Simulating the Components of Resource Intensity Weight: A Good Proxy for Allocating Health Human Resources Across Inpatients?

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Randall Wood
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1 Suatg the Cooets of Resouce Itesty Weght: A Good Poxy fo Aocatg Heath Hua Resouces Acoss Iatets? a a a, b Ksaaya Basu, Stéhae L. Paé ad Road Wa a Mcosuato Modeg ad Data Aayss Dvso Aed Reseach ad Aayss Dectoate Heath Caada b Caada Isttute fo Heath Ifoato Abstact Heath Caada s Regsteed Nuses (RNs) dead ode fo Abeta assgs fu-te euvaet egsteed uses (FTE RNs) by usg fucto (e.g., aedatc, ocoogy, eta heath etc.) to atet age-sex gougs ooto to the exected use of hosta esouces (.e, usg ad othe hosta staff te, euet, sues, dugs). The RIW -- a eatve vaue assged to each atet uo dschage edcts the use of hosta esouces o the bass of atet case-x, sevety, age, ad ocedues efoed. Ths ae vadates usg the RIWs to assg RNs to atet-gougs by usg a se atheatca cocetua ode ad a suato. It shows that RIW s a good edcto of use-use acoss usg fucto. Dffeeces heath hua esouce testy acoss dffeet usg fuctos, ad dffeeces ces of o-hua eeets, e.g., dugs, aso does ot affect the ootoa eatosh betwee tota RIW ad FTE of RNs wth a usg fucto the absece of techoogca chage. Thus, we fd stog assocato betwee the RIW ad the -hosta eueet fo uses. Key Wods: Resouce Itesty Weght, Nuses, Suato, Hosta Itoducto The Mcosuato Modeg ad Data Aayss Dvso of the Aed Reseach ad Aayss Dectoate, Heath Caada, has but a Heath Hua Resouces (HHR) ode to oect futue eueet fo Regsteed Nuses (RNs) Abeta [1]. I bef, the ode uses the base-yea eatosh betwee the deogahc/cca chaactestcs of actve cae atets (.e., age, sex, ost esosbe dagoss), the eatve eed fo usg ad othe esouces (case-x ad case-coexty), ad the fu-te euvaece (FTE) of RNs who ovde such usg cae. The base-yea eatosh s estated usg atet data eoted fo each dschage ad the Caada Isttute fo Heath Ifoato (CIHI) Regsteed Nuse Database (RNDB), whch s a aua egsty of a RNs egbe (.e., egsteed) to actce by usg fucto ad eoyet status. The sestvty of oectos of futue eueets fo RNs takes to accout sceaos of ossbe chages ouato eed fo actve atet cae ad attes of RN staffg. As the RNDB eots head-couts by eoyet status (at-te, fu-te) ad atet usg fucto (.e., aedatc, edca/sugca, ocoogy, ehabtato, sychatc/eta heath, ctca cae, oeatg oo/ecovey oo) the foowg stes ae addessed: - estate FTE status of RN-staffg by usg fucto [2], ad - atto RN-staff aog atet gougs (age, sex) see these uts usg the CIHI Resouce Itesty Weghts (RIW) as the bass of aocato. We assg FTE RNs by atet-gougs ooto to the actua shae of the tota RIWs wth each usg fucto. Ths assues that the RIW s a vad edcto of exected use of usg cae. The RIW s a eatve vaue assged by CIHI to each atet uo dschage accodg to the aout of esouces they wee exected to use. These esouces cude the cooet costs of atet cae (e.g. usg sevces, dugs, etc.) ad the RIW s a dex that exesses atet use of esouces eatve to the aveage fo ceta age ad sevety of ess. The estato of the RIW accouts fo dffeeces age (thee gougs), case-x gou (909 gous), ad case-coexty (fou categoes). Cost s geate fo ode

