診電腦資料。林口長庚醫院為醫學中心、教學醫院、及重度急救責任醫院。林口長庚急診目前為全台灣全年來診量最多的急診。本研究所使用的資料皆為常態性由電腦收集的資料，包含的變項有病患基本資料(年齡、性別)、病患檢傷資料(科別、心跳、血壓、呼吸、檢傷級數、清醒程度)、急診醫師基本資料(年資、性別、科別)、環境相關資料(急診當天來診人數、平日/假日、週間/週末、白班/小夜班/大夜班)、以及時間變項包括檢傷時間、看診時間、離院時間及離院動向等。 研究方法 (1) 急診病患停留時間長短分析 第一部份以病患總共停留時間為最終結果，使用的是存活分析(Survival analysis)中的加速失敗時間模型(Accelerated failure time (AFT)) 模型來分析。由於病患之最後去向大致可分成住院、出院與死亡三大類，故在分析方法另加入競爭風險 (Competing risk) 的模型。分析方法除了停留時間的描述外，更加入各種可能的變項，來探討影響病患滯留時間長短的因子，並作出預測模型。 (2) 急診醫師人力調配分析 醫師診察在急診的醫療過程可視為關鍵步驟。隨著一整天平均病患來診人數的變化，各醫院多會在看診醫師人數上作適當的調配。本階段的統計方法使用儲列模型加以描述，分析不同時間點、不同科別看診醫師數量的配置合適程度，以及人力改變對於急診看診效率的影響。 (3) 急診病患處理流程分析 延續第一部份，病人在急診的處理可再細分成等待看診、醫師診療、與留觀/待住院等不同的階段，而結果也可能是出院、住院、或甚至死亡。不同的階段可能的影響因子亦可能不同。本研究使用馬可夫多階段模型(Markov Multi-state Models)來分析急診病患的處理流程，將每個階段發展到下個階段視為隨機 (Markov process)，以預設的分佈來描述並分析各階段處理速度的快慢與可能的影響因子。這一部份的參數使用貝氏蒙地卡羅馬可夫算法估計，並加入了隨機效應來解釋醫師處置的個別差異。為了瞭解處理流程在一天24小時中的變化，也將時間分成四個不同的時段來估算分段馬可夫模型的各項結果。 研究結果 本研究共收集149,472筆病患資料作分析。病患停留急診時間之中位數為2.15小時。若依不同動向來區分，出院、住院、死亡病患之停留時間中位數分別為1.46小時、11.3小時、與7.53小時。各部份分析結果如下： (1) 在總停留時間的分析方面，本研究結果顯示，常見的影響因子，如年齡、科別、檢傷級數等，對於不同動向的病患有不同的影響。例如檢傷級數越低，在住院族群是造成縮短停留時間的因子(檢傷一級 vs. 檢傷五級, TR=0.532, p < 0.0001)，然而在出院族群卻是延長停留時間的因子(檢傷一級 vs. 檢傷五級, TR=2.371, p < 0.0001)。又例如半夜就診病患在住院族群是造成延長停留時間的因子(與白天病患相比, TR=1.136, p<0.0001)，然而在出院族群卻是縮短停留時間的因子(與白天病患相比, TR=0.689, p<0.0001)。 對於占總病患數目約七成的出院病患族群，特別將之獨立出來作進一步的深入分析，此因出院病患總停留時間不受住院待床時間的影響，所有處理均與急診相關。在這部份的分析仍然以AFT模式為主軸，但加入了更多病患本身、急診環境相關、及醫療處置的因子，並作出預測模型，可讓輕症病患在就診時較能掌握預期時間，或作為臨床上人力配置的參考。 (2) 在醫師人力調配分析方面，儲列模型結果顯示，急診平均來診速率約為每小時17人，若分內、外、兒科來看來診速率分別是10.1人、2.95人、3.93人。在考量急診醫師人力調度及急診醫師同時間照顧人數之後，估算出的急診系統利用率約為0.7。而內、外、兒科三科的平均系統利用率為0.77、0.54、0.74。因一天當中24小時來診速率及醫師人力均有不同，故需再細看各時段、各科別的系統利用率係數，可發現急診成人內科於上午11時及下午9時為系統利用率的高峰。另外兒科在晚間九點至十二點系統利用率係數有顯著的上昇，顯示這段期間醫師人力較為不足。 (3) 在細部處理流程分析上，經過幾次專家會議後，本研究將急診流程分成五階段馬可夫模型，各階段的轉移速率分別由資料估算出，並且加上影響因子如檢傷級數、年齡等變項，看對於各階段的影響為何。整體而言，在任一小時內，只有非常少的病患直接從檢傷離開，而正在看診的病患約有10%會轉到觀察室、23%回家、4.5%住到病房，正在觀察室的病人則有1.1%會回家、1.9%住到病房。影響因子當中，年齡的影響分析結果顯示年齡對於掛號到醫師處置(β=0.126, 95% HPDI: 0.123-0.130)、及醫師處置到留觀 (β=0.438, 95% HPDI: 0.431-0.446)有加速的效果，但是對於醫師處置到出院(β=-0.258, 95% HPDI: -0.263 ~ -0.253)卻有減速的效果，應是因作更多的檢查所致。另一方面，檢傷級數越緊急的病患，在等待看診、決定住院、等待住院這些過程均有加速的效果，但是對於出院卻有減緩的效果。 本研究也更進一步嘗式不同的多階段模型分析，如依一日當中不同時段處理流程的不同而作分段式的分析(piecewise multi-state model)，也嘗式在適當的階段轉移加入隨機效應(random effect)來解釋可能的變異來源，最後更加入死亡這個新的階段，不過加入死亡後並沒有對於原本的估計值有很大的影響，推測應是死亡人數不多所致。 結論 本研究利用多種統計方法來分析急診病患在急診的停留時間以及病患處理，以作為優化急診人力配置、處置流程的參考。本研究顯示常見的影響因子，如年齡、科別、檢傷級數等，對於不同動向的病患有不同的影響。而在醫師人力配置的部份，亦可由各時段來診人數及醫護人力所建構的儲列模型看出急診人力較為吃緊的時段及科別。若細看急診病患處置的各階段流程，則可經由分析而瞭解不同階段的影響因子及可能造成壅塞的部份為何。由分段馬可夫模型所繪出的圖型也可以讓急診醫師更加瞭解在不同時間點病人在各個處理階段的動態變化。若善加利用本研究所建構的各式模型，急診室應可針對本身急診特性，對於不同動向的病患設計不同的改善方針，以利緩解急診壅塞，增進國內緊急醫療品質。

Background Emergency medicine, now recognized as an essential part of public health service, has gained momentum recently since it was founded 40 years ago. As the services provided by emergency departments (ED) increase and the management process becomes more complicated, patients stay in EDs for longer and EDs become more crowded. A number of studies have discussed the adverse impacts of ED crowding, which include prolonged waiting times, increased complications, and increased mortality. Previous literature has also demonstrated that prolonged ED length of stay (LOS) is not only a cause but also a result of ED crowding, yielding a vicious cycle. While a body of descriptive or analytic researches regarding the associated factors accounting for ED LOS and ED management process has been carried out in western society over the last decade, relevant research in Taiwan are still scarce. More importantly, the application of queue process and multi-state Markov model to decompose waiting time in emergence room into different compartments (including triage, physician, observation/waiting, admission, and discharge) accounting for the heterogeneity of ED LOS has been never addressed. This thesis aimed to use two-state statistical models to explore factors associated with ED LOS and further to develop multi-state Markov model to predict ED patient LOS and patient management flow in order to