The positive stable frailty model application to assess survival effect of health care reform on patients with acute myocardial infarction

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1 The Pharma Innovaton Journal 2014; 3(8): ISSN: TPI 2014; 3(8): TPI Receved: Accepted: Ocheredko Oleksandr Progov memoral Vnntsa Natonal Medcal Unversty, Ukrane Klmenyk Volodmr Progov memoral Vnntsa Natonal Medcal Unversty, Ukrane The postve stable fralty model applcaton to assess survval effect of health care reform on patents wth acute myocardal nfarcton Ocheredko Oleksandr, Klmenyk Volodmr Abstract Background: notorously known worldwde leadng cause of dsablty and mortalty n adults cardovascular dseases experence ther rse n Ukrane, takng formdable death tall of people wth vcous rate 1 person per mnute beng the hghest among uropean countres. Acute myocardal nfarcton (AMI) leads the way. The am was to unvel the mpact of ongong health care reform to survval of patents wth AMI ncdent n Vnntsa regon, Ukrane. Data: organsed by cohort desgn. Control cohort comprsed 400 patents wth frst epsode of AMI treated n cardologcal Vnntsa cty department on the eve of reform, namely years. xpermental cohort conssted of 400 patents wth frst epsode of AMI treated n Vnntsa regonal cardologcal centre n years at the moment of reform ntaton and openng of the centre. Dagnoses comprsed ICD-10 codes І21.0-І21.3, І21.4, І21.9, І22. The most pervasve localzaton happened to be anteror (33,2%), posteror (37,4%), and frontolateral (12,0%). AMI-related lethal cases happened n frst 5 years from the hosptalzaton were nvestgated. In gven tme perod 270 out of 800 patents ded, that s 33,7%. Methods: postve stable fralty model processed by SAS macro. Results: after adjustment on mportant clncal and bologcal confounders the mplementaton of reform rendered hazard reducton effect of the largest magntude among other covarates (=-0,179, р=0,029). Basc rsk of lethalty because of reform dropped by 19,6%, savng addtonal 0,8788 survval months to patent n frst 5 years from AMI ncdent. It was unveled that man effect (84,2%) was related partcularly to mprovement n tmelness of medcal care. Keywords: acute myocardal nfarcton, survval, medcal reform, Ukrane. 1. Introducton By our prelmnary nvestgatons the lnchpn of pvotal mportance to mprove survval n AMI patents s tmelness of treatment and hosptalzaton (RR=1,44) [2]. Related dervatve s severty of patent s condton at hosptalzaton (RR=1,98), exgent admnstraton of β- blockers (1-RR=0,549), along wth reperfuson (1-RR=0,35). Treatment ntensty and accomplshment s yet another sgnfcant factor to reduce lethalty (RR=2,767) [3]. Wdely dscussed ssues n research publcatons are effectveness of ntensve treatment procedures, thrombolytc therapy, PCI, CABG are most popular among them, as well as severty of patent s condton, comorbdty load (mostly measured by Charlson s ndex), ejecton fracton and systolc blood pressure values at hosptalzaton, presence of pathologcal Q, nstances of heart arrest before or at hosptalzaton, patent s gender and age [8]. Whereas ongong health care reform (HCR) greatly nfluenced all abovementoned ssues the necessty to make n process assessments s obvous. Many nnovatons were ntroduced n emergency care; actually hghly nterspersed servces and facltes were unted snce 2009 nto emergency medcne wth compartmentalzed budgetng, management, and greatly enhanced capabltes. Most effcently t was mplemented n Vnntsa regon. Another remarkable nnovaton was establshment of Vnntsa regonal centre of cardo-surgery n They serve procedures of percutaneous coronary nterventon (PCI) free of charge. Among obvous advantages there are: extraterrtoral organzaton of emergency cases management, attenuaton of geographcal dsparty n coverage wth emergency care servces. Correspondence: Ocheredko Oleksandr Progov memoral Vnntsa Natonal Medcal Unversty, Ukrane 2. Materals and Methods Data were organsed by cohort desgn. Control cohort comprsed 400 patents wth frst epsode of AMI treated n cardologcal Vnntsa cty department on the eve of reform, namely years. xpermental cohort conssted of 400 patents wth frst epsode of AMI treated n Vnntsa regonal cardologcal centre n years at the moment of reform ~ 67 ~

