ABSTRACT Intensive Care Units have beencarrying vital importance in these days. These hospital units, affecting mostpeople’s lives, have recently become more crowded. Due to this crowd, patientswho have to enter intensive care units unfortunately get vital risks because ofnot getting access to these units.

The greatest reason for the occurrence ofthis condition is that the time to be spent in intensive care units is notpredictable without modelling the system. In this study, we will model theintensive care units with continuous absorbing markov chain structure andestimate the length of stay at intensive care unit by using phase-typedistribution. Study will follow the order as gathering data of the system,modelling the markov chain with apporapiate amount of states then applying thePhase Type Distribution to the model. At the end, It will be predictable thatlegth of stay at intensive care units. Regression Models Utilizingregression incorporates bend fitting, expectation (forecasting), demonstratingof causal connections, and testing logical theories about connections betweenvariables. Regression examination is a technique for exploring usefulconnections among variables that is communicated as a condition or a modelinterfacing the reaction or ward variable and at least one logical or indicatorvariables. 1) Linear Regression If we distribute our dataaccording to their values on the x-y coordinates, they have a distance betweeneach other.

The goal is to draw a line that passes through all the data andpasses the most correctly. The correct drawing here is for regression in alinear structure. Our goal is to simulate the distribution of our train data onthe plane as a mathematical model so that we can find the correct regression model.For example, if you have a fluctuation set of data, using linear regressionwill not make sense. Using logistic regression for this will help you achievemore successful results. Because the logistic regression tries to capture thedata logarithmically on the plane with curve. According to Combes, Kadri andChaabane (2014)’s study about predicting the length of stay at emergencydepartment. They have contucted two different linear regression model, in thefirst model there are 4 variables and in the second there are 8 variables.

Inthe second model, accuracy of the model is more reliable because of variableamount highness. It is easy to observe that more the variable amount in linearregression model provides better accuracy of the model. In order to bestfitting it is require to choose right variables with many amounts.

From thissituation Combes, Kadri and Chaabane (2014) states linear regression suffersfrom the well linearity. According to their reliability test there was ±2 hourserror. Moreover, basic linear regression method is not valid for non-linear variables.

And also classification and regression are two methods that used for predictionabout discrete outcomes(Tan, 2007). There is also another study aboutpredicting lenght of stay with using linear regression method. With respect toBadreldin(2013), the linear regression model evaluated as failed in accuracy of prediction. Study was also suggest thatreconsideration of the variables could gave better prediction. From thePourhoseingholi’s Study (2009) there was a fitting comparison between linearregression and quantile regression. At the end, he stated that linearregression remained incapable when the comparing with quantile regression.Combes C., Kadri F.

and Chaabane S.(2014, November 5).PREDICTING HOSPITAL LENGTH OF STAY USING REGRESSION MODELS: APPLICATION TOEMERGENCY DEPARTMENT. Optimisation etSimulation- MOSIM’14. Retrieved fromhttps://hal.

inria.fr/hal-01081557/documentTan, P. (2007). Introduction ToData Mining. Pearson EducationBadreldin, A. M., Doerr, F.

, Kroener, A., Wahlers, T., &Hekmat, K. (2013).

Preoperative risk stratification models fail to predicthospital cost of cardiac surgery patients. Journal of CardiothoracicSurgery, 8, 126. http://doi.org/10.1186/1749-8090-8-126 Pourhoseingholi,, M.

A., Pourhoseingholi, A., Vahedi, M., Dehkordi,B.M., Safaee, E.

, Mserat, E., Ghafarnejad, F. & Zali, M.R.

(2009). Comparing linear regression and quantile regression toanalyze the associated factors of length of hospitalization in patients withgastrointestinal tract cancers. Italian Journal Of Public Health.6,2.

http://dx.doi.org/10.2427/57872) Logistic Regression It is aregression model and the dependent variable is categorical. Moreover, Logisticregression is a statistical strategy for breaking down a dataset in which thereare at least one free variables that decide a result. The result is measuredwith a two conceivable variable.

The objective of logistic regression is tolocate the best fitting model to present the relationship.For estimating theprobabilities, its using the logistic function in other words logistic curve. Ittries to catch data on an algorithmic curve. This leads us to a higherprediction success in up-and-down data.The author Austin (2010) compared athis study that performances of classification techniques for prediction purposeand he found that the logistic regression has gave better result than regressiontree, multi-layer perceptron and radial basis function with using Receiver OperatingCharacteristic curve and Hierarchical Cluster Analysis performance measure. Inaddition to this information Kurt, Ture and Kurum (2008) states that comparisonbetween acuracy of regression trees with logistic regression model forpredicting length of stay in hospital.