improve ED management efficiency and alleviate ED crowding status. Research Aim (1) To describe and analyze patients ED LOS and its associated influential factors with competing risk accelerated failure time model (AFT). (2) To quantify the traffic intensity in terms of arrival rate and service time distribution of ED using the queue model analysis. (3) To estimate the transition rates between each compartment and also the departure rate from each compartment using multi-state Markov model in order to quantify the dynamics flow of ED patients and the influential factors of each management process. Data Sources The study was conducted in the ED of LCGMH, a tertiary medical center and teaching hospital with a 3,600-bed capacity and an annual ED visit of 150,000 patients. All patients who visited the ED of LCGMH and had been discharged from the ED from January 2013 to December 2013 were included. The data was extracted from the hospital administrative electronic database. Patients with missing registration time or leaving time were then excluded from the analysis. Time variables include triage time, physician time, and departure time. Other variables collected include patient entity, patient characteristics, disease acuity, triage vital signs, disposition endpoints, total daily census, and physician characteristics. Statistical Methods (1) Analysis of total ED LOS using event-time analysis The first part of the research used total ED LOS as primary endpoint. A competing risk Accelerated failure time (AFT) model was used to describe and model ED LOS and its associated correlates. Patients were divided into three groups according to different disposition endpoints including discharge, admission, or mortality. Possible covariates were included into multivariate analysis and predictive models were built. (2) Analysis of ED staffing policy with the queue process Queueing model was used in the second part of this research. As physician management in the ED could be regarded as the critical step of the whole process, physicians can be taken as servers in queueing models. Furthermore, one physician was regarded as multiple identical servers to cope with the fact that ED physicians take care of more than one patients at the same time. In this section, different time point of the day, different patient entities, and different staffing policy will be compared according to the model. (3) Compartment model of ED management process with Multi-state Markov Model Following the first and second part of the research. The process of ED management was further divided into different states including “waiting for physician”, “physician management”, and “observation or waiting for admission”. Furthermore, the disposition of the patient, discharge, admission, or mortality, could be regarded as absorbing states that once entered cannot be left. Thu, the multi-state Markov model was used to model the ED management process. Underlying distributions were given and possible influential factors of each state transition were analyzed. Parameter estimation was implemented by using Bayesian MCMC method. In addition, a piece-wise Markov model was also developed to deal with different time periods during a day, and random effect was added to cope with the correlation resulting from patients within the same physician practice. Results A total of 149,472 patients were included for analysis with an overall medium ED LOS of 2.15 hours. The medium LOS for discharged, admission, and mortality patients were 1.46, 11.3, and 7.53 hours, respectively. The different parts of the results are presented as below: (1) In the analysis of total ED LOS, common influential factors such as age, patient entity, triage acuity level, or arrival time-period posed different effects on different disposition groups of patients. For instance, higher acuity (triage level I vs. level V, TR=2.371, p < 0.0001) and day shift arrival (compared with night shift, TR=1.451, p < 0.0001) were associated with prolonged ED LOS in