SSRG International Journal of Medical Science (SSRG-IJMS) Volume 3 Issue 12 December 2016

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1 EuroSCORE overesimaed cardiac surgery relaed moraliy: Comparing EuroSCORE model and Bayesian approach using new generalized probabilisic model wih new form of prior informaion 1 Jamal A. Al-Saleh, 2 Saish K. Agarwal, 3 Rashed Al-Bannay 1 Deparmen of Saisics and Operaion Research, Faculy of Science, Kuwai Universiy, P.O. Box 5969, Safa, 13060l Kuwai Tel: , Fax: Deparmen of Mahemaics, College of Science, Universiy of Bahrain, P.O. Box 32038, Bahrain 3 Cardiology uni, Inernal Medicine Deparmen, Salmaniya Medical Complex, PO Box 12, Bahrain Absrac Objecives: An aemp is made o sugges an alernaive approach using Bayesian analysis in predicing he moraliy during cardiac surgery. The risk index prediced hrough Bayesian approach is compared wih he radiional approach EuroSCORE Model for known daa ses available in he inerne [see [4]]. Mehods: The overall moraliy relaed o cardiac surgery was raced from 2002 o 2012.The daa was exraced from he official blue book websie of he Sociey for Cardiohoracic Surgery in Grea Briain & Ireland. The cohor included paiens who underwen cardiac surgery in NHS hospial and oher privae hospials in U.K. During each year, he rue moraliy, prediced moraliy by EuroSCORE, and esimaed moraliy hrough Bayesian approach were compared. Resuls: Overall moraliy raes derived from EuroSCORE Model were much higher (more han double) of rue repored moraliy rae for he period 2006 o 2012, and almos 60% higher for he period 2003 o 2005, han he rue moraliy repored by he Sociey for Cardiohoracic Surgery in Grea Briain & Ireland in is official websie. While he Bayesian approach prediced moraliy raes esimaes ha are more consisen, significanly lower han he one esimaed by EuroSCORE, and much closer o he repored rue moraliy. Conclusions: Moraliy rae pos-surgery is considered a qualiy meric o hospials. Bayesian approach provides greaer advanage over EuroSCORE in predicing moraliy pos cardiac surgery. Boh are noiced o overesimae he real surgical risk, being less wih he Bayesians. Bayesian approach is an alernaive predicor o esimae moraliy pos cardiac surgery and should be verified by furher research. Key words Bayesian Analysis, Cardiac Surgery Aciviy, Daa Analysis, EuroSCORE Model, Markov Chain Mone Carlo, Moraliy Rae, Informaive Prior. I. Inroducion Surgical moraliy is considered a qualiy meric for hospials. Elevaed risk migh no be acceped by many paiens and hence heir reamen can be compromised. Moreover, insurance services expeced o raise heir premium in case he anicipaed surgical moraliy is high. Consisen moraliy predicion ha can mimic he rue moraliy is crucial. Various Therapeuic decisions can be balanced wih he mos appropriae risk benefi raio. The presen sudy is an aemp o validae a risk predicor pos cardiac surgery model and compare i o he EuroSCORE. This sudy migh have a paricular ineres o cardiologiss, and cardiac surgeons.[1] Au e al (2007) compared he models, EuroSCORE [[2] Nashef e al (1999)] and Parsonne model [[3] Parsonne e al (1989)] o predic he moraliy rae, using adul paiens daa wih cardiac surgery aciviies. For he comparison hey used he daa on he number of paiens 1247 (observed moraliy rae 2.9%) undergone coronary arery bypass graf (CABG) and he paiens 1407 (observed moraliy rae 4.8%) undergone CABG a he Granham Hospial, Hong Kong from November 1999 o July They found ha EuroSCORE model performed much beer han Parsonne model in predicing moraliy. However, hey observed a endency for boh models o over predic moraliy rae. II. Mehodology In his paper, we considered Bayesian approach, using a new informaive prior we call i Informaive Uni inerval prior [infuip )] in he inerval ISSN: Page 1

