MONITORING THE EFFICIENCY OF USE OF OPERATING ROOM TIME WITH CUSUM CHARTS

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1 103 MONITORING THE EFFICIENCY OF USE OF OPERATING ROOM TIME WITH CUSUM CHARTS Zeynep Flz Eren-Dogu, Eralp Dogu Mugla Stk Kocman Unversty, Mugla, Turkey Emal: Abstract Health care organzatons often need to assess operatng room (OR) performance n order to measure the effcency. In practce, to estmate surgery duratons hosptals use varous estmatng systems ether based on surgeon s estmate and/or software. Accurate estmates are vtal for hgh qualty OR performance and effcency. Thus, surgeons estmates are sgnfcant nputs for effectve OR sute schedule n surgeon based systems. To acheve a successful OR management, not only utlzaton performance measurement but also montorng t s crucal. Control charts could be constructed for montorng the OR effcency. Montorng the effcency of use of OR tme mght nclude montorng operatve and/or non-operatve tmes. In ths study, cumulatve sum (CUSUM) charts are ntroduced for the performance of surgery tme estmatons. An example nvolvng surgcal tmes s also provded to support our dscusson. Some scenaros are defned and surgeons estmaton errors are smulated for llustratve purposes. Key words: control charts, CUSUM, OR effcency, utlzaton, surgery tme. Introducton In a hosptal settng, managng the OR sute s of great mportance n terms of the performance of a hosptal, revenues and patent satsfacton. On the other hand, t s dffcult to acheve an effcent management approach due to conflctng prortes and costly resources. All these factors strongly emphasze the need for an adequate OR plannng and schedulng procedure. Cardoen et al. (2010) states that watng tme, throughput, utlzaton, levelng, makespan, patent deferrals, fnancal measures and preferences are the commonly used performance crtera to evaluate operatng room plannng and schedulng procedures. They menton that especally the utlzaton rate of the OR has been the subject to recent research. Macaro (2006) states that allocaton of the rght amount of OR tme to each servce on each day of the week s the most mportant thng n OR management. Effcency of use of OR tme s defned by underutlzed and overutlzed OR tme (Strum et al., 1997). Another aspect of effcent OR management s estmatng surgery tmes wth low amount of estmatng error. Strum et al. (2000) emphaszes that to mprove the utlzaton of OR, makng accurate tme estmates are essental. Bas, whch s defned as the systematc underestmaton or overestmaton of case duratons, affects the usage of capacty of the OR sute and avalable capacty of electve surgeres.