2 The Pharma Innovaton Journal ntaton and openng of the centre. Dagnoses comprsed ICD- 10 codes І21.0-І21.3, І21.4, І21.9, І22. The most pervasve localzaton happened to be anteror (33,2%), posteror (37,4%), and frontolateral (12,0%) AMI. AMI-related lethal cases happened n frst 5 years from the hosptalzaton were nvestgated. In gven tme perod 270 out of 800 patents ded, that s 33,7%. Relevant covarates such as trombolytc therapy, PCI and CABG procedures admnstraton, severty of patent s condton, comorbdty load (measured by Charlson s ndex), ejecton fracton and systolc blood pressure values at hosptalzaton, presence of pathologcal Q, nstances of heart arrest before or at hosptalzaton, patent s gender and age were observed. We have chosen flexble sem-parametrc postve stable fralty (PSF) model to study survval effect of health care reform. Fralty model ncapactates the assessment of ndvdual propensty to survve, ncorporatng unobserved patent s characterstc nfluenced survval dfferently across patents. Overlookng fraltes entals based and neffcent estmaton of survval effects. Fralty model bascally ncorporates three man components: 1. Basc hazard functon, changeable n tme. 2. Functon of factors, modfyng basc hazard. 3. Fralty dstrbuton. These components were specfed as followng. We dd not specfy basc hazard functon parametrcally nstead t was estmated sem-parametrcally by the Aalen estmator [5]. Dong so, we avoded possblty of basc hazard functon msspecfcaton. We exploted classcal exponental functon of predctors that nsures proper space of predcted survval values. We opted for postve stable dstrbuton (PSD) of fraltes: 1 f ( z) ( 1) k1 k 1 ( k 1) z k! k 1 sn( k ).(1) wth z fraltes values, z 0, sngle parameter of PSD, that n fact s nverse dsperson measure (.e. precson of PSD), wth bounds 0 <1, Г( ) Gamma functon. In specal case wth =1 dstrbuton degenerates to constant mass pont z=1, evdencng on the equal ndvdual propenstes to survve across cohort members. To the contrary, proxmty to zero bares evdence on hgh heterogenety of fraltes dstrbuton. We opted for PSD (1) yet for another reason. PSD s unque statstcal dstrbuton, that nsures proportonalty of survval effects n tme after ntegraton out fraltes. In smple case of bnary factor Х hazard rato at levels 1 aganst 0 doesn t depend upon tme t: ( t X 1) e ( t X 0) (2) Besdes, (2) secures smple proper expresson n Laplace u transformaton: L( u) e, exploted to derve uncondtonal survval functon S(t): S( t) H ( t) e, t H( t) h( u) du 0 (3) and H(t) functon of cumulatve hazard h(t). Model coeffcents (survval effects) β and fralty dsperson parameter were reckoned by two sem-parametrc methods: M (expectaton-maxmzaton) and PL (penalzed lkelhood) algorthms. ach operates wth classcal log-lkelhood functon (LL) for PSF condtonal proportonate hazards model: L N M I j X j ln h( tj ) zh ( tj )exp( X j ) 1 j wth і patent s d number: є{1 N}, N sample sze (800), j month s d number: j є{1 M}, М =12х5=70, І j rght censorng ndcator for th patent n jth month (1 demsed, 0 censored); z th patent s fralty score. Whle fraltes are tme constant, model may ncorporate dynamc predctors Х j. Full formulae (4) expresson ncludes constants І j *ln(z ), latter don t nfluence (4) maxmsaton for ther dervatves by β tantamount to zero. Maxmsaton of (4) consttutes M-step of M algorthm. By derved vectors β and Н Е-step (expectaton) takeovers. In -step expected fraltes scores Е(z β,x ) are calculated by formulae (Wang et al., 1995): z z M D1 D z exp H z exp H z (4) (5) D I j 1 j and s cumulatve outcome (death / censored) of th patent. In ths study z assumes PSD wth expectatons [6]: J q 1 q z exp sz s exp s J q, s q 0,1, ; s 0 q1 m q, s s m0 q, m (6) wheren Ω qm stands for polynomnal of degree m. Havng lethal case can happen once, D (5) values are confned to ntegers 0 or 1, n turn q (6) possble values 0, 1, and 2, therefore degree m n (6) are lmted to 0 and 1, that greatly smplfed calculus, whereas polynomnal gven recursvely by: q,0 q,1 1; q1,1 q1,0 q 1/ q m; (7) Generally polynomnal consttuents numerous and can t be expressed n close form: q / 1 ; 1q q, q1.(8) Puttng reckoned by (5 7) expected scores z nto (4) M ~ 68 ~