discharged patient group. Whereas opposite results were noted for higher acuity (triage level I vs. level V, TR=0.532, p < 0.0001) and day shift arrival (TR=0.88, p<0.0001) in admission patient group. A subgroup detailed analysis for discharged patients was done because this patient group consisted of 70% of the total included cases, and the ED LOS of the discharged patients were not affected by whether the floor bed is available. More covariates were added and a predictive model was built. (2) In the results for the queueing model, the patient mean arrival rate is 17 ( SD=7.32) patients per hour. The arrival rates for trauma, adult non-trauma, and pediatric non-trauma patients are 2.95, 10.1, and 3.93 patients per hour, respectively. After considering the staffing policy and the multi-tasking nature of the ED physicians, the system utilization (traffic intensity) was 0.7 when treating the whole process as a single queue, meaning the equilibrium distribution would be reached after long-run queue. The average system utilities for adult non-trauma, trauma, and pediatric non-trauma patients were 0.77, 0.54, 0.74. The hourly system utilization parameters for different patient entities were calculated and diagrams were drawn for analysis. The system utilization trend showed a peak system utilization parameter at 11am and 9pm. Most of the system utilization were under 1 except 9pm to 11pm in pediatric patients. (3) In the analysis of dynamic management process. A five-state Markov model was built after several expert meetings held. The results demonstrated that higher acuity accelerated the rate of leading to physician management and admission, but decelerated the rate of discharge. In any hour, very few patients were discharged before seeing physician, and 9.85%, 23% and 1.14% of patients moved from physician to observation/waiting, to discharge, and to admission after seeing physician, respectively. The percentage of patients moving from observation/waiting to discharge or to admission were 1.1% and 1.9%, respectively. Older patients were quicker to see physician, but more time spent before being admitted or sent home, which might be because a greater number of exams or image studies needed to be performed in the ED. When comparing differences in transition rates among different time points within a 24-hour day, waiting time before physician management was longest in the evening, and patient flow from ED to admission was fastest after noon. Piece-wise Markov model was also applied and dynamic curves of each compartment were also illustrated. In the last part of the Markov model analysis, random effect model was build which showed moderate variations among different physicians, but the estimated transition rates between states were not significantly altered. A six-state Markov model including death was also tested in the end of the research. Conclusion Statistical methods were used in this research to describe, analyze, or predict ED patient LOS, traffic intensity, and patient management flow from triage to discharge . The event-time analysis of ED LOS showed that common influential factors posed different effects on different disposition groups of patients, and that it is possible to build up a predictive model for discharged patients based on individual covariates. The results of the queue model revealed the time trend on ED traffic intensities and appeared to be a good tool for planning staffing policy. The multistate Markov model estimated the transition rates between the triage, physician management, observation room, admission, and discharge states. The incorporated covariates helped to better understand the effect of relevant factors on different state transitions. Piecewise dynamic curves drawn demonstrated the trend of patients entering and leaving each states with time. These findings and the suggested model could be used for emergency departments to develop individually tailored approaches to minimize ED LOS and further improve ED crowding status.