2 (0,1). By applying Markov Chain Mone Carlo simulaion, o obain he poserior summaries required for an uncerain parameer for he daa of he observed moraliy raes afer he cardiac surgery aciviy. This daa analysis may be of some ineres o demographers, cardiologiss, acuaries, biosaisicians and healh policy makers. The Sociey for Cardiohoracic Surgery in Grea Briain & Ireland in is official websie [see [4]], allows access o informaion abou he clinical condiion of he paien, ype of cardiac surgery, and posoperaive oucomes including moraliy. Recenly, we came across he daa relaed o observed moraliy rae and prediced moraliy rae using EuroSCORE model when a cardiac surgery conduced in an NHS hospial and a number of he privae hospials during he financial year 2003 o EuroSCORE model is commonly used o predic moraliy rae. Such model required he daa on paien relaed facors as well as cardiac relaed facors. I has been adoped worldwide, becoming he mos widely used risk index for cardiac surgery. Using Bayesian approach, we compared he poserior esimaes (wih acual deahs) and wih ones prediced using EuroSCORE model. This comparison a micro level can be used as a measure of he qualiy of hospial performance. This sudy may give some insigh, how he Bayesian mehod for making inference abou an uncerain parameer p on he basis of prior knowledge ha behaves as proposed infuip ). The parameer p of success in a number of n rials, wih x number of successes such ha x~genbin(n,p,a,b,c) a generalized binomial probabilisic model [equ (2.1)], along wih he hree daa ses used (Table 1).The Bayesian approach by using new prior informaion, he informaive prior infuip( ) [eqn (VII.1)] and he Bayesian summary in Tables 2, 3, and 4 are presened. The comparison of he poserior esimaes obained by using he proposed prior, are made in secion 4, using Tables 2, 3, and 4 and figures1-3. Lasly, in Appendix we have given he pdf of new infuip( ), he cumulaive disribuion funcion along wih he r-h momen, for furher research and for he researchers who wan o verify he resuls for more daa ses obained in differen regions of he world. III. The moraliy raes afer cardiac surgery and he probabiliy model The parameer of ineres is he probabiliy p of success in n number of rials, which can resul in success or failure. The esimae, if here is a fixed number of rials, wih x number of successes, such ha x~genbin(n,p,a,b,c) a generalized binomial probabilisic model of index x and parameers p, a, b, c. Considering he hree daa ses in Table 1, which represen he number of operaions and he moraliy raes from he period 2003 o The years given in he hree daa ses represen a financial year. For example 2011 represens 1s April s March I is worh o menion ha hough i is yearly daa, ye i is no ime series daa. The hree daa ses in Table 1 were analyzed using compuer sofware. Therefore, if we le x and n be he number of deahs, and he number of cardiac surgery performed in respecive year, his problem will be modeled as a binary response variable wih rue failure probabiliies p. Thus x can follow genbin(p,n,a,b,c ) a generalized binomial probabilisic model, where x =0,1,,n, =1,..,10, ha is (II.1) f(x p,a,b,c ) = n p x a x ( 1 (1 p, a > 0, b 0, c 0. c b n ) ) 1 1 (1 p c b ) p a n x We should emphasize ha when a =1, b =1, and c =0, equaion (II.1) is reduced o convenional binomial disribuion [i.e., genbin(p,n,1,1,0) bin(p,n )]. The Bayesian approach, using prior informaion abou he parameer p, o consruc a new process before collecing and analyzing he daa and updaing he previous knowledge by using Bayes heorem is well esablished in he lieraure. To obain he Bayesian summary esimaes we use a hierarchical model, because of is versailiy [5]. Hence, for he presen hree daa ses, we assume ha he rue failure probabiliies for each year [see Table 1] having informaive prior disribuion for he p 's, namely infuip( ),=1,..,10. A realisic model for he surgical daa is o sugges he hierarchical models, which is implemened as follows: (a) A he firs sage we assume a prior belief ha follows infuip( ) for he rue failure probabiliies p for each hospial. (b) A he second sage, we assume he following prior specificaion for he hyperparameers and, ~gamma(,), and ~gamma(,) independen. ISSN: Page 2