3 The Pharma Innovaton Journal algorthm proceeds to М-step wth output of modfed vectors β and Н and so forth. Vector Н we calculate by modfcaton of Aalen estmator (Wang et al., 1995). We modfed the algorthm of SAS PS Fralty macro (avalable download The ntate values for zero step of algorthm were estmates of β and Н, obtaned by PL algorthm that greatly mproved solvng. Furthermore, nstead of (8) wth Gamma functon we exploted much smpler close form polynomnal expresson (7). In summary, the estmaton routne proceeds wth four consequent steps: Step 0. stmates of β and Н, obtaned by PL algorthm together wth ntal fraltes scores z =1 (mplyng =1) are used as nput to (8) to proceed wth М-step. Step 1. Fxes. Usng the current values of, β, and Н algorthm computes expected fraltes scores Е(z β,x ) by formulae (5 7), -step. Step 2. Havng z і from Step 1 vectors β and Н are updated by (4) (М-step). Step 3. Iterates between Steps 1 and 2 untl convergence of β. Step 4. Repeats Steps 1-3 to construct the profle lkelhood (9) dependent on only. Search for value that maxmses (9). Maxmsaton was mplemented by golden search method after set bounders on soluton space by grd-search technque. Lprofle M I j ( ) X j ln h( tj ) j1 N 1 D ln 1ln H H lnj D, H 3. Results and Dscusson Lnear predctor s set by factors that ndcate accessblty, tmelness, qualty of servces, as well as covarates known to be moderators of survval n AMI patents [7, 8] to make adjustment for. So we nclude covarates: treatment wth thrombolytc therapy, PCI, CABG severty of patent s condton, comorbdty load (measured by Charlson s ndex), left ventrcular ejecton fracton (LVF) and systolc blood pressure (SBP) values at hosptalzaton, presence of pathologcal Q, nstances of heart arrest before or at hosptalzaton, patent s gender and age. stmates of sgnfcant effects of PSF model by M algorthm are dsplayed n Таble 1. Non-sgnfcant effects dscarded from dsplay. (9) Table 1: stmates of sgnfcant effects by M algorthm, PSF model Factors m 2 df p RR 1 Health care reform -0,179 0,082 4, ,029 0,836 2 Age (+1 over 40) 0,013 0,006 5, ,017 1,013 3 Gender (m=1/f=0) -0,275 0,121 5, ,023 0,759 4 Delay n hosptalsaton over 10 hours 0,362 0,118 9, ,002 1,436 5 Severe condton* 0,197 0,072 7, ,006 1,218 6 Charlson s ndex >=5 0,179 0,100 3, ,074 1,196 7 LVF <=0,3* 0,333 0,119 7, ,005 1,395 8 SBP >170* 0,321 0,185 5, ,023 1, Q 0,169 0,070 5, ,016 1, Heart arrest* 0,483 0,247 3, ,050 1, PCI, CABG -0,271 0,103 6, ,009 0, Trombolytc therapy -0,236 0,104 5, ,023 0,790 PSD dsperson parameter =0,305 *at hosptalzaton Columns headers are: estmate of regresson coeffcent; m standard error of regresson coeffcent estmate; 2 ch-square dstrbuton quntle servng test statstc on effect sgnfcance; df test s degrees of freedom; р ch-square test based sgnfcance of effect; RR relatve rsk. The man effect of nterest was mpact of health care reform, provng to be sgnfcant after adjustment for covarates (=- 0,179, р=0,029). By RR value (0,836), we can conclude that HCR decreased hazard of lethalty by 19,6%, that s [1/RR- 1]*100%. Takng nto consderaton organzatonal functonals mproved by HCR, t appeared that t s tmelness of treatment that was the crucal pvot n reducton of lethalty (hazard) n AMI patents. In case of delay wth hosptalzaton over 10 hours hazard experenced ncrease shft by 43,6%, that s [RR- ~ 69 ~ 1]*100%. ffectveness of thrombolytc therapy, PCI, CABG closely related to tmelness of admnstraton, frst hours from ncdent n partcular. Admnstraton of thrombolytc therapy n frst hours reduced basc rsk of lethalty by 26,6%, whle tmely performed PCI or CABG reduced hazard by 31,1%. It corresponds wth conclusons of other researches, ndcatng up to two-fold reducton wth dstnct age model,.e. maxmal reducton n younger patents groups, and even ncrease n

