應用資料科學研究醫院門診就診排隊候診之虛耗時間成本分析及改善策略－針對某醫學中心骨科門診之就診時間資料之研究

Abstract

目前大醫院門診給人的刻板印象，是病患等候壅擠，且耗費很多時間在叫號。本研究利用醫院的叫號系統之資料（登錄病人報到，看診叫號，以及看診完成時間），比較各種情況下“總虛耗成本”（估算出病人/陪病者以及醫師的加權虛耗時間成本）的差異。並模擬各項叫號措施，期能提出改善對策。

資料來源及清理：本研究收集2021年1~12月T大醫院骨科門診就診資料，經過刪除同一筆資料（同一帳號）兩次以上者，叫號等待時間過長者(>240分 2.2%)，看診時間過長者（>60分 1.6%），共收錄71598筆就診資料，分散於2359節門診。結果顯示平均等候耗時（叫號時間-報到時間）56.0±45.6分，平均看診時間（看診完畢時間 – 叫號時間）4.9±4.2分。 病患及陪病者等候時間成本係依國民 GDP估算，為6.98元/分，而醫師醫師看診每分鐘機會成本，係依骨科門診一個月骨科門診總收入，除以骨科門診總時間而定（74.65元/分）。

因候診區壅塞而造成的成本: 本研究採用一篇針對捷運系統的壅塞所做的研究，設定每單位面積增加乘客一人會增加等同1.12倍travel time的感受（travel time multipliers），無座位會增加等同於1.265倍的travel time的加乘。從而計算出三種“因壅擠而加權”的病患/陪病者等候虛耗時間成本（每位骨科病人以一位陪病者計算）： 模型一：每一位病患（等待耗時+看診耗時相加），再乘以每單位時間之平均GDP(6.98元 / 分)，相加即為總病患耗時成本。 模型二：計算每單位時間中，依該診各時段候診的總人數，加權計算“病患耗時成本”。(每增加一人/M2，該時段時間加權0.12 倍)。其中候診空間以19.5M2計算。 模型三：除模型二的擁擠程度加權計算外，若等待人數超過4.67人（每診平均僅有4.67張椅子），再將前述數值乘以“無座位”加權（X 1.265）。 經計算，模型二的 25%, 50%, 75%, 95%分別為9041元，19798元，42761元，154740元，並且與“最高等待人數”與“累積總等待時間和”有高的正向判定係數。 比較兩種叫號方式之總候診成本（模型二）：在比較 “依掛號序”(1964診) 與“依報到序”(395診)之門診病人就診效率上，原始資料顯示“依報到序”有較高之加權總候診成本(模型二) (88662 vs 35763元)，但因兩者平均看診人數差距大（39.8 vs 28.6人/診），所以經1:1配對後，發現“依報到序”仍較“依掛號序”等後加權時間成本高（57632 vs 38366元），顯示“依掛號序看診”較有效率。

報到距建議時間差距之建模與模擬：針對47%有建議報到時間的病患，分析其報到時間與建議時間差異。結果顯示，三種建議報到時間 (＋0分，+60分，+120分）分別有相同的眾數（mode）位於+0-15 分，但有不同的左右分佈比率，其中建議+0分者分佈圖右側面積較大（較多人晚到），而建議+60分及+120 分者分佈圖左側面積較大（較多人早到）。另外，現場抵達者（約20%）有一較平均之分布散佈於-30~+180分。 上述分布模型帶入EXCEL，以規劃求解 (Solver)，來探討如何安排建議報到的人數。共三種模型： 1. 假定所有來診病人都可接收到某一“建議報到時間” 2. 部分來診病人可接收到“建議報到時間，而部分且超過固定比例者屬於“現場櫃檯掛號”。3.. 部分來診病人可接收到“建議報到時間，而部分且不限比例屬於“現場櫃檯掛號”。結果顯示“現場掛號”與“建議何時報到”的比例是一種動態的組合，透過巧妙的人數安排，方能達成“總加權等候成本”最小化。

結論：本研究是一項新方向，結合資料科學，管理會計，以及統計學，應用於醫院管理實務。採用大量資訊數據，也提供“醫院管理”研究上，除了“問卷調查”或“抽樣深入訪談”外，另一種客觀的研究方式的新面貌。

Long queueing and crowding in waiting at out-patient clinic service is a stereotyped impression in Taiwan. The present study is aimed to analysis the wasted time cost during waiting for out-patient department (OPD) service by using big data from the digitalized OPD service system which included check-in time, calling time, and complete time. The study endpoint is total waste time, which equals the sum of guests’ (patients and accompaniers) waiting time for the doctor and doctors’ waiting time for the patients.