2 104 Zeynep Flz EREN-DOGU, Eralp DOGU. Montorng the Effcency of Use of Operatng Room Tme wth CUSUM Charts Researchers have nvestgated dfferent statstcal models to estmate surgery tmes (Strum et al., 2000; Stepanak et al., 2009; Larsson, 2013). In practcal, hosptals use varous methods to estmate surgery duratons ncludng automated systems and statstcal models based on the average duratons of the prevous surgeres. However, the most wdely used methods are based on the surgeons estmates snce some factors affectng the surgery duraton are taken nto account by the surgeons but cannot be ncluded n the computer based systems. Thus, surgeons estmates are sgnfcant nputs for effectve OR sute schedule. Overestmatng surgery tme leads to underutlzed OR tme whch s the postve dfference between the allocated and observed OR tme and results n lower utlzaton of resources and the performance of fewer surgeres (Dexter et al., 2005; Larsson, 2013). In contrast, underestmatng surgery tme leads to overutlzaton and results n personnel workng overtme and the cancellaton of surgeres. Thus, reducng estmatng errors are vtal for relable, effectve and effcent OR performance. Recent studes show that not only utlzaton performance measurement, but also montorng t s crucal for a successful OR management (Macaro, 2006). In terms of montorng, t s possble to just plot estmatng errors (of dfferent servces, surgeons or types of surgeres) n a tme seres plot, or to calculate daly, weekly, etc. descrptve statstcs. Moreover, statstcal montorng algorthms such as control charts can be used for evaluatng utlzaton performance. Control charts have been attractve tools for ndustral professonals for the last decades. They practcally plot mportant statstcs on a chart and provde a vsually attractve decson support envronment. Tradtonal statstcal montorng technques have been wdely appled n ndustry and successfully mplemented for many ndustral processes. Recently, medcal professonals have been attracted by these tools to montor health related processes. Examples vary n a range from dsease montorng to fnancal montorng of health care processes (for detals see Thor et al., 2007 and Tenant et al., 2007). Usng control charts for montorng OR tme effcency s our focus for ths study. Recent research on control charts and OR performance ncludes usng control charts for montorng cardac surgcal performance (Rogers et al., 2004), for montorng the nonoperatve tme (Sem et al., 2006), for montorng obstetrcans performance (Lane et al., 2007) and for analyzng the performance of surgeons n OR and settng benchmarks (Chen et al., 2010). Control charts can be used successfully for OR performance montorng and may provde practtoners valuable knowledge on specal causes of varablty n ther OR plannng processes. They also help them elmnate the sources of varablty. In ths study, we consder control chart mplementatons for OR tme effcency. CUSUM control charts, ther mplementaton and nterpretaton are consdered. The paper proceeds as follows. In secton 2, the general framework for the control charts for OR effcency s gven brefly. The dscusson s supported by mplementng the methods to the smulated case duraton data and results are gven. Followng these applcatons conclusons are provded n secton 4. Materals and Methods OR Effcency Measures Accordng to Dexter et al. (2005), there are two components of naccurate case schedulng. The frst one s bas and the other one s absolute error where the error equals the actual case duraton mnus the estmated case duraton. To Macaro (2006), bas s present f the surgeon consstently makes overestmatons or underestmatons; whle precson ndcates the magntudes of the errors of the estmates. OR effcency s measured n terms of both the underutlzed and the overutlzed hours of OR tme. Many researchers (e.g. Dexter et al., 2002; Dexter et al., 2007) deal wth procedures based on the OR effcency n terms of utlzaton. When estmatng case duratons, researchers search for methods that are near perfect for preventng bas and also have small varablty of errors (Joustra et al., 2013; Larsson, 2013). Joustra et al. (2013) uses () the mean of the estmated operaton tme, () the average dfference between predcton and actual duraton, () the average absolute dfference between predcton and actual duraton, (v) the root mean squared error and (v) the proporton of over/underpredcton by more than 10 and 30

3 Zeynep Flz EREN-DOGU, Eralp DOGU. Montorng the Effcency of Use of Operatng Room Tme wth CUSUM Charts mnutes as performance measures. Dexter et al. (2005) mentons that effcent OR sutes should have bas less than 15 mnutes per 8 hours. They frst derve a rato of the sum of dfferences between the actual and scheduled case duratons to the sum of all duratons performed for each servce and then multply t by eght hours to obtan the estmated bas. As a performance measure, they calculate 95% confdence ntervals for bas n the servce s scheduled case duratons reported per eght hours of used OR tme. Larsson (2013) calculates both the mean value and the standard devaton of the estmatng error to determne the level of accuracy of dfferent estmaton systems. Accordng to the lterature, there s a general consensus that the normal and log-normal dstrbutons are the most practcal and effectve dstrbutons to represent the surgcal procedure tmes (May et al., 2000; Strum et al., 2000; Stepanak et al., 2009). Dexter et al. (2005) shows that the statstcal dstrbutons of bas estmates are consstent wth a normal dstrbuton. In ths study, we wll use the mean value and the varablty of the estmatng error as performance measures and montor them smultaneously. We assume that estmatng error follows a normal dstrbuton. ISSN A Framework for Montorng the Effcency of Use of OR Tme Control charts have recently played a major role n statstcal montorng. Control charts for normally dstrbuted characterstcs can be dvded nto three major branches; Shewhart, exponentally weghted movng average (EWMA) and CUSUM charts. We consder CUSUM charts and am to ntroduce them to the area of OR performance management. As a powerful montorng algorthm, a combnaton of the standardzed two-sded mean CUSUM (SD2mCUSUM) and the standardzed two-sded scale CUSUM (SD2sCUSUM) can be appled to surgery duraton data successfully. When the process professonals measure the estmatng error for surgeres, they may use these control charts to montor mean and varablty shfts smultaneously. Thus, they can easly dentfy a specal cause such as nsuffcent surgery duraton estmaton performance of a surgeon or ncreasng OR tme bas of a servce. Our approach can be summarzed n three smple steps; data collecton, control chartng and nterpretaton. Data collecton step s of great mportance, because the qualty of nput data drectly nfluences the qualty of the overall montorng process. Generally, a data gatherng and parameter estmaton step called Phase I study s appled. Wthn that phase, n-control process parameters and control lmts are obtaned. Control chartng and real tme applcatons are consdered after achevng Phase I. In ths study, we assume Phase I study s done successfully and llustrate Phase II control charts. Along wth the mplementaton, the practtoners should follow the sgnals gven by the control charts. In the last step, each sgnal and non-random pattern should be examned carefully by the OR professonals and managers to dentfy the specal causes of varaton. SD2mCUSUM and SD2sCUSUM Charts SD2mCUSUM and SD2sCUSUM charts both have complex desgn parameters when compared to Shewhart counterparts. However, they have superor ablty to detect small shfts. In order to smplfy desgn complexty we consder standardzed estmatng errors of case duratons z as the chart nput as dscussed by Hawkns and Olwell (1998) and Montgomery (2008). For our case, SD2mCUSUM essentally s a tabular CUSUM wth the standardzed estmatng errors. In general, constructng ths control chart requres knowng the process mean and process standard devaton. If the practtoner does not know the parameters, then t s possble to estmate them from the Phase I study. Bascally, SD2mCUSUM plots two types of CUSUM statstcs; one for postve mean shfts and the other for negatve mean shfts. Let x be the th estmatng error and z be the th standardzed estmatng error on the process. Standardzaton enables easly benchmark among dfferent surgeons estmatng performances or dfferent servces OR effcency and reduce desgn complexty nto a consderably smple level. The magntudes of postve and negatve CUSUMs are as follows:,, where s the th CUSUM for postve mean shft and s the th CUSUM for negatve mean shft. If or s larger than h, the process s consdered to be out of control where h s the control lmt to acheve a specfed type I