4 The Pharma Innovaton Journal hazard n patents aged above 70 [9, 10, 11, 12]. Severe patent s condton at hosptalzaton ncreased basc rsk of lethalty by 21,8%. Heavy comorbdty load (Charlson s ndex >=5) ncreased basc rsk of lethalty by 19,6% wth margnal sgnfcance р=0,074. Independent researches stpulated RR approachng 2 wth Charlson s ndex >=4 [13, 14]. That hgh RR values may be to some extend explaned by the lack of adjustment for the other mportant confounders. Low ejecton fracton (values <= 0,3%) at hosptalzaton ncreased basc rsk of lethalty by 39,5%. Values of systolc blood pressure more than 170 mm. Hg at hosptalzaton ncreased basc hazard by 37,8%. Other studes [8, 10, 14] arrved at the lkewse RR values wth typcal range 1,2-2,0. Presence of pathologcal Q related to ncreased rsk aganst basc hazard by 18,4%. Our fndngs concde wth other study ndcatng the range of RR typcalty from 1,15 to 1,30 [3, 8]. Heart arrest before or at hosptalzaton ncreased basc rsk of lethalty by 62,1% wth margnal sgnfcance р=0,05. As wth Charlson s ndex margnal sgnfcance related to low frequency of condtons. Obtaned value falls n lne wth publshed by other researchers gven suggested boundares of 1,2 1,8 [3, 8]. very next year of age after 40 ncreased rsk aganst basc hazard by 1,3% that agrees wth other studes range of 1,01 1,07 [8]. Females experenced hgher (by 31,7%) hazard aganst males ([1/0,759-1]*100%) that agan supported by other researchers [7, 8]. Therefore after adjustment on mportant clncal and bologcal confounders the mplementaton of the model of medcal care to patents wth acute myocardal nfarcton n the process of HCR proved to reduce basc hazard sgnfcantly. Stll the most effcent way to demonstrate treatment effect n survval terms s to buld up survval curves across cohorts. Besdes observed curves we have analyzed mpact of man components of HCR, that s mprovements n acceptablty and qualty of medcal care for AMI patents. We also made prognostcaton of the best survval outcomes assured by most ntensve (unbounded) mplementaton of HCR. Fgure 1 dsplays observed survval curves of the members of control and expermental cohorts (before and after HCR). Postve effect of HCR s obvous and determned by dfference n curves squares, that secures gan of 0,8788 months. It s tantamount to mprovement n survval of 100 AMI patents by 87,88 months n frst 5 years from the ncdence of dsease. Havng about 2000 cases annually n Vnntsa regon the mpact of HCR envsages gan of 1757,6 months n frst 5 years from the ncdence of dsease annually throughout the regon. Takng nto consderaton organzatonal functonals mproved by HCR, t s tmelness of treatment that was credted to be crucal n reducton of lethalty n AMI patents wth ncrease shft of 43,6% n case of delay wth hosptalzaton over 10 hours. ~ 70 ~

5 The Pharma Innovaton Journal That s why we bult up survval curves for control and expermental cohorts wth adjustment for tmelness of care and graphed them by Fgure 2. Obvously, mpact of HCR reduced substantally to almost ntangble 0,139 months of gan n frst 5 years from the ncdence of dsease. It consttutes only 15,8% of total HCR mpact. These percentages vrtually related wth mproved treatment. It stands to reason, that mplementaton of new doctrne n HCR s confned to resources, poltcal wll, communty and physcan support. Never do we have all flat out mplementaton. What we can do s to evaluate reserves to pursue n the frame of HCR. So we marked out maxmal possble benefts for AMI patents gven best possble scenaro dsplayed by Fgure 3. Accordng to predctons we envsage survval mprovement by 4,674 months of average gan per patent n frst 5 years from the ncdence of dsease. That s on-gong realzaton consoldates 18,8% only of the maxmal possble. ~ 71 ~