As a result of his study, logisticregression is more accurate than regression trees. Sharma, Dunn, O’Toole,Kennedy (2015) have also studied length of stay with using logistic regression,they have used a psychiatric hospital with population of 1.2 million. Moreover,they also used IBM SPSS v21 statistical analysis software. They found that theresult does not seem to mirror the requirements of an intense mentalaffirmation benefit and may speak to the absence of group emergency determinationassets. As a measure the modular completed length of stay shows something aboutwhat is occurring in an administration, yet as a measure of focal propensity itis of restricted esteem and needs sensitivity emergency determination assets.In short, sensitivity of the logistic regression is not adequate for Length ofStay studies and not representing the real system.Austin, P.

C., Tu, J.V., Lee,D.S., (2010).

Logistic regression had superior performance compared withregression trees for predicting in-hospital mortality in patients hospitalizedwith heart failure. J. Clin. Epidemiol.63, 1145–1155.Kurt, I.

, Ture, M., Kurum, A.T.,2008.

Comparing performances of logistic regression, classification andregression tree, and neural networks for predicting coronary artery disease.Expert Syst. Appl. 34, 366–374.Sharma, A., Dunn, W., O’Toole,C.

, & Kennedy, H. G. (2015). The virtual institution: cross-sectionallength of stay in general adult and forensic psychiatry beds.

International Journal of Mental HealthSystems, 9, 25. http://doi.org/10.1186/s13033-015-0017-7 3) Machine Learning Regression Generallyused regression tree algorithms such as CART and CHAID. CART is used fornon-parametric in other words non-linear regression tree. CHAID is an statisticalapproach that can derive regression trees. One of the machine learning study hasoccured in a Federal hospital because of its variable richness’ positiveeffects on regression models (Hulshof, 2013). The first variable was predictionof patients’ length of stay and other one was prediction of readmission (Kelly,2013).

From the studies of this Federal hospital, Pendharkar and Khurana (2014)states that the ANCOVA (Analysis of Covariance) model tests linear connections,and significantly show that non-linear machine learning models may performmarginally superior to linear models. It means that machine learning regressionfits better than linear regression to real data. Moreover, when they looked to Root-Mean-Squareerror, there was no better regression technique than machine learning regression.

However, their sample size was limited with small section of the hospital. Inshort, it is not generalizable for other studies.Hulshof, P. J.

H.; Boucherie, R.J.

; Hans, E. W.; Hurink, J. L.

(2013): Tactical resource allocation andelective patient admission planning in care processes, Health Care ManagementScience, 16(2), pp. 152–166.Kelly, M., Sharp, L., Dwane, F.,Kelleher, T., Drummond, F. J.

& Comber, H. (2013): Factors predictinghospital length-of-stay after radical prostatectomy: a population-based study, BMC Health Services Research, 13(1),244-244.Pendharkar, P.C. & Khurana,H.

(2014). MACHINE LEARNING TECHNIQUES FOR PREDICTING HOSPITAL LENGTH OF STAYIN PENNSYLVANIA FEDERAL AND SPECIALTY HOSPITALS. International Journal of Computer Science and Applications, 11, 3. http://www.tmrfindia.org/ijcsa/v11i33.pdf Markov Chain Patientactivities can be modelled by using Markov Chains. ?t describes a system withdifferent states and transitions between them.

Markov Chain has memorylessproperty thats why the next state depend on only the current state not theprevious states. When we look at operational view, markov chain can be describewith different states. The Markov chains evaluated utilizing the improvementdatasets were joined with the initial state probability vector to create the expectedlength of stay in every goal for Intensive Care Units or Hospitals. In discretemarkov chains, it is not possible calculate in hours or minutes like continiousproperty. However, if we turn the data only days and which days spended inwhich department of hospital. It is possible to create an discrete markov chainwith absorbing state. According to Perez, Chan and Dennis(2006)’sstudies about length of stay at intensive care unit with using Markov Modelwith absorbing state in other words “first-step analysis”(Kapadia, 2000).

Themarkovian model lack of goodness of the fit to real length of stay data forsome departments in the hospital. The markovian model as a discrete propertyhave not calculated the discharges at middle of the day. In short, there has tobe an continious property markov model for able to model all kind of serviceand waiting times. According to Perez’s study (2006), there is also positiveside of the markov model with discrete property such as high correlationbetween utilization and length of stay. However, its outcomes are mostly notreliable and not fitting the real data in the continious matter because oflimitations. Moreover, according to Bhat (2002) sequence size is important formarkov chain structure in order to best fitting to the real data.

However,Perez’s study (2006) has only 30 sequence which are days of a month. Because ofthis reason markov model needs too much sequences (states) for fitting the realdata better.Perez, A. Chan, W. & Dennis,R.J. (2006): Predicting the Length of Stay of Patients Admitted for IntensiveCare Using a First Step Analysis. HealthServ Outcomes Res Methodol; 6(3-4): 127–138.

Kapadia, A.S., Chan, W.

,Sachdeva, R., Moye, L.A.

, Jefferson, L.S.(2000) Predicting duration of stay ina pediatric intensive care unit: A markovian approach. European Journal of Operational Reseach;124:353-359.

Bhat, U.N., Miller, G.K.(2002);Elements of applied stochastic processes.

Third Edition. John Wiley & Sons Inc; Hoboken, New Jersey.