4 106 error for CUSUMs. We use,, h and h n our approach snce one specfc standardzed error may have both negatve and postve CUSUMs at the same tme. It allows the practtoners easly dstngush between the statstcs for negatve and postve mean error shfts. The ntal values and Zeynep Flz EREN-DOGU, Eralp DOGU. Montorng the Effcency of Use of Operatng Room Tme wth CUSUM Charts are chosen to be zero. Montorng mean s an mportant task of a montorng procedure. However, process professonals should also evaluate the precson performance of the process. In other words, t s crucal to montor varablty as well. It s possble to construct a varablty or scale CUSUM wth the followng calculatons. When z s the th standardzed estmatng error, then s a new standardzed normal quantty and senstve to varablty changes. The montorng statstcs are and s smlar to SD2mCUSUM. If the error varablty ncreases. The nterpretaton of SD2sCUSUM statstc wll ncrease and eventually exceed the threshold h. On the other hand, f error varablty decreases, then statstc wll decrease and eventually exceed the threshold h. The ntal values and are chosen to be zero. SD2mCUSUM and SD2sCUSUM charts become a par of control charts to montor mean and varablty smultaneously. They can be plotted together usng the same reference values and decson ntervals on the same chart because the statstcs z and v follow standard normal dstrbuton. Illustratve Example A case study whch explores bas and the varablty of the estmatng error produced by a system whch solely depends on surgeons estmatons s llustrated. It s assumed that the average duratons of a specfc type of operaton can be calculated based on hstorcal data, and the n-control error follows a normal dstrbuton wth 0 mnutes mean and 10 mnutes standard devaton. Suppose there are four surgeons (A, B, C, D) performed the same type of operaton wth the followng propertes. Surgeon A makes accurate and precse estmates wth 0 mnutes mean estmatng error and 10 mnutes standard devaton; surgeon B consstently underestmates the surgery tme, however s/he s precse (s/he estmates case duratons wth 6 mnutes mean estmatng error and 10 mnutes standard devaton); surgeon C generally makes accurate estmates but tends to overestmate the surgery tme for a perod of tme (s/he estmates case duratons wth -10 mnutes mean estmatng error and 10 mnutes standard devaton for a perod of tme) and surgeon D sometmes underestmates and sometmes overestmates the surgery tme wth a consderably large (15 mnutes) standard devaton of estmatng error. We assume that all four surgeons complete 100 surgeres and smulate 100 estmatng errors for each surgeon reflectng ther estmatng behavor. Control lmts for the charts are -5 and 5 n order to acheve a specfed false alarm rate. Fgures 1-4 show SD2mCUSUM and SD2sCUSUM results for surgeons A-D, respectvely.

5 Zeynep Flz EREN-DOGU, Eralp DOGU. Montorng the Effcency of Use of Operatng Room Tme wth CUSUM Charts ISSN Fgure 1: SD2mCUSUM and SD2sCUSUM charts for surgeon A. Fgure 2: SD2mCUSUM and SD2sCUSUM charts for surgeon B.