6 The Pharma Innovaton Journal All n all after adjustment on mportant clncal and bologcal confounders the mplementaton of the model of medcal care to patents wth acute myocardal nfarcton n the process of HCR n Vnntsa regon proved to reduce basc hazard sgnfcantly securng substantal gan n months of survval. stmators are safeguarded aganst bases due to unobservable factors by takng nto account fraltes. HCR effect (=-0,179, р=0,029) secures basc hazard reducton by 19,6%. Among all organsatonal functonals of medcal care t appeared that t s tmelness that of paramount mportance n hazard reducton n patents wth AIM. If patent was hosptalsed wth 10 hours delay or more basc rsk of lethalty ncreased by 43,6%. ffectveness of admnstraton of trombolytc therapy, PCI, and CABG closely related to tmelness of admnstraton, especally to frst hours. Admnstraton of trombolytc therapy n frst hours reduced basc rsk of lethalty by 26,6%, whle tmely performed PCI, and CABG reduced hazard by 31,1%. Severe patent s condton at hosptalzaton ncreased basc rsk of lethalty by 21,8%. All these covarates are tme related and bare ndrect evdence on mportance of tmelness of treatment. Further nvestgaton of survval curves revealed that mplementaton of the HCR saved addtonal 0,8788 survval months to average patent n frst 5 years from AMI ncdent that sum up to gan of 1757,6 months annually throughout the Vnntsa regon. It was unveled that man effect (84,2%) was related partcularly to mprovement n tmelness of medcal care. 4. Conclusons 1. The mplementaton of the model of medcal care to patents wth acute myocardal nfarcton n the process of HCR n Vnntsa regon proved to reduce basc hazard sgnfcantly securng substantal gan n months of survval. stmators are safeguarded aganst bases due to unobservable factors by takng nto account fraltes. HCR effect (=-0,179, р=0,029) secures basc hazard reducton by 19,6%. 2. Among all organsatonal functonals of medcal care t appeared that t s tmelness that of paramount mportance n hazard reducton n patents wth AIM. If patent was hosptalsed wth 10 hours delay or more basc rsk of lethalty ncreased by 43,6%. 3. ffectveness of admnstraton of thrombolytc therapy, PCI, and CABG closely related to tmelness of admnstraton, especally to frst hours. Admnstraton of thrombolytc therapy n frst hours reduced basc rsk of lethalty by 26,6%, whle tmely performed PCI, and CABG reduced hazard by 31,1%. Severe patent s condton at hosptalzaton ncreased basc rsk of lethalty by 21,8%. All these covarates are tme related and bare ndrect evdence on mportance of tmelness of treatment. Investgaton of survval curves revealed that mplementaton of the HCR saved addtonal 0,8788 survval months to average patent n frst 5 years from AMI ncdent that sum up to gan of 1757,6 months annually throughout the Vnntsa regon. It was unveled that man effect (84,2%) was related partcularly to mprovement n tmelness of medcal care. Journal of COPD 2012; 7: Bleecker R, Meyers DA, Baley WC, Sms AM, Bujac SR, Goldman M et al. ADRB2 polymorphsms and budesonde/formoterol responses n COPD. Chest 2012; 2(2): Schwabe K1, Vacca G, Dück R, Gllssen A. Glucocortcod receptor gene polymorphsms and potental assocaton to chronc obstructve pulmonary dsease susceptblty and severty. uropean Journal of Medcal Research 2009; Suppl 4: Sprometry for health care provders. Global Intatve for Chronc Obstructve Lung Dsease (GOLD), 2010, Global Intatve for Chronc Obstructve Lung Dsease. Global strategy for dagnoss, management, and preventon of chronc obstructve pulmonary dsease. (updated 2011) URL: ATS Statement: gudelnes for the sx-mnute walk test. Amercan journal respratory and crtcal care medcne 2002; 166: Cell BR, Cote CG, Marn JM, Casanova C, Montes de Oca M, Mendez RA et al. The body-mass ndex, arflow obstructon, dyspnea, and exercse capacty ndex n chronc obstructve pulmonary dsease. The New ngland Journal of Medcne 2004; 350(10): Martnez FD, Graves P, Baldn M, Solomon S, rckson R. Assocaton between genetc polymorphsms of the beta2-adrenoceptor and response to albuterol n chldren wth and wthout a hstory of wheezng. Journal Clncal Investgaton 1997; 100(12): Fleury I, Beauleu P, Prmeau M, Labuda D, Snnett D, Krajnovc M. Characterzaton of the BclI polymorphsm n the glucocortcod receptor gene. Clncal Chemstry 2003; 49(9): Turgut S, Turgut G, Atalay O. Genotype and allele frequency of human multdrug resstance (MDR1) gene C3435T polymorphsm n Denzl provnce of Turkey. Molecular Bology Reports 2006; 33(4): References 1. Bossé Y. Updates on the COPD gene lst. Internatonal ~ 72 ~