STATISTICAL ANALYSIS OF RISK FACTORS OF MALARIA RELATED IN-HOSPITAL MORTALITY: A CASE STUDY AT BUSHULO MAJOR HEALTH CENTER, HAWASSA

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1 Intrnatonal Journal of Latst Rsarch n Scnc and Tchnology Volum 4, Issu 5: Pag No32-42, Sptmbr-Octobr ISSN (Onln): STATISTICAL ANALYSIS OF RISK FACTORS OF MALARIA RELATED IN-HOSPITAL MORTALITY: A CASE STUDY AT BUSHULO MAJOR HEALTH CENTER, HAWASSA 1 Chala Gmchu Gut, 2 DrOChandraskhara Rddy, 3 Ayl Tay, 4 DrKVasudva Rao 1 Lcturr, Dpartmnt of Statstcs, Ambo unvrsty, Ethopa 2 Assocat Profssor, Ambo Unvrsty, Ethopa 3 Assocat Profssor and NORHED Projct Coordnator at Hawassa Unvrsty, Ethopa 4 Assstant profssor,dpt of Mathmatcs, Ambo Unvrsty,Ethopa Abstract- Malara s a major challng to publc halth and soco-conomc dvlopmnt worldwd and n sub Saharan Afrca n partcular It causs an stmatd 300 to 500 mllon cass and 15 to 27 mllon daths worldwd ach yar, of whch 80% of th cass and 90% of th daths occur n Sub-Saharan Afrca Th man objctv of ths study was to dntfy th rsk factors of malara rlatd nhosptal mortalty; so that modlng and smulatng th rlatd rsk factors Th data wr takn from hosptal rcords at Bushulo major halth cntr from Jun 2009 to Jun 2012, Hawassa From a total of 6594 laboratory confrmd malara postv n th halth cntr, a sampl of 539 patnts wr slctd usng stratfd random samplng tchnqu Th data wr analyzd usng th classcal logstc rgrsson and Baysan logstc rgrsson approachs In ths ffort th two approachs wr compard usng standard rrors of modl paramtrs Th rsults of th study showd that 785% of malara patnts wr found to b dschargd whl th rst 215% dd of malara n th halth cntr From Baysan smulaton analyss ag, rsdnc, tm from symptom onst to dagnoss, typ of malara spcs dagnosd, body tmpratur n th last dagnoss, malara complcatd, prgnancy cass, total lngth of stay n hosptalzaton, rfrral status and sason whn patnt dagnosd, wr found to b statstcally sgnfcant at 5% lvl of sgnfcanc Th classcal logstc rgrsson analyss could slct th frst ght of ths as sgnfcant prdctors Modl comparson also rvald that, th Baysan modlng approach has gvn stmats of th paramtrs wth smallr standard rror valus showng that, wth approprat choc of pror dstrbutons, th Baysan modlng approach mght lad to a mor accurat stmaton than th classcal approach It can b concludd from ths study that th most contrbutng rsk factors of malara rlatd n-hosptal mortalty n th halth cntr ar undr fv ag group, rural rsdnt, Pfalcprum typ of malara spcs, havng malara complcatd cass, longr tm (days) from symptoms onst to dagnoss, wt sason, hgh body tmpratur n th last dagnoss, womn of prgnancy cass, shortr tm (days) of stay n hosptalzaton Ky words: Baysan, Logstc rgrsson, Malara, Rsk factors, In-hosptal mortalty Bushulo 1 INTRODUCTION rports, approxmatly 70,000 popl d of malara ach 11 Background yar n Ethopa Malara s a vctor-born dsas causd by Plasmodum parasts Th parasts ar sprad to popl through th bts of nfctd Anophls mosqutos, calld "malara vctors It rmans to b a major challng to publc halth and sococonomc dvlopmnt worldwd and n sub Saharan Afrca n partcular It causs an stmatd 300 to500 mllon cass and 15 to 27 mllon daths worldwd ach yar, of whch 80% of th cass and 90% of th daths occur n Sub- Saharan Afrca (WHO, 2010) In Ethopa, t s also a ladng publc halth problm, whr 75 % of th country s land surfac s malarous and 68% of th populatons ar at rsk of malara nfcton (FMOH & ENMIS, 2011) Thus, malara s a publc halth concrn and all ag groups of th populaton ar vulnrabl Chldrn undr fv yars of ag and prgnant womn ar gnrally consdrd to b at a hghr rsk In 2009, malara was stll th frst ladng caus of halth problm accountng for 48% of out patnt consultatons, 25% admssons and 296% npatnt daths (MOH, 2009) Accordng to th MOH Nowadays, although malara daths do not occur as oftn as prvously, t stll rmans a major publc halth problm and t s too arly to rach any frm concluson about th possblty of achvng MDGs, bcaus of rsstanc of th parast to antmalaral drugs, th complxty of dsas, xpnsvnss of th control program, sasonal varablty natur of th dsas (WHO, 2010) In SNNPR, th hgh transmsson sason of malara cass usually gos from August to Dcmbr (Sharg t al, 2010) Evn though, thr s a lttl rducton of dath cass, th rsults of th survy as wll as th routn survllanc data dmonstratd that malara contnus to b a sgnfcant publc halth challng and a major publc halth problm n Hawassa (Sharg t al, 2010) Howvr, masurng malara burdn n a populaton s a challng n most dvlopng countrs, bcaus most dsas ncdncs and daths occur outsd of th formal halth car, partcularly at hom (Lawrnc t al, 2011) Instad, routn hosptal data provd a proxy for masurng th ncdnc of svr malara and for stmatng ISSN:

2 mortalts or quvalnt clncal ndcators (Lawrnc t al, 2011) In spt of th fact that, varous malara rlatd cass or ssus ar assssd n Hawassa, on of whch has hgh malara prvalnc rats n Ethopa, thr has bn no Baysan modlng don so far about rsk factors of malara rlatd n-hosptal mortalty That s th motvaton to undrtak ths study basd on n-hosptal mortalty data collctd at Bushulo major halth cntr covrng a prod from Jun 2009 to Jun 2012 yars among patnts of laboratory confrmd malara postvs n th halth cntr 12 Statmnt of th Problm Evn though, th currnt malara survllanc stmats ndcat som ncouragng sgns n that th pdmc s stablzng, t rmans a major publc halth problm and nfctons wth ths parast can b crtcal and whch lads to dath Ths may b du to th fact that th parast changs to complcatd cass, sasonal varablty natur of th vctor dsas and rsstant to ant malaral drugs and ts on of th ladng causs of dath n hosptals and halth cntrs admssons (Ldrbrg and Oaks, 2012) It s known that, masurng malara burdn n a populaton s a challng n rsourc poor countrs lk Ethopa Bcaus most dsas ncdncs and daths occur outsd of th formal halth car, partcularly at hom Instad, routn hosptal data provd a proxy for masurng th ncdnc of svr malara and for crudly stmatng morbdty rats or quvalnt clncal ndcators (Alxandr and Patrck, 2012) Dtrmnng th major factors that may affct malara rlatd n-hosptal mortalty s mportant to dsgn bttr stratgy and ultmatly mprov th car provdd or tratmnt condton at all lvls of halth car (Lawrnc t al, 2011) Furthrmor, th Baysan modl approach whch s a powrful statstcal mthod n mdcal rsarchs, n modlng and smulatng malara rlatd hosptal mortalty usng routn hosptal data has bn not yt addrssd n ths country On account of ths, th mthodologcal framwork s usd to provd a usful tool for analyzng th data at hand and of smlar structur So, ths study s ntndd to modlng and smulatng th rsk factors of malara rlatd n-hosptal mortalty Accordngly, th cntral rsarch quston of ths study s whch factors hav th major rsk factors of malara rlatd mortalty at Bushulo major halth cntr? 13 Objctvs of th Study Th gnral objctv of ths study s modlng th rsk factors of malara rlatd n-hosptal mortalty at Bushulo major halth cntr Spcfc Objctvs: Spcfc objctvs of th study ar: To dntfy th rsk factors of malara rlatd mortalty at Bushulo major halth cntr To dvlop Baysan logstc rgrsson modl and Smulat th chanc of dschargd/dath status of laboratory confrmd malara postv patnt To compar th Classcal and Baysan logstc rgrsson approach n paramtr stmaton of th modl Intrnatonal Journal of Latst Rsarch n Scnc and Tchnology To provd nformaton for polcy makrs and rsarchrs 14 Sgnfcanc of th Study Th outcom of th rsarch wll hlp halth car workrs to nform patnts about th rlatd rsk factors of dath thy mght ncountr Morovr, clncans can dcras mortalty among malara postvs by arly dagnoss and approprat ntrvnton Th rsult of th study mght ultmatly mprov th car provdd at all lvls of halth car to assst n montorng and plannng rsourc nds n a halth systm and dsgnng approprat ntrvntons, talord towards communts at hgh rsk and nabl clncans and polcy makrs to nhanc th awarnss of th socty about factors whch ncras th probablty of dath n- hosptal of malara patnts Furthrmor, th rsult of ths study can also b usd as a sourc of nformaton to othr rsarchrs for furthr study to dntfy mportant rsk factors of malara rlatd n-hosptal mortalty 2 METHODOLOGY 21 Data Th study s rtrospctv, whch was rtrvd from th patnt cards of malara postvs So n ths study, th data wr obtand from rcord rvws of all npatnt malara cass of laboratory confrmd malara postv admttd to th pdatrc ward from Jun 2009 to Jun 2012 Data wr collctd n Octobr 2012 usng a structurd format and carrd out by numrators to gt avalabl nformaton for ths study Thus, n ths rsarch w us scondary data whch was collctd from patnt admsson card of laboratory confrmd malara postvs and a total of 6594 patnts ar rcordd as confrmd malara postv from 2009 to Jun 2012 n Bushulo major halth cntr 22 Samplng Dsgn and Samplng Procdurs Th targt populaton for ths study was rcordd patnts of laboratory confrmd malara postv at Bushulo Major Halth Cntr from Jun 2009 to Jun 2012 Th 6594 patnts who wr laboratory confrmd malara postv wr takn as th populaton of th study In ths study, stratfd random samplng mthod was adoptd as an approprat samplng dsgn for slctng a rprsntatv sampl of laboratory confrmd malara patnts Ths wr stratfd nto two strata basd on thr plac of rsdnc (urban and rural) So that th rqurd sampl sz for th study was dtrmnd from ach stratum Hnc th dvsons /stratfcatons of a populaton ar: Stratum 1: Patnts who ar laboratory confrmd malara postvs n th halth cntr from urban rsdnc wth populaton sz N 1 and sampl sz n 1 Stratum 2: Patnts who ar laboratory confrmd malara postvs n th halth cntr from rural rsdnc wth populaton sz N 2 and sampl sz n 2 Lt N= N 1 + N 2 b total numbr of laboratory confrmd malara patnts admttd to th major halth cntr and ISSN:

3 n=n 1 +n 2 b total sampl sz of patnts that was usd n th study Intrnatonal Journal of Latst Rsarch n Scnc and Tchnology th patnt dschargd of malara postv undr laboratory confrmd 23 Sampl Sz Dtrmnaton In spt of th fact that, thr ar svral formulas dvlopd for sampl sz calculaton that conform to dffrnt rsarch stuatons, th sampl sz dtrmnaton tchnqus for ths study s basd on stratfd random samplng tchnqus In stratfd random samplng, a sampl s drawn from ach stratum of th populaton of whch s assumd to b dvdd nto subpopulatons /strata accordng to a spcfc charactrstc Th sampl sz dtrmnaton formula that s adoptd n ths study s dscrbd as follows (Cochran, 2007): n N L 1 2 d 2 2 N 2 p ( 1 W Np p ) ( 1 p ) Z whr, n = th sampl sz ndd, N = th total populaton sz, Z á = Standard normal dstrbuton that corrspond to th á lvl of confdnc, p= th probablty of dyng of malara n hosptal n th stratum (), d = th lvl of prcson, L= th total numbr of strata(urban and rural rsdnc), N = th sz of stratum (), whch s th sz of th populaton n ach rsdnc and th stratum wght, W = th stmatd proporton of N to N Accordng to Msganaw t al (2011) 241% n-hosptal dath was du to malara at Butajra Hosptal, SNNP Rgon Thrfor, p=0241 was takn as th probablty of dath du to malara n ach stratum Th samplng rror s calld lvl of prcson n samplng contxt dnotd by d gvs th rsarchr som da rlatng to th accuracy of th statstcal stmat Th lvl of prcson takn for ths study was 35% (, d= 0035) Th lvl of confdnc that s usd n ths study was 95% In ths study th total populaton N=6594, th lvl of prcson, d=0035, th probablty of dyng du to malara nhosptal, p=0241, lvl of sgnfcanc, =005 wr usd as nputs to comput sampl sz Th total rqurd sampl sz was 539 Th halth cntr gvs srvc for both urban and rural rsdnc, whch was consdrd to b strata for ths study Th sz of th sampl n ach stratum was dtrmnd basd on approprat sampl sz allocaton to ach stratum In ths study proportonal allocaton mthod wr usd to yld 284 and 255 from urban and rural stratas rspctvly Fnally, usng patnt s admsson cards of thr unqu dntfcaton numbr from ach rsdnc a smpl random sampl of laboratory confrmd malara patnts was slctd from ach stratum Th Indpndnt Varabls Th xplanatory varabls that ar ncludd n th study and assumd to b rsk factors of malara rlatd mortalty n th major halth cntr ar prsntd n Tabl Mthod of Statstcal Analyss In ths study, snc th rspons varabl s a dchotomous varabl, that s dschargd/dath status of patnts (dschargd =0 or dath =1) so th ffct of xplanatory varabls on th dpndnt varabl can b nvstgatd usng logstc rgrsson modl that can b formulatd undr th classcal or th Baysan st up Both approachs ar consdrd n ths study 251 Classcal Logstc Rgrsson Modl Logstc rgrsson analyss xtnds th tchnqus of multpl rgrsson analyss n whch th outcom varabl s catgorcal It s usd whn th dpndnt varabl s dchotomous (bnary), such as (dschargd or dd, prsnc or absnc, succss or falur, and tc) logstc rgrsson s usd (Stphnson, 2010) Thr ar two man uss of logstc rgrsson: Frstly, t s usful to prdct th group mmbrshp Snc logstc rgrsson calculats th probablty of succss ovr th probablty of falur, th rsults of th analyss ar n th form of an odds rato Scondly, t xplans th rlatonshps and strngths among th varabls Tabl 21: Lst of Varabls wth thr Cods and Dscrptons 24 Varabls n th Study Th varabls ncludd n th study wr slctd basd on som prvous studs and thos that ar xpctd to b rsk factors/dtrmnants of malara rlatd n- hosptal mortalty Th Dpndnt Varabl Th rspons or dpndnt varabl n ths study s th bnary rspons varabl whch s namd as Dschargd/Dath status of patnts lvld as whthr prsons dd of malara n hosptal or not Ths status of patnt s codd as 1, f th patnt dd n hosptal and 0, f 252 Modl Dscrpton Snc th rspons varabl n ths study s dchotomous and w wll dnot t as Y, and dnot th vnt Y=1, whn th subjct has th charactrstc of ntrst and Y=0, whn ISSN:

4 th subjct dos not hav that charactrstc of ntrst In logstc rgrsson, a sngl outcom varabl Y (=1,,n) follows a Brnoull probablty functon that taks th valu 1 wth probablty of succss p or th valu 0 wth probablty of falur 1-p Th bnary logstc rgrsson modl s dscrbd as follows Lt Y nx1 b a dchotomous outcom random varabl wth catgors 1 (dd n hosptal) and 0 (dschargd) Lt nx (k+1) dnot th collcton of k- prdcator varabls of Y, whr n n 2 s calld rgrsson matrx and wthout th loadng column of 1 s s trmd as prdctor data matrx Thn, th condtonal probablty that a malara patnt dd n hosptal gvn th st of prdctor varabls s dnotd by P(Y =1/ ) =p Thn p can b xprssd n th form: 0 P 1 x x 1 1 x x o 1 1 k k k k Intrnatonal Journal of Latst Rsarch n Scnc and Tchnology th maxmum lklhood functon of Y s gvn by: k 2 k nk ( 1) Whr: â = (k+1) x1 vctor of unknown paramtrs and x = (1, x 1,, x k ), =1, 2,, n Howvr, th rlatonshp btwn th prdctor and rspons varabls s not a lnar functon n logstc rgrsson; nstad, th logarthmc transformaton of quaton ylds th lnar rlatonshp btwn th prdctor and rspons varabls So an altrnatv form of th logstc rgrsson quaton s th logt transformaton of P gvn as follows: Th coffcnts can b ntrprtd as th chang n th logodds assocatd wth a on unt chang n th corrspondng ndpndnt varabl kpng th othr varabls constant or th odd ncrass multplcatvly by for vry on unt chang ncras n x 253 Paramtr Estmaton for th Bnomal Logstc Rgrsson Th maxmum lklhood stmaton s th most computng stmaton mthods usd n fttng logstc rgrsson modl (Hosmr Lmshow, 2011) Hnc, n ths study th maxmum lklhood stmaton tchnqu wll b appld to stmat paramtrs of th modl Consdr th logstc modl P, snc obsrvd valus of Y say, Y s 1 (=1, 2,,n) ar ndpndntly dstrbutd as bnomal and, Th fact that th paramtrs o, 1,, k and stmats of P for ach subjct could b facltatd by th wdly avalabl Statstcal softwar such as SAS, SPSS, STATA, GLIM and WnBUGS But n ths study SPSS and WnBUGS softwars wr usd 254 Baysan Logstc Rgrsson Modl Baysan modlng s concrnd wth gnratng th postror dstrbuton of th unknown paramtrs gvn both th data and som pror dnsty for th unknown paramtrs Baysan modlng approach provds a much mor complt pctur of th uncrtanty n th stmaton of th unknown paramtrs, spcally aftr th confoundng ffcts of nusanc paramtrs ar rmovd (Drapr, 2008; L, 2010; Tannr, 2011) Suppos w obsrv a random varabl Y and assum th paramtr â s random varabl havng pror dstrbuton f () Th condtonal probablty dstrbuton of th postror probablty dstrbuton functon s dfnd as: whr f(y) = f (y ) f ( )d s a normalzng constant 255 Baysan Infrnc for Logstc Rgrsson Paramtrs A computatonally tractabl Baysan nfrnc for logstc rgrsson modls wth paramtrc lnk s drvd utlzng a Markov Chan Mont Carlo algorthm to smulat from th jont postror dstrbuton of th rgrsson and th lnk paramtr Classcal statstcal nfrnc s basd on maxmum lklhood stmaton Maxmum lklhood stmaton chooss th paramtrs that maxmz th lklhood of th data, and s ntutvly appalng In maxmum lklhood stmaton, paramtrs ar assumd to b unknown but fxd, and ar stmatd wth som confdnc Instad of consdrng just a sngl valu for a modl paramtr, as don by maxmum lklhood stmaton, t s known that Baysan approach provds a vry dffrnt approach to th problm of unknown modl paramtrs n that th uncrtanty about th unknown paramtrs s quantfd usng probablty dstrbutons so that th unknown paramtrs ar rgardd as random varabls 256 Lklhood Functon Th lklhood functon of th Baysan formulaton for n ndpndnt Brnoull tral s gvn by, lt y 1, y 2,, y n b ndpndnt wth succss probablts P 1, P 2, P 3,, P n, that s Y = 1 wth probablty P or Y =0 wth probablty 1- P, for = 1,2,,n Th lklhood contrbuton from th th subjct s gvn by: ISSN:

5 Intrnatonal Journal of Latst Rsarch n Scnc and Tchnology w know that, n quaton (1) th probablty of succss wrttn as: P 0 1 x 1 o 1 x 1 1 k x k k x k Whr: P = th probablty of th patnt has dd of malara n-hosptal and th lklhoods functon ovr a data st of subjcts s: 257 Pror Dstrbuton Exstng vdnc about th paramtrs of ntrst may b avalabl from arlr studs or from xprts opnons and can b formalzd nto what s calld pror dstrbuton of th paramtr of ntrst A pror dstrbuton can b non nformatv, nformatv, or vry nformatv Non nformatv pror dstrbutons ar usd n cass n whch no xtra-sampl nformaton s avalabl on th valu of th paramtrs of ntrst (Clark t al, 2002 and Mla t al, 2003) Informatv pror dstrbutons ar usd whn som pror knowldg about th paramtrs of ntrst s avalabl, such as whn xstng blf or vdnc ndcats that a paramtr should tak a valu wthn a rang Formally, ths knowldg s rprsntd wth a dstrbuton that has a known man and larg varanc Vry nformatv pror dstrbutons ar usd whn vry strong pror knowldg about th paramtrs of ntrst should b a spcfc valu In statstcal trms, ths knowldg can b rprsntd wth a dstrbuton that has a known man and small varanc So a crtcal fatur of any Baysan analyss s th choc of a pror Th choc can nclud also nformatv pror dstrbutons f somthng s known about th lkly valus of th unknown paramtrs 0, 1,, k or non-nformatv prors f thr lttl s known about th coffcnt valus or f on wshs to s what th data thmslvs provd as nfrncs On may prfr to provd pror nformaton on th oddsrato=xp () scal, and transform back to th logstc scal For ths purpos, w wll us th most common prors for logstc rgrsson paramtrs, whch ar of th 2 form: j N j, j ~ Ths mpls th normal dstrbuton wth man ì j and wth varanc ó 2 j It can b xprssd as follows: 258 Postror Dstrbuton Gvn th lklhood of logstc rgrsson and th pror dstrbuton gvn abov, th postror dstrbuton of th Baysan logstc rgrsson modl s drvd by multplyng th pror dstrbuton ovr all paramtrs by th full lklhood functon W can wrt postror dstrbuton as: In ths study, th lklhood functon s basd on th data st that was obtand from a rvw of patnt cards of laboratory confrmd malara patnts n Bushulo major halth cntr In rgard to pror dstrbutons for modl paramtrs, non nformatv pror dstrbutons of th typ gvn abov wr usd Computng th stmat of â of th postror dstrbuton may b dffcult; on account of ths, w nd to us non analytc mthod such as smulaton tchnqus Th most popular mthod of smulaton tchnqu s th Marcov Chan Mont Carlo (MCMC) mthods and that was appld n ths study 259 Markov Chan Mont Carlo (MCMC) Mthods A major dffculty towards mor wdsprad mplmntaton of Baysan approachs s that obtanng th postror dstrbuton oftn rqurs th ntgraton of hgh dmnsonal functons MCMC mthods ar attmptd to smulat drct draws from som complx dstrbuton of ntrst such as postror dstrbuton A popular way of smulatng from a gnral postror dstrbuton s by usng MCMC mthods Markov Chan Mont Carlo tchnqus nabl quanttatv rsarchrs to us hghly complcatd modls and stmat th corrspondng postror dstrbutons wth accuracy In ths way, MCMC mthods hav gratly contrbutd to th dvlopmnt and propagaton of Baysan thory Smulaton can also b usd to stmat and vsualz th postror dstrbuton of f ( y) tslf Th man problm n th abov mntond procdur s how to gnrat from th postror dnsty f (ß y) random sampl Th opraton of a Marcov Chan untl t rachs ts statonary dstrbuton s xactly th procss mployd n MCMC Gnrally th most commonly usd MCMC tchnqus ar Mtropols-Hastng and Gbbs samplr algorthm In ths study w gv th dtals of Gbbs samplr algorthm as follows 2510 Th Gbbs Samplng Algorthm Th Gbbs samplr (Gman and Gman 2009) s most wdly us MCMC tchnqu On advantag of th Gbbs samplr s that, n ach stp, random valus must b gnratd from unvarat dstrbutons for whch a wd varty of computatonal tools xsts (Glks t al, 2011) In spt of th fact that thr ar dffrnt wdly avalabl Softwar for Baysan statstcal nfrnc such as Wn BUGS/BUGS, Bays, R, BACC, but n ths study Wn BUGS/BUGS and R softwar was mplmntd Th Gbbs samplr algorthm was mplmntd by samplng th st of full condtonal dstrbutons or up on n turn from th k- condtonal postror dstrbutons as follows: It s ssntal that thr b a dfnabl condtonal statmnt for ach coffcnt n th â vctor and compltly artculatd so that t s possbl to draw sampls from th dscrbd dstrbuton Ths rqurmnt facltats th tratv natur ISSN:

6 of th Gbbs samplng algorthm dscrbd and statd as follows: Convrgnc of th Algorthm Th mprcal rsults from a gvn MCMC analyss ar not dmd rlabl untl th chan has rachd ts statonary dstrbuton On account of ths, th trm convrgnc of an MCMC algorthm rfrs to whthr th algorthm has rachd ts qulbrum (targt) dstrbuton If ths s tru, thn th gnratd sampl coms from th corrct targt dstrbuton Hnc, montorng th convrgnc of th algorthm s ssntal for producng rsults from th postror dstrbuton of ntrst Convrgnc dagnoss was adoptd Varabl Intrnatonal Journal of Latst Rsarch n Scnc and Tchnology to answr th quston of how to dtrmn whthr th samplr has rachd ts statonary dstrbuton (Albrt, 2010) Tsts for Convrgnc Dagnostcs Gnrally t s unclar how much w must run an algorthm to obtan sampls from th corrct targt dstrbutons Svral dagnostc tsts hav bn dvlopd to montor th convrgnc of th algorthm Among svral ways, th most popular and straght forward convrgnc assssmnt mthods ar Autocorrlaton, Tm srs plots, Glman- Rubn statstc, and Dnsty plot 3 RESULTS AND DISCUSSION 31 Rsults 311 Dscrptv and Tst of Assocaton Rsults Th data wr obtand from rcords of 539 patnts who wr laboratory confrmd malara postv n-patnts durng Jun 2009 to Jun 2012 Th rsults dsplayd n Tabl 1 shows prcntags and counts of dschargd/dath status of patnt wth rspct to th xplanatory varabls Out of th 539 patnts consdrd, 423 (785%) patnts wr dschargd whl 116 (215%) wr dd Th assocaton btwn th outcom varabl and ach prdctor of th varabls wth ch-squar and lklhood rato tsts, frquncy dstrbutons of ach catgory of prdctor varabls was ncludd n dtal n Tabl 1 Tabl 1: Tst of Assocaton btwn Dschargd/Dath Status and Explanatory Varabls Catgory Dschargd/dath status Dscharg Dath Count % Count % Total Count % Ch-squar (Sg) LR (Sg) Sx of patnt Mal Fmal (0152) < Ag of patnt (0000) Rsdnc of patnt Urban Rural (0000) Sason whn patnt Dry dagnosd (wt or dry) Wt (0016) P Falcprum Typ of malara P Vvax (0000) spcs dagnosd Mxturd Rfrral status No Ys (0002) Tm from symptom < 3 days onst to dagnoss 3-5 days (0000) (days) > 5 days Body tmpratur n ( C) th frst dagnoss ( C) 41 ( C) (1476) ( C) Body tmpratur n ( C) th last dagnoss ( C) (0000) 41 ( C) Malara complcaton No Ys (0000) Prgnancy cass No Ys (0000) < 3 days Total lngth of stay n days hosptalzd(days) (0000) > 5 days Tratmnt gvn Qunn (drugs) Chloroqun (0045) 3795 (0151) (0000) (0000) 4454 (0015) (0000) (0001) (0000) 3127 (1477) (0000) (0000) (0000) (0000) (0042) ISSN:

7 312 Bnomal Logstc Rgrsson Analyss It was shown abov Tabl 1 that out of thrtn catgorcal prdctor varabls, only two prdctor varabls, namly sx of patnt and body tmpratur n th frst dagnoss hav no sgnfcant assocaton n th rspons Elvn prdctor varabls hav sgnfcant assocaton wth th rspons varabl But usng multpl logstc rgrssons by th Forward Stpws (Lklhood Rato) mthod n SPSS, only ght prdctor varabls wr slctd by th modl Ths ar ag of patnt, rsdnc of patnt, typ of malara spcs dagnosd, tm from symptom onst to dagnoss (days), body tmpratur n th last dagnoss ( C), Intrnatonal Journal of Latst Rsarch n Scnc and Tchnology malara complcatd, prgnancy cass and total lngth of stay n hosptalzaton (days) contrbutd sgnfcantly to th Dschargd/Dath status of patnts wth p-valu, 0034, 0001, 0000, 0009, 0000, 002, 0038, and 0019 whch s lss than lvl of sgnfcanc, = 005, rspctvly (S Tabl 2 ) W not that th xp(ˆ ) whch s also calld odds multplr or odds rato, n Tabl 2 column prsnts th xtnt to whch rasng th corrspondng masur by on unt nfluncs th odds rato Tabl 2: Varabls n th Fnal Logstc Rgrsson Modl (Bushulo Major Halth Cntr, Oct 2012) 950% CI for Prdctor Varabl ˆ SE(ˆ ) Wald Df Sg Exp(B) Exp(B) Lowr Uppr Ag(Rf) Ag(1) Ag(2) Ag(3) Rsd(1) Typmalaspcdag(Rf) Typmalaspcdag(1) Typmalaspcdag(2) Tmsymptodag(Rf) Tmsymptodag(1) Tmsymptodag(2) Bodytmplastdag(Rf) Bodytmplastdag(1) Bodytmplastdag(2) Malcomp(1) Prgncas(1) TLS(Rf) TLS(1) TLS(2) * Rf; n th brackts ndcats th rfrnc catgory for ach prdctors W can ntrprt Exp ( ˆ ) as changs n odds If th valu xcds 1 thn th odds of succss occurrng ncras (dath du to malara ); f th valu s lss than 1, any ncras n th prdctor varabls lads to a drop n th odds of dyng Th rsults n Tabl 2 show that th valus of th odds rato ntrprtaton of ag catgorzd as < 5, 5-14, and 45 yars Th patnt of 5-14 ag group was 0159 tms lss lkly to d of malara than th rfrnc catgory (< 5 yars) patnt Also for ndvduals n th ag group yars and 45 yars th odds of dyng of malara s 0216 and 0125 tms lss lkly than for undr fv chldrn ag (th rfrnc catgory) rspctvly Ths mpls that, dath to malara s hgh for thos n th ag group of lss than fv yars Whn w com to s th odds rato of rsdnt of patnt, t s catgorzd as urban and rural Apparntly, th rsults shown that th odds of dath du to malara for rural rsdnt ar 4989 tms mor lkly than for patnts from urban aras and othr rsults ar ntrprtd accordngly 313 Baysan Logstc Rgrsson Analyss Th Baysan logstc rgrsson modlng wr usd to mak nfrnc and th Gbbs samplr algorthm was mplmntd wth tratons n thr dffrnt chans, burn-n trms dscardd, so that th tratons ar sampld from th full postror dstrbuton Th modl dntfd thos all ght sgnfcant varabls (n classcal logstc rgrsson mthod) and addtonal two prdctor varabls as havng sgnfcant mpact on malara npatnt dschargd/dath status (s Tabl 3) Th algorthm uss dffrnt convrgnc tsts and th convrgnc of th chan can b ntally chckd vsually usng trac plots and MC rror n comparson to ts postror standard rrors (Ioanns, 2009 and Glman, 2005) Tm srs plot: Th tm srs plot n Baysan smulaton ndcats a good convrgnc whr thr ndpndntly gnratd chans wll mx togthr or ovrlappd and th Wn BUGS packag gvs th plot wth traton numbr on th - ISSN:

8 axs and paramtr valu on th Y-axs for ach prdctor varabls (S Fgur 1) Intrnatonal Journal of Latst Rsarch n Scnc and Tchnology Glman Rubn Statstc: Glman-Rubn convrgnc statstc wth wdth of th poold runs grn, th avrag wdth of wthn th ndvdual runs blu and thr rato rd rato clos to 1 so that t s an ndcaton of convrgnc (s n Fgur 3) Fgur 3: Convrgnc usng Glman-Rubn Statstc Plots for th Baysan Smulatons of Postror Dstrbuton of th Modl Paramtrs for Slctd Prdctors Dnsty plot: Th plots for most prdcator varabls ndcat th coffcnt has normal dstrbutons (bmodal dnsty) and hnc th smulatd paramtr valu ndcats convrgnc (s Fgur 4) Fgur 1: Convrgnc of Tm Srs Plots for th Baysan Smulatons of Postror Dstrbuton of th Modl Paramtrs for Slctd Prdctors Autocorrlaton Plot: Th plots show that th thr ndpndnt chans wr mxd or ovrlappd wth ach othr and pass out for hghr lags and hnc ths s an vdnc of convrgnc (S n Fgur2) Fgur 2: Convrgnc of Autocorrlaton Plots for th Baysan Smulatons of Postror Dstrbuton of th Modl Paramtrs for Slctd Prdctors Fgur 4: Convrgnc of Dnsty Plots for th Baysan Smulatons of Postror Dstrbuton of th Modl Paramtrs for Slctd Prdctors 314 Assssng Accuracy of Baysan Smulaton If th Mont Carlo rror valu n MCMC algorthm of Baysan smulaton s low n comparson to ts postror standard rror, thn th postror dnsty s stmatd wth accuracy Espcally, to hav accurat postror stmats th smulaton should b run untl th Mont Carlo rror for ach paramtr of ntrst s lss than about 5% of ts postror standard rror, snc small valus of MC rror wll ndcat that w hav calculatd th quantty of ntrst wth prcson and hnc vdnc for accuracy of postror stmat s accomplshd In Tabl 3, MC rror for ach sgnfcant prdctor s lss than 5% of ts postror standard rror Ths mpls convrgnc and accuracy of postror stmats ar attand and th modl s approprat to stmat postror statstcs also th 95% confdnc ntrvals of paramtrs do not contan zro ISSN:

9 Intrnatonal Journal of Latst Rsarch n Scnc and Tchnology Tabl 3: Summary Statstcs of th Postror Dstrbuton of th Modl Paramtrs Nod Man( ˆ ) SE( ˆ ) MC rror 95% CI Lowr Uppr bag bbody tmpn last th dag bmalara complcatd bprgnancy cass brsdnc brfrral status bsason whn patnt dag btotal lngth of stay n hosptalz btyp of malara spcs dag btm from symptom Modl Comparson For modl comparson purposs, th rsults of th tchnqus that usd to compar Baysan and classcal logstc rgrsson analyss wr dsplayd n Tabl 4; SE B and SE C stands for standard rror of Baysan and classcal mthods, rspctvly So w can say that th Baysan logstc rgrsson modl to gnrat th postror dstrbuton of th unknown paramtrs usng MCMC smulaton tchnqu can b mor prfrabl than th classcal logstc rgrsson mthod Tabl 4: Th Modl Comparson Basd on Standard Error (Bushulo Major Halth Cntr, Oct 2012) Varabls Classcal logstc rsults Baysan logstc rsults Man( ˆ ) SE C ( ˆ ) ( ˆ ) SE B ( ˆ ) SE Comparson Ag of patnt SE B < SE C Rsdnc of patnt SE B < SE C Rfrral status SE B < SE C Sason whn patnt dagnoss SE B < SE C Malara complcatd SE B < SE C Tm from symptom to dagnoss SE B < SE C Typ of malara spcs dagnoss SE B < SE C Body tmp n th last dagnoss SE B < SE C Prgnancy cass SE B < SE C Total lngth of stay n hosptalzaton SE B < SE C 32 Dscusson Ths study attmptd to modlng and smulatng th rsk factors of malara rlatd n-hosptal mortalty at Bushulo Major Halth Cntr, Hawassa Th rsults of th study showd that, out of a sampl of 539 patnts hosptalzd for malara from Jun 2009 to Jun 2012, 785% wr patnt dschargd whl 215 % wr patnt dd of malara In th Baysan approach of logstc rgrsson modl th Gbbs samplr algorthm wth Wn BUGS softwar was mplmntd wth tratons n thr ndpndnt dffrnt chans, burn-n trms wr dscardd, so as to obtan sampls from th full postror dstrbuton Th Baysan smulaton of logstc rgrsson dntfd tn prdctor varabls, ncludng all ght sgnfcant varabls n classcal approach and two othrs Th fact that th varabls rfrral status and sason whn patnt has bn dagnosd com out to b sgnfcant n th Baysan approach, but not n th classcal approach s n ln wth th studs conductd by Lawrnc t al (2011) n Zomba dstrct hosptal n Malaw and Bachou t al (2011) n Mulago hosptal n Uganda and Guyatt t al (2010) n Knya, wr found to b th major rsk factors of malara patnt dscharg/dath status Th Baysan logstc rgrsson approach took mor prdctor varabls than th classcal approach To hav accurat postror stmats, th smulaton was run untl th Mont Carlo rror for ach paramtr of ntrst s lss than 5% of ts postror standard rror, and hnc vdnc for accuracy of postror stmats n Baysan smulaton of logstc rgrsson s accomplshd In ths study MC rror for ach sgnfcant prdctor was found to b lss than 5% of ts postror standard rror Ths mpls convrgnc and accuracy of postror stmats of th Baysan smulaton wr attand As w can s n th Tabl 4 n Baysan approach th standard rror valus for tn prdctor varabls wr lss than that of classcal approach So w can say that Baysan approach mght lads to a bttr accurat stmaton than th classcal on ISSN:

10 Fnally, n ths study usng Baysan modlng and smulaton of MCMC algorthm, smlar rsults for ag of patnt, rsdnt of patnt, malara complcatd, typ of malara spcs dagnosd and total lngth of stay n hosptalzaton hav sgnfcant mpact and rlatonshp wth malara patnt dscharg/dath status as study n Zomba dstrct hosptal n Malaw by Lawrnc t al (2011) Th rsults for tm from symptom onst to dagnoss, wr also smlar wth th study rportd n Ethopa by Msganaw t al (2011) and n Uganda by Bachou t al (2011) and also for prgnancy cass th rsult confrms wth th study by Nwman t al (2008) n Ethopa Smlar rsults wr also rportd n arlr studs n South Afrca n St Augustns Hosptal, wr found that body tmpratur of patnt n th last dagnoss wr sgnfcant to th rsk of malara patnt dath (Zungu t al, 2011) 4 CONCLUSIONS AND RECOMMENDATIONS 41 Conclusons Among th sampls consdrd for th study, th dath rat du to malara was stmatd to b 215% Th halth status of malara patnts at th cntr was found to b sgnfcantly assocatd wth ag of patnt, rsdnc of patnt, sason whn patnt dagnosd, typ of malara spcs dagnosd, rfrral status, tm from symptom onst to dagnoss (days), body tmpratur n th last dagnoss ( C), malara complcaton, prgnancy cass, total lngth of stay n hosptalzaton (days) and tratmnt gvn Factors lvls wth hghr rsk to dath du to malara n th halth cntr wr found to b: undr fv ag group, rural rsdnt, Pfalcprum typ of malara spcs dagnosd, longr tm (days) from symptoms onst to dagnoss, havng malara complcatd cass, hgh body tmpratur n th last dagnoss, womn of prgnancy cass, and shortr tm (days) of stay at th cntr Morovr, th stmats of th paramtr valu of standard rrors n Baysan approach wr found to b smallr than that of th classcal mthod and also, mor prdctor varabls wr slctd by th modl n Baysan approach than n th classcal mthod Fnally, w conclud that th applcaton of Baysan logstc rgrsson modl to gnrat th postror dstrbuton of th unknown paramtrs gvn both data and pror dnsts of th unknown paramtrs usng MCMC smulaton tchnqu partcularly, Gbbs samplr mght lad to a mor accurat stmaton than th classcal logstc rgrsson mthod 42 Rcommndatons To mnmz th rsk of dyng n hosptal du to malara, halth workrs should b cautous whn a patnt has a complcatd malara cass, hgh body tmpratur n th last dagnoss and laboratory confrmd plasmodum falcprum typ of malara spcs Whn ths s th cas approprat clncal and spcal attnton should b gvn For th populaton at rsk of malara dath partcularly th most vulnrabl groups, chldrn undr 5 yars of ag and prgnant womn spcal attnton should b gvn lk arly dtcton and prompt dagnoss Intrnatonal Journal of Latst Rsarch n Scnc and Tchnology Morovr, patnt from rural rsdnts ar partcularly at hgh rsk of dath than patnts from urban rsdnts hosptalzd n th halth cntr In ordr to addrss ths problm, govrnmntal and non-govrnmntal organzatons thos workng n th aras should focus on contnuous awarnss craton of arly dagnoss and tratmnt to th halth faclty Fnally, th concrnd body has to xpand and mantan halth promotons on dsgnng approprat ntrvntons, talord towards communts at hgh rsk and ffctv tratmnt at hom or wth communty Mthodologcally, ths modl can asly b adaptd to analyz othr halth ndcator of smlar structur and n lk sttngs Morovr, furthr modlng rsarchs mght b ncssary, n ordr to modl rsk of malara rlatd hosptal mortalty wth data from a numbr of hosptals May b Gostatstcal modlng or Spatal modlng could consdrd, snc malara data ar gographcally rfrncd 5 ACKNOWLEDGEMENT Abov all, I would lk to thank th on God, for hs uncountabl hlp n my ntr lf span My spcal grattud and apprcaton gos to Ayl Tay, PhD, for all hs constructv commnts throughout ths work I would lk to xprss my sncr thanks to all th admnstratv staff and halth workrs of Bushulo Major Halth Cntr (BMHC), for allowng m to us th data for ths study and provdng m ncssarly nformaton for ths rsarch work Morovr, I would lk to apprcat all numrators for thr fforts n th data collcton wth grat commtmnts REFERENCES 1 Agrst, A (2012) Baysan Infrnc for Catgorcal Data 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