Using the DTW method for estimation of deviation of care processes from a care plan

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1 Using the DTW metho for estimation of eviation of care processes from a care Alexey Molochenov Mihail Khachumov Feeral Research Center Computer Science an Control of Russian Acaemy of Sciences, Moscow aim@isa.ru, hmie@inbox.ru Abstract Hospitals increasingly use process moels for structuring their care processes. Activities performe to patients are logge to a atabase or a log. These ata can be use for managing an improving the efficiency of care processes an quality of care. In this article, we propose the metho for estimation of eviation of care processes from a care. efines the steps of a patient treatment for a certain isease in a specific hospital. is built on the base of care process moel. A care process moel is built on the base of exemplars of care processes, store in a atabase or a log. The Dynamic Time Warping (DTW) algorithm was use for estimation of eviation. The DTW algorithm measures a istance-lie quantity between two given traces containing information about execution or not execution of actions efine by care. Introuction Explore of methos for management of care process (CP) as a flow of therapeutic an iagnostic activities allows us to analyze situations with patients an recommen to ecision-maers (DM) appropriate action for the treatment of patients. In this connection, occurs increase interest in an automation of hospitals units (accounting, reception, offices, warehouse an so on) an an analysis an a formal representation of care processes in orer to support octors wor. The first area is eep enough elaborate - powerful meical information systems for supporting of therapeutic an iagnostic processes are evelope. Flows of patients can be optimize by simulation in orer to ientify bottlenecs. The secon area requires aitional researches to estimate stages of a care process an to evelop recommenations for ecision-maers. Currently tools for analysis an meical iagnostics, using ifferent classifiers with high accuracy an precision are evelope [3, 4, 8,, 7, 8, 4]. This area has a number of features an is of great interest for us. A care process, Proceeings of the XVIII International Conference «Data Analytics an Management in Data Intensive Domains» (DAMDID/RCDL 06), Ershovo, Russia, October - 4, 06 espite the stanars, always has an iniviual (personalize) character. There may be various eviation from the selecte care, epening on the changing care conitions, concomitant eceases, etc. Therefore, there are not only problems replying of a care process, an operational management of a care process in terms of possible eviations. Management is a particular sequence of treatment actions (operations), which is base on states of a patient, a prescribe care an meical atabases, i.e., preceents. The aim of our research is to evelop algorithms an tools that assist to a octor by maing proposals (recommenations) on the organization of care process in accorance with an actual patient s state an care. One of the objectives is to assess the quality of the renere meical services by comparing a patient s care process an care. The care efines the actions of the octor an is base on the care process moel, iscovere from preceents. The multi-imensional istance base on Dynamic Time Warping (DTW) algorithm is use to ifferences between care process an care. Experiments show that DTW algorithm is effective to compare sequences of actions in relation to care processes. We consier the use of DTW algorithm to etect eviations between real care process of a patient an care. Formalization an optimization of care processes Some methos for formalization an application of care processes are escribe in [,, 7]. Methos an algorithms for iscovery of moels of care processes on the base of event logs an preceents are escribe in [3, 6, -6, 9]. The moel inclues all traces from event logs an preceents. Fig. illustrates the Petri net worflow process efinition for hanling a meical complaint. In this figure we can ientify the following routing constructs: transitions Ientification an Cariologist are AND-splits, I iagnosis OK, I iagnosis NOK an ecie surgery are AND-joins, c4, c5, c8 an c0 are OR-splits an c6, c9 an c are OR-joins. Automatic iscovery of care process moel is ifficult an actual problem. Some methos an algorithms to solve this problem are escribe in articles [3, 6, -6, 9]. Every trace in event logs an in a care 4

2 process moel are characterize, in general, the timing associate with the time of applying operations by physician, an is characterize by quality inicators (signs), efining the current state of the patient. In real life we have eviations of real care processes from care s built on the base of care process moel. These eviations can be associate with a change in the patient's state, lac or replacement of some rugs or other meical evices, influence of other isease or other causes. echocariogra m с7 Raiologist с8 Ientification с3 с Cariologist thorax ECG Bloo test с care process, non-compliance of actions sequence, performance of actions not provie by care process, etc. [, 9] are consiere to be eviations. In care process it is necessary to emphasize the eviations associate with time limits impose on actions. For example, some actions have to be performe on the first ay of the patient arrival. The situation when the action has been performe after the specifie time interval is the eviation in this case. The metho for etection an visualization of the eviations associate with performance of actions not inclue in the moel of care process an nonperformance of actions that nee to be is escribe in the article [0]. In articles [, 4,, 3] the fitness function is use to chec conformance of a care process moel an processes in event log. Petri nets are use as formal representation of the care process moel. Let is the number of ifferent traces from the aggregate log. For each log trace i, ( i ), n i is the number of process instances combine into the current trace, m i the number of missing toens, r i the number of remaining toens, c i the number of consume toens, an p i the number of prouce toens uring log replay of the current trace. The toen-base fitness metric F is efine as follows [,, 3]: с9 с5 I iag NOK с4 I iag OK F i i n m i i n c i i i i n r i i n p i i Decie surgery с6 In case of eviation etection in the course of treatment of a specific patient, n an are equal to since there is one trace an one instance. Function f will be as follows: No surgery с0 с Archive Surgery Figure A Petri net of a care process. 3 Ientification of possible eviations of a care process from the care Qualitatively expert assessment of a trace as a way on the graph with temporary mars will allow to reveal an estimate various eviations from the course of meical an iagnostic process ue to both objective an subjective reasons an to eliminate them in the subsequent realizations of care process. Nonperformance of action which has to be surely in m f c If f is equal to, then the trace is completely consistent with the care process moel. Otherwise, there are eviations. In [3] it is shown that eviations from the care lea to increase cost of treatment. In [5] the metho that coul chec for eviations of care process of a patient from a an locate specific points of these eviations is escribe. Let s consier a metho for etection of the eviations associate with the performance of actions not provie by the care an non-performance of actions provie by care process. The DTW metho was applie calculate the eviation or istance. The metho allows to fin closeness between two measurement sequences for a certain perio of time. Generally, the length of sequences can be ifferent, an measurements can be mae with ifferent rates [7]. DTW metho became wiely sprea in meicine. A theory of moifie DTW algorithms an its applications are presente in []. In particular, recognition of human activity is consiere by comparison of the gestures presente in r p 43