3 (c) A he hird sage, we assume he following prior specificaion for he hyper-hyperparameers where ~exponenial(), ~exponenial(), =0.1. A Markov Chain Mone Carlo (MCMC) Gibbs sampling approach implemened in using compuer sofware is capable o analyze he esimaes of surgical moraliy in each year. A burn in of 1000 updaes followed by a furher updaes give esimaes of p, for each year =1,,10. Table 1. The moraliy raes from Year All cardiac surgery Number of Operaion s Moraliy raes (%) Isolaed firs ime CABG (overall cohor) Number of Operaion s Moraliy raes (%) Isolaed firs ime CABG (elecive paiens) Number of Operaion s Moraliy raes (%) IV. Resuls Table 2, for informaive prior infuip ), represen he esimaes of surgical moraliy for each year, along wih sandard deviaion, median and MC error. From Table 2, i can be noiced ha here is a marginal shif o he righ in he esimaes poserior median from he rue moraliy rae for all cardiac surgery for all years (Table 1). Almos similar ype of observaions can be seen for he res of he years from 2003 o From able 2, i is eviden ha he predicion of surgical moraliy rae by using proposed infuip prior wih hierarchical model for each year is more close o he rue moraliy raes for his daa se. When he EuroSCORE model is used, i over predic moraliy rae by almos 100% for mos of he years. The over predicion is almos more han 150% from he rue values for he years 2011 and Table 3, represen he esimaes of surgical moraliy isolaed firs ime CABG (overall cohor), for each year, along wih sandard deviaion, median and MC error for informaive prior infuip. From Table 3, i is clearly seen ha here is a marginal shif o he righ in he esimaes poserior median from he rue moraliy rae for all daa se isolaed firs ime CABG (overall cohor), for all years (Table 1). Almos consisen observaions can be seen for he res of he years from 2003 o As shown in able 3, i can be noed ha he predicion of surgical moraliy rae isolaed among firs ime CABG paiens (overall cohor) calculaed by proposed infuip prior wih hierarchical model for each year is more close o he rue moraliy raes for his daa se. When he EuroSCORE model is employed, he esimaed moraliy almos doubled he rue values for he years 2003 o 2006, and ripled he acual rae in years 2007 o Table 4, represens he esimaes of surgical moraliy isolaed firs ime CABG (elecive paiens) for each year, along wih sandard deviaion, median and MC error for informaive prior infuip. Table 4 has shown he similar marginal shif o he righ in he esimaes poserior median from he rue moraliy rae for daa se isolaed firs ime CABG (elecive paiens), for all years (Table 1). A similar ype of observaions can be seen for he res of he years ISSN: Page 3

4 from 2003 o From able 4, i can be noed ha he predicion of surgical moraliy rae isolaed firs ime CABG (elecive paiens) by using proposed infuip prior wih hierarchical model for each year is more close o he rue moraliy raes for his daa se. When he EuroSCORE model is used, i over predic moraliy rae by almos wice from he rue values for mos of he year. The over predicion is almos more han hree imes from he rue values from he years 2007 o As depiced in able 5, across he daa ses for he years 2002 o 2012, he Bayesian prediced moraliy is significanly lower han calculaed by EuroSCORE(P-value<.05). Table 2. Bayesian summary of all cardiac surgical moraliy for each year wih informaive prior infuip Yea r Mean SD MC error 2.5% Median 97.5% E E E E E E E E E E Table 3. Bayesian summary of cardiac surgical moraliy isolaed firs ime CABG (overall cohor) for each year wih informaive prior infuip Yea r Mean SD MC error 2.5% Median 97.5% E E E E E E E E E E E E E E E E E E E Table 4. Bayesian summary of cardiac surgical moraliy isolaed firs ime CABG (elecive paiens) for each year wih informaive prior infuip Yea r Mean SD MC error 2.5% Median 97.5% E E E E E E E E E ISSN: Page 4

5 E E E infuip True mor Escore es Fig 1. Char of summary of all cardiac surgical moraliy predicion in (%) for each year compared wih moraliy raes Fig 2. Char of summary of cardiac surgical moraliy predicion in (%) isolaed firs ime CABG (overall cohor) for each year compared wih moraliy raes ISSN: Page 5