Data input and pre-processing: The present study included orthopedic OPD service data between 2021/1/1 and 2021/12/31. Data with duplicated account number were filtered to choose the one with last complete time. The waiting period > 240 minutes were treated as outliners and excluded from the statistics (2.2%). The consulting time > 60m minutes were also treated as outliners (1.6%). As a result, 71598 records from 2359 clinics were included in the analysis. Average waiting time (calling time – check-in time) was 56.0±45.6 minutes, and average consult time (complete time – calling time) was 4.9±4.2 minutes. The unit time cost of patients/accompaniers was 6.98 NTD/minutes, derived from Gross domestic product (GDP) of Taiwan 2021 divided by working hours of that year. The opportunity cost of doctor’s clinic time was 74.56 NTD/ minutes, derived from total monthly revenue of orthopedic OPD divided by total OPD time in a month.

Time multiplier by “crowding”: In the present study, we adopted parameters derived from a previous study on MRT for the time multiplier by crowding (X1.12 for every increase of one person/M2 in density) and no seat (X 1.265.) We developed three models as follow: Model 1: Total guest waiting time cost: The summation of every individual’ waiting time, multiplied by unit time cost. Model 2: Crowding-weighted total guest waiting time cost: The summation of weighted time cost of each time interval. The weighted time cost is the summation of the number of waiting guests in a specific time interval, weighted by time multiplier (1.12) if density over 1 person / M2, multiplies unit time cost. Model 3: Crowding-weighted and no-seat-weighted total guest waiting time cost: Similar to Model 2, and multiplied by another multiplier (1.265) if waiting guests beyond 4.67 person / clinic). Results: Weighted time cost by Model 2 has high correlation coefficient with one- and two-dimensional regression equation.

Comparison of crowding-weighted time cost between two calling strategies: There were two types of calling patients into clinics (1) 1964 clinics with calling rule by registration numbers and (2) 395 clinics with calling rule by check-in orders. Statistics on the original data revealed that calling rule (2) was with higher weighted time cost (by Model 2) as compared with rule (1). But due to the discrepancy between service numbers of both groups (39.8 and 28.6 in group 2 and group 1,) we used 1:1 case match method to equalize service numbers. The post-match comparison still found that that calling rule (2) was with higher weighted time cost (by Model 2) as compared with rule (1). This finding suggests calling by registration numbers is with lower guest crowding.

Distribution pattern of Check-in-to-suggest time difference: For those with a “suggest time” printed on a sheet for next OPD clinic (accounting for 47%), we analysis the suggest time, and exact check-in time, to derive a check-in-to-suggest time difference, the aim is to find a distribution pattern with respect to three suggest times (early, +0 minutes; middle, +60 minutes; late, +120 minutes.) The results revealed that the distribution pattern of +0 group was right skewed, and that of +60 and +120 groups were left skewed. On the other hands, the check-in-to-suggest time difference for those who register at the same day with the clinic was relatively smooth and evenly scattered between -30 and +180 minutes. All the patterns were input into a simulation model as described in the next session. This simulation was performed on EXCEL SOLVER program. Three models were tested as follow: Model 1: All patients were with suggest arrival times. Model 2: Part of patients were with suggest arrival times, and at least with a given proportion of the remaining register at the same day. Model 3: Part or all of patients were with suggest arrival times, and the remaining patients register at the same day. Results: The simulation result suggests that a minimum of weighted total time cost can only be achieved through a dynamic combination of varying proportion of patients in different groups.

Conclusion: The present project provides a new method to combine data science, statistics, and accounting to solve a problem in hospital management. Big data might be a new era in the research of hospital management beyond traditional questionnaire survey and sampling interview methods.