3 the form of two-imensional time series. Recognition of such activity of the patients can be very useful in moern healthcare for monitoring of patients conition an automatic reporting creation for health worers. The results of experiments confirme the sufficient accuracy of one moification. DTW algorithm calculates the optimal sequence of transformation (eformation) between two time series [7, 0]. Let two numerical sequences (a, a,, a n ), (b, b,, b m ) are given. We obtain eviations matrix D, where ij = a i - b j, i =,..,n, j =,..,m. At the secon step we buil eformations matrix. Each element r ij is efine by means of ynamic programming algorithm an local optimization criteria: r ij = ij + min(r i-, j-, r i-, j, r i, j- ). The path in the eformation matrix efining a eviation begins in its left upper corner an ens in the right lower. The value R of eformation is efine by the sum of the minimum local eviations of each path element. R is ivie by the number of path elements an is consiere as istance estimation between sequences. We consier the example of DTW algorithm application for comparison of processes of bronchial asthma treatment that is presente in Table (ata are provie by the Meical center of the Central ban of the Russian Feeration). Table contains care that inclues operations manatory to perform an reports of real care processes of three patients. To formalize care process reporting we will efine the following variables: α =, «not» β = -, «not require» σ = 0.The istance between an «not» operations we will efine as α - β =, an the istance between («not») an «not require», respectively α - σ = β - σ =. Obtaine care process parameters are inclue in Table in the form of sequences The sequences can now be compare. We will apply the DTW metho to calculate care process eviations of care processes from the care. In Fig. the process of comparison of the Patie (P3) course of treatment with the (P) is presente as comparison of two sequences by the DTW metho using the ynamic programming scheme. In the table the way etermining the minimum value of eviation R is highlighte in color. In this case R =.57. We will apply the DTW metho to calculate eviations of Patients an 3 (respectively P an P3) care processes. All necessary ata for comparison of processes are shown in Fig. 3. Table 3 emonstrates possibility of istances calculation between preceents. The more the istance, the more preceents are iffere from each other. The table shows that Preceent (care trace of the Patient ) is close to the. Table Bronchial asthma therapy process Operations of the care Precee nt Progress report Precee nt Reception area / Intensive care unit (ICU) Transfer from the reception area to the war with bes /ICU through hours or less function or Pea expiratory flow rate require 3 Pulse oximetry require 4 Chest raiography ay in ICU / war with bes 5 Pulse oximetry require require 6 Pea Flow Meter Inhale shortacting ß-agonists or formoterol Consultation of an exercise therapy octor Consultation of a physiotherapist 0 Pea Flow Meter 3 function Inhale s Inhale ß- agonists 4 Pea Flow Meter function require -7 ays in war with bes 8- ays in war with bes require Systemic s Inhale s Inhale ß- agonists require require require require require Precee require 44

4 Table The summary table of the formalize inicators of care process performance Transaction number Preceent Preceent Preceent Figure Calculation of care process eviation from the care (on the example of Patie) Figure 3 Calculation of care processes eviation from the care (on the example of Patients an 3) The istance accoring to the establishe scheme is R =.935. Results of pair comparison of all patients care processes are given in Table 3. Table 3 Deviations of care processes (pair istances) Precee nt Precee nt Precee 3 Conclusion Precee nt Precee nt Precee 0,000 0,486, ,486 0,000 0, ,43 0,333 0,000 4, ,4 0,000 Meical processes escribing care of patients are useful in aily wor of physicians, especially in ifficult situations. Certain step towars the creation of tools to support physician s wor in the course of care process is taen in the article. At the current stage of research, methos for the analysis an evaluation of eviations associate with performance an non-performance of actions for elementary care processes are chosen an stuie. The problem is solve on the existing generalize care process moel an reuce to evaluation of eviations of care preceent from available traces. The propose metho allows verifying compliance of treatment with the care an proceures establishe by care stanar. In aition it helps the ecision-maer with the choice of a rational way of the treatment carrie out with the use of strategies an rules. In reality, to mae a choice of a rational way of treatment it is necessary to sort an estimate rather large number of amissible trajectories taing into account strict bining of operations at the time-point that certainly complicates process of comparison an etermination of istances. Authors inten further to research similar processes. The reporte stuy was fune by RFBR accoring to the re-search project No «Research an evelopment of methos for analysis of eviations of meical processes from their moel» References [] Wil M. P. van er Aalst, Process Mining: Discovery, Conformance an Enhancement of Business Processes, Springer Publishing Company, Incorporate, 0, 35 p. [] Ariansyah, A.: Aligning Observe an Moele Behavior. Ph.D. thesis, Einhoven University of Technology, 04. [3] Breiman L., Frieman J. H., Olshen R. A., Stone C. T. Classification an Regression Trees. Wasworth, Belmont, California, 984. [4] Carroll, Robert J., et al. "Portability of an algorithm to ientify rheumatoi arthritis in electronic health recors." Journal of the American Meical Informatics Association 9.e (0): e6-e69. 45

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