6 108 Zeynep Flz EREN-DOGU, Eralp DOGU. Montorng the Effcency of Use of Operatng Room Tme wth CUSUM Charts Fgure 3: SD2mCUSUM and SD2sCUSUM charts for surgeon C. Fgure 4: SD2mCUSUM and SD2sCUSUM charts for surgeon D.

7 Zeynep Flz EREN-DOGU, Eralp DOGU. Montorng the Effcency of Use of Operatng Room Tme wth CUSUM Charts In Fgure 1, t can be seen that the estmates of the surgeon A are consstent wth the n-control process or n other words, surgeon A has accurate and precse estmates. The control charts generate no sgnals and show that surgeon A works qute consstent wth the n-control dstrbuton. Fgure 2 s a good example of a surgeon who consstently underestmates the surgery duratons. Ths case s mportant because the operatons tend to fnsh later than expected and the bas creates a bottle-neck for plannng the future operatons. As t can be seen n Fgure 2, the mean bas ncreases so SD2mCUSUM statstc exceeds ts upper control lmt persstently after about 30 th operaton. SD2sCUSUM chart for surgeon B shows that the varablty of the errors s n-control. Surgeon C s consdered to overestmate the surgery duratons for a short tme perod of her/hs operatons. The bas can be observed lookng at Fgure 3. SD2mCUSUM for surgeon C shows that s/he underestmates surgery duratons n between her/hs 50 th and 80 th operatons. The results for surgeon D are ndcated n Fgure 4. Fgure 4 shows that surgeon D s not very concentrated on makng case duraton estmatons. S/he provdes adequate average error; however, her/hs varablty of case duraton estmaton s hgher than the n-control varablty. SD2sCUSUM statstcs postvely tend to exceed upper lmt whch shows that s/he provde a large standard devaton of the estmatng error. ISSN Conclusons Makng accurate and precse estmatons for surgery duratons helps to () decrease the rsk that cases wll be cancelled due to lack of tme, () mprove the utlzaton of resources and () ncrease the effcency of use of ORs. Therefore, t s essental to decrease the estmatng errors. As the bas s an mportant ssue for OR tme effcency, the need for montorng tools whch able to detect bas emerges. Accumulaton control charts, SD2mCUSUM and SD2sCUSUM for our case, have the potental to detect consstent overestmaton or underestmaton of case duratons whch s defned as bas. Cumulatve statstcs of these control charts successfully reflect a persstent estmaton behavor of a surgeon. They are also proven technques to be effectve when the bas s consderably small. Montorng the mean value of the bas n estmated case duratons, we can observe whether there s a tendency of underestmaton or overestmaton of surgery duratons. On the other hand, the varablty of the bas shows whether surgeons are focused or not focused on the estmatng duratons. Ongong debate on montorng OR effcency ndcates that montorng OR tme s as mportant as measurng t. In ths study, the smulated cases present the mportance of measurng and montorng the mean and varablty of estmatng error. For surgeon B and C, we show that shfts n mean bas can be detected usng CUSUMs. In such cases, nstead of relyng solely on surgeons estmates, a combned estmaton method of hstorcal mean and surgeons estmate could be appled, f the hosptal has a long hstorcal duraton data set. The results of varablty ncrease are obvous for surgeon D even f s/he s accurate. It s concluded that surgeon D should focus on estmaton more serously and mprove her/ hs duraton estmaton performance. Ths study s a practcal montorng approach that would contrbute to mprove the effcency of surgeon based surgery tme estmaton systems. Our llustratve case nvolves surgeons. However, the method can easly be adapted to other felds such as benchmarks of varous type of operatons, surgcal servces or hosptals OR effcency. The methods ntroduced n our study have ther own setbacks. A problem can emerge for rare operatons. If the total number of operatons s low n count, then t s nevtable to have problems about parameter estmaton and dstrbutonal assumptons. For such cases, some other approaches should be consdered and ongong research of the authors deals wth these challenges. References Cardoen, B., Demeulemeester, E., & Belën, J. (2010). Operatng room plannng and schedulng: A lterature revew. European Journal of Operatonal Research, 201 (3), Chen, T. T., Chang, Y. J., Ku, S. L., & Chung, K. P. (2010). Statstcal process control as a tool for controllng operatng room performance: retrospectve analyss and benchmarkng. Journal of Evaluaton n Clncal Practce, 16 (5),

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