Estimating hospital inflation from routinely collected DRG data: Application to Swiss Hospitals

Transcription

1 Esimaing hospial inflaion from rouinely colleced RG daa: Applicaion o Swiss Hospials Auhors: Hélène Chevrou-Séverac, Tiago Ribeiro and Albero Holly Affiliaion: HEC-Lausanne, IEMS (Insiue in Healh Economics and Managemen), universiy of Lausanne, Swizerland. 1 Inroducion In many indusrialized counries he financing of he hospial indusry has been evolving owards a prospecive paymen sysem where hospials are paid a fixed fee for each paien in a cerain diagnosic caegory. In Swizerland, sudies for he implemenaion of such a sysem are currenly under way. The shif o prospecive paymen sysems based on paiens caegorized according o heir diagnosics and he procedures hey underwen is in accordance wih many healh economiss belief ha he relevan uni of analysis for pricing decisions is he cos of a reamen episode. Accordingly, he sudy of prices and heir evoluion in he hospial secor and of he healh care secor a large should be based on he same concep of oupu. This conrass wih he conceps currenly underlying he consrucion of healh care price indices. In paricular he healh care componen of he Swiss consumer price index is based on he prices of inpus o he producion of medical services and no on he concep of oupu jus described. A he producer level, here does no exis oday in Swizerland a price index for he hospial secor. Such a producer price index, which akes as a saring poin he same concep of oupu used in prospecive paymen sysems, would be he relevan one o consider for he purpose of sudying he evoluion of prices in he hospial secor and in paricular for updaing fees paid o hospials. The objecive of his research paper is o sudy and propose a mehodology for measuring hospial inflaion from rouinely colleced RG daa in order o enable he Sae governmen o adjus he prospecive paymen sysem per RG by he hospial inflaion rae. The inflaion measure invesigaed will have as a guiding principle he reamen of a case as ypified by he classificaion of diagnosics and procedures ino AP-RGs.(All Paien iagnosic Relaed Groups), aking ino consideraion he prospecive paymen sysem which is currenly being sudied for poenial implemenaion in Swizerland. In he second secion, we deal wih he issues relevan o he consrucion of a healh care price index. We hen presen he Swiss hospial RG sysem and our daase. In secion 4, we deail how we esimae hospial inflaion rae from RG daa using regression mehods. In secion 5, we ake his a sep furher by describing a sequenial procedure o he calculaion of a hospial PPI ha can be made o mimic he regression calculaions. And finally we will discuss our resuls. HCS, TR & AH IEMS-25

2 2 Issues - price indices 2.1 Price indices in he healh care secor The healh care indusry presens, in he opinion of some auhors (Triple 2), he same challenges as oher service indusries albei on a larger scale. The major measuremen problem presened by he consrucion of price and quaniy indices in service indusries and in paricular in he healh care secor arises from he fac ha in mos cases i is no clear wha is being ransaced, wha he correc definiion of oupu is and o wha services correspond he prices being paid (Griliches 1992). Furher, in he healh care secor, he correc concep of oupu is even harder o esablish. Associaed wih he problem of defining he oupu is he one of deermining changes in he qualiy of wha is being produced. If a new reamen for a cerain disease becomes available a he same price as he old reamen bu is much more effecive in delivering he desired oucome hen one should consider ha here was an effecive price decrease if our concep of oupu is he oucome of a reamen. We briefly describe each of hese aspecs in urn Concep of oupu In he mid 196 s Sciovsky (1964, 1967) proposed he relevan oupu o be priced as an illness episode. This was in opposiion o he implici oupu definiion which was obained by deflaing he naional accouns of he healh care secor by a healh secor deflaor calculaed based on he prices of iems such as a hospial room rae, a visi o a docor, he price of a frequenly prescribed medicine, ec (see for example Bernd, Culer, Frank, Griliches, Newhouse and Triple ( 21)). I is well known ha he measuremen of inpu prices in a producion process is a poor proxy for he evoluion of he prices of he oupu, especially in secors where here is subsanial echnological progress such as in he healh care secor. Neverheless Sciovsky s iniial proposal was followed only much laer by work of oher auhors such as Culer e al (1998) who esimaed he price of reaing hear aacks, Shapiro and Wilcox (1996) who esimaed he price of caarac surgery and Bernd, Busch and Frank (21) who sudied he cos of he reamen of depression. These sudies show ha here can be subsanial differences in he evoluion of prices once echnological/qualiy facors are aken ino accoun The reamen of qualiy changes In a classical sudy Griliches (1967, 1971) addresses he consequences of no accouning for qualiy changes in he auomobile indusry using a mehodology now known as hedonic pricing. Griliches (1967, 1971) and Rosen (1974) provided he basic hedonic pricing framework. In summary, prices are regressed agains he produc characerisics and he price o be used in he price index is he price of an homogeneous produc, ha is, once influences of differen characerisics on prices have been removed. Under cerain HCS, TR & AH IEMS-25

3 condiions, namely compeiive markes, he regression coefficiens on he produc characerisics reflec consumer valuaions of he differen characerisics, hence providing an economic heoreical framework for he consrucion of he price of an arificial homogeneous good. I is well known ha healh care markes are far from saisfying he condiions of compeiive markes. Neverheless in he hospial conex and for he purpose of consrucing a producion index ha reflecs he evoluion of coss applying he same mehodology reflecs only he more limied and implici assumpions ha hospials minimize coss and ha hey don have marke power in he markes for he inpus hey use. One is no aemping o measure he consumers valuaion for he services provided as in a consumers cos-of-living index where consumer prices reflec hese valuaions under marke condiions In he healh care secor he applicaion of he hedonic approach o heah care prices in he conex of cos-of-living indices has been discussed a lengh in Bernd e al (21). For he specific case of pharmaceuicals Griliches and Cockburn (1994) and Jacobzonne e. al. (1997) are examples. There is also a srand of lieraure in which paricular diseases are sudied. Here he effeciveness of a reamen is aken ino accoun and he decrease (increase) in he cos of reaing a cerain disease ha resuls from he use of differen echnologies is correced for any observable change in he oucome. The work of Culer e al (1998), Shapiro and Wilcox (1996) and Frank, Bernd and Busch (21) are examples of his approach as is he more recen work of Chevrou-Severac, Jeanrenaud and Wasserfallen (23) on he coss of hear disease. 2.2 Curren pracice in price index consrucion in he healh care secor The American medical price indices The American consumer price index (CPI) and producer price index (PPI) have very differen heriages and consequenly ake disinc approaches o measuring healh care secor prices. The hospial componen of he CPI has as iem componens he prices of inpaien and oupaien hospial services measured per say in hospial (independen of he number of days of he say), and oher inpu prices such as he price of x-rays, laboraory ess ec.. Only abou 6% of he quoes obained for he CPI are based on iagnosic Relaed Groups (RGs), ha is, on iems ha perain o he reamen of cerain illnesses as opposed o iems ha refer o he inpus in reaing hose illnesses (Bernd e al 21). The medical PPI is much more recen ha he CPI. The Bureau of Labor saisics (BLS) has only published a PPI for he healh secor since ecember 1992, he base period. The hospial services PPI aemps o measure he ne price paid o hospials for he enire bundle of services received during a hospial say. The sampling uni wihin he hospial is a paien bill classified by is RG. The concep of oupu adoped is ha of he cos of an episode of illness (see Appendix 1 for more deails). Furhermore, he hospial PPI includes correcions for changes in he average lengh of say. A decrease in he average lengh of say for he reamen of a cerain condiion is considered as a qualiy change and no as a reducion in cos (Bernd e al 21 and Caron