6 Fig 3. Char of summary of cardiac surgical moraliy predicion in (%) isolaed firs ime CABG (elecive infuip eur sco rue mor paiens) for each year compared wih moraliy rae V. Discussion Here an aemp is made o propose an alernaive approach o predic moraliy pos cardiac surgery oher han EuroSCORE. As being eviden in he lieraure he laer ended o overesimae such moraliy [9]. Figures 1, 2 and 3 represen he summary of rue surgical moraliy in (%), predicion in (%) for each year, by Euroscore model and by Bayesian approach by using proposed infuip prior wih hierarchical model for each year. For hese paricular daa ses prior infuip wih hierarchical model performed he bes, and he poserior medians are consisen wih he observed values han he prediced value using EuroSCORE model. I is eviden ha by employing he Bayesian analysis, he poserior esimaes using priors infuip wih hierarchical resuled in more consisen esimaes han prediced values using EuroSCORE model, and closer o observed values for all he years. I can be seen ha EuroSCORE model had consisenly overesimaed he moraliy for he years 2003 o 2012, which is far from concordance wih rue values. While Bayesian analysis he poserior esimaes using prior infuip wih hierarchical model had more coheren resuls which rue values have. Ineresingly, he predicion is quie close o he rue values for all hree daa ses. Poenial errors are anicipaed when applying he EuroScore. Afer he original EuroSCORE was developed, he use of off-pump CABG gained considerable populariy, especially beween 1997 and Advances in medical reamen, hrombolyic herapy, and percuaneous inervenions in recen years have also alered he profile of paiens referred for cardiac surgery [10]. To mainain accurae predicion, saisical models should have periodic recalibraion ha can parallel he meamorphosis of he disease profile and herapeuic advances. VI. Conclusion EuroSCORE ofen overesimaed cardiac surgery relaed moraliy. Bayesian approach seems a valuable alernaive ha worh furher research. A he same ime cauion o be praciced when deciding he individual candidacy prior o cardiac surgery. Cardiac eam approach raher han decision based merely on EuroSCORE is srongly encouraged. VII. Bayesian approach by using new prior informaion Firs, le us inroduce he following new prior, he pdf of he new informaive uni inerval ype prior infuip( ) of a random variable X, wih parameers > 0, 0 (or 0, 0), is defined in equaion (VII.1) as follows: (VII.1) f(x) =, The (cdf) cumulaive disribuion funcion of (VII.1) is F(x). From he pdf (VII.1), and F(x) funcion, i can be seen ha hey do no have special funcions in he equaions. I can be noed ha for = 0, = 1, he disribuion reduces o uniform and sraigh line and ISSN: Page 6

7 hence add o versailiy, and can be used as noninformaive prior in case where exper s informaion eiher no rue or doubful or he equal probabiliies are assigned o all possibiliies. The disribuion is also, unimodal and hence convenien o handle. The rh momen abou origin of infuip( in eq (VII.2) (V[[.2) = ) is given [5] Gelman A., Carlin JB., SernHS. and Rubin D.B. Bayesian daa analysis. 2nd ediion. Chapman and Hall/CRC. Boca Raon, FL; pp 696l [6] hp:// asx [7] Sensi L, Tedesco D, Mimmi S, Rucci P, Pisano E, e al. Hospializaion Raes and Pos-Operaive Moraliy for Abdominal Aoric Aneurysm in Ialy over he Period PLoS ONE, 8:12, [8] Andrews LC, Special Funcions of Mahemaics for Engineers, Oxford Universiy Press, Oxford, UK [9] Gummer, J.F., Funka, A., Osswald, B. e al. EuroSCORE overesimaes he risk of cardiac surgery: resuls from he naional regisry of he German Sociey of Thoracic and Cardiovascular Surgery. Clin Res Cardiol, 98: 363, [10] Sanon S, Lee V-V, Elayda MA, e al. Predicing Early Deah afer Cardiovascular Surgery by Using he Texas Hear Insiue Risk Scoring Technique (THIRST). Texas Hear Insiue Journal. 2013;40(2): [11] Feng Li., R code webpage (online) a hps: //gihub.com/fengli/fluils/blob/maser/mah/ghypergeo. Where,, and F is he generalized hypergeomeric series. [see [8] Andrews, Chaper 9, p 365], and is defined by: (VII.3) Unlike he pdf eq (VII.1) and F(x) of infuip( ), he r-h momens do have special funcions in he eq (VII.2). However, by using eq (VII.2) we can compue he mean and he variance and/or he r-h momens which are no difficul o obain. [10] Feng, Li wroe an R funcion o calculae he generalized hypergeomeric funcion for real numbers. Wih minor changes we can use his funcion o compue eq (VII.2). Acknowledgmens The suppor by he Research Adminisraion, Kuwai Universiy, Kuwai, is acknowledged by he firs auhor. References [1] Au WK, Sun MP, Lam KT, Cheng LC, Chiu SW and Das SR. Moraliy predicion in adul cardiac surgery paiens: comparison of wo risk sraificaion models, Hong Kong Med J;13:pp , [2] Nashef SA, Roques F, Michel P, Gauducheau E, Lemeshow S, Salamon R. European sysem for cardiac operaive riskevaluaion (EuroSCORE). Eur J Cardiohorac Surg;pp16:9-13, [3] Parsonne, V., Dean D and Bernsein AD. A mehod of uniform sraificaion of risk for evaluaing he resuls of surgery in acquired adul hear disease. Circulaion;79:pp I3- I12, [4] EuroSCOR websie (online) a hp://bluebook.scs.org ISSN: Page 7