2 atets (e.g., 70+ vesus othes), ceta case-x gous (e.g. ustabe aga wth cadac cathezato; co-obd dabetes vesus that wthout secfed cadac codtos ad wthout dabetes), ad by degee of coexty [3,4] (e.g., eated to otetay fe-theateg codtos vesus ucocated). The vadato of ths ethod of assgg FTEs eues two teked codtos: Fst, ce ust ot fuece RIW ad secod, tota RIW wth a usg fucto (aedatc, ocoogy, eta heath, etc.) ust be ootoa to the RIW attbuted to the use of RNs. The vadato of the fst eueet s otat because t ay be agued that a hghe o a owe ce ca ove-estate o ude-estate the tota RIW wth a usg fucto. If so, oectg eueets fo RNs based o tota RIW wth a usg fucto ay be seadg. Fo exae, the ce of cheotheay ad eated theaeutcs to teat cace, geea, s hghe tha that of othe dugs used fo othe dseases. Theefoe, t ay be asseted that tota RIW fo ocoogy w be ove-estated ad hece the eueet fo RNs based o that RIW woud aso ove-estate the eueet fo RNs the oecto. I ths ae, we show that the ce of the o-hua factos (e.g., dugs) does ot affect the tota RIW wth a usg seget. We futhe show that tota RIW attbutabe to uses those fuctos (e.g. ocoogy) s ootoa to the tota RIW that usg fucto, the absece of techoogca chage. The assuto that RIWs ae a dcato (edcto) of RNs sevces s vad. Cocetua Faewok A RIW s assged to each atet uo dschage fo the hosta, accodg to the aout of esouces they used. We ca obseve the tota RIW of each usg fuctos. Howeve, the RIW of the usg segets, whch ae the cooets of the tota RIW wth a atcua usg fucto ae ot obsevabe. Ths ae suates the o-obsevabe RIW of dffeet usg segets ad the fds the eatosh betwee the tota RIW wth a usg fucto ad usg seget that s attbutabe to the sevce of the uses. Fgue 1 shows the dffeet o-obsevabe cooets attbuted to the tota RIW. Fgue 1: Cocetua Mode Tota RIW a usg fucto (Obsevabe) Tota RIW attbutabe to uses (No-obsevabe) Tota RIW attbutabe to dugs (No-obsevabe) Tota RIW attbutabe to techcas (No-obsevabe) Tota RIW attbutabe to othe esouces (No-obsevae) Does ce atte? The chat shows that a usg fucto voves sevea segets such as the dect sevces of the uses, adstato of dugs, sevces of dffeet techcas etc. Fo the sake of scty, fo the te beg, we assue that a usg fucto s ted to oe seget, whch s dsesg theaeutc dugs to atets. Let eeset the ce of dug ad the uatty of dug cosued by atet k the gve 2

3 yea. s the doa vaue of oe RIW coesodg to the gou of atets. These gous ae based o atet age ad sevety of ess. The ube of gous of atets based o age ad sevety of ess, the ube of dffeet dugs, ad ube of atets ae eeseted by,, ad esectvey. The RIW fo a dugs s sy: RIWDugs. (1) 1 Dugs vaues of RIW (1). Ths eas that f the dug ce s owe tha the weghted aveage, RIW s udeestated, ad f the ce s above the weghted aveage, RIW s oveestated. Howeve, oveestato ad udeestato cace out each othe wth a gou ad as such tota RIW fo a the atets wth the hosta seget eas uaffected. Note that two atets wth sae ce ad uatty of dugs w have dffeet RIW f s dffeet. Ths s se-aaetc ad does ot eue ay 1 Let us suose that fo a dugs the ce s eua to P, the weghted aveage of ces. The, P. Now, et RI W Dugs be the tota RIW f the ce fo a the dugs ae eua to P. The RIW 1 Dugs k k 1 RIWDugs (2) Ceay, RI W (2) s eua to RIW whch s deved fo dffeet ces ad dffeet Dugs assuto about the dstbuto. Does the use of usg sevces ad RIW show a ea ted the futue? The aveage weghted uatty of dugs fo each atet s: Dugs Q ad the aveage weghted ce s st: P The tota dug cost ca be exessed as: 3

4 PQ Let K P, the the tota dug cost ca be exessed as K Q. The RIW assocated wth dug cost, RIWDC ca be exessed as: KQ Q RIWDC K Now, suose that the cost of deveg each atet the aveage uatty of dugs s K. The cost fo the K Q esoe deveg these dugs s the K Q. We ow we have: Q RIWHHR K. Thee s o estcto o K ; t ca take ay ostve vaue deedg o the testy of the use of heath hua esouces wth a usg fucto. Howeve, K s assued to be costat wth a usg seget, though t ca vay acoss usg seget. Now, we have the tota RIW : Q Q Q RIW + ( + RIWDC + RIWHHR K K K K ) (3) We ca eaage (3) as Q K ( ) ( K + K ) Q ( K + K ) RIW K + K K RIWHHR. K K K That es that RIWHHR s ootoa to RIW. Fo a atcua seget wth a usg fucto the absece of techoogca chages, the ooto of dffeet categoes of heath hua esouces s fxed. So t s easoabe to beeve that RIW Nuses s ootoa to RIWHHR ad hece to RIW whe thee s o techoogca chage. Extedg the cocet to a segets wth a usg fucto A usg fucto voves sevea segets. We assue that each usg fucto has segets. Suose the subtota of RIW fo each of these segets wth a usg fucto s deoted by RIW. We the have RIW K RIW (4) RIW Nuse K RIW (5) Now, RIW RIW K RIW. (6) Nuses Nuse Substtutg the vaue of RIW (6) we get RIWNuses K K RIW. (7) Ths es that RIW s ootoa to RIW. Nuses Suatg the tota RIW ad RNs eueet I ths secto we ustate soe suato of RIWtota ad RIWuses a usg fucto based o ou cocetua ode. Tabe 1 shows a efect coeato betwee tota RIW ad the tota RIW attbutabe to 4

5 the sevces of the uses. Ths s tue deste dffeet ces ad heath hua esouce testes acoss usg segets. Howeve, as we deostated, that t s the utzato of hua esouces ad ot the ce of the o-hua factos that ae efected RIW. Tabe 1: Reatosh betwee Tota RIW ad Tota RIW attbutabe to Nuses RIW Nuses / Tota RIW ea Tota RIW RIW Nuses ,437,825 1,073, % ,848,991 1,381, % ,439,771 1,823, % ,757,772 2,063, % ,455,367 1,834, % Note: Coeato Coeffcet betwee Tota RIW ad RIW Nuses s Cocuso The su of RIWs acoss dvdua atets by usg fuctos tus out to be a good oxy fo the eueet of usg sevces the absece of a techoogca chage. Vaato the ooto of uses acoss dffeet usg segets does ot dstot the eatosh betwee tota RIW ad tota RIW eated to uses, whch we have show s ootoa. Ths aso hods fo dffeg vaues of RIW by age gous ad sk gous. Dffeeces heath hua esouce testy acoss dffeet usg fuctos ad dffeeces ces of o-hua eeets aso do ot affect the ootoa eatosh. Thee s a stog assocato aog the eueet of uses, tota heath hua esouces ad tota RIW wth a usg fucto. Ad, thee s a sgfcat assocato betwee the eueet fo uses wth a usg fucto ad the tota RIW that usg fucto. Thus, the RIW s a good edcto of fu-te euvaet use eueets by usg fucto. Ackowedgeets We ae gatefu fo coets fo Steve Lehe, Ruoz Aste ad othes o a eae daft of ths ae eseted at the Caada Ecooc Assocato Meetg, Ottawa, Jue The vew exessed ths ae ae those of the authos ad do ot ecessay eeset the vews of Heath Caada. We thak Godo Hawey fo hs suot ad coets o the ae. Ay eag eos ae ous. Refeeces 1. Wa R, Basu K, Guta, A, Bazeau L. The dead fo egsteed uses Caada. Natoa ad ovca estates. Oa esetato/oste eseted at HEA 4 th Wod Cogess, Sa Facsco, Cafoa, Jue 15-18, Basu K, Wa R. Estatg the Fu Te Euvaece of Pat-Te ad Fu-Te Regsteed Nuses. MSDAD Tssaaatchy P. Befg Note o Resouce Itesty Weghts. MSDAD Caada Isttute of Heath Ifoato. DAD Resouce Itesty Weghts,

Data Compression. Prof. Ja-Ling Wu. Department of Computer Science and Information Engineering National Taiwan University

Data Compression. Prof. Ja-Ling Wu. Department of Computer Science and Information Engineering National Taiwan University ata Coresso Prof. Ja-Lg Wu eartet of Couter Scece ad Iforato Egeerg Natoa Tawa Uversty ata Coresso ca be acheved by assgg short descrtos to the ost frequet outcoes of the data source ad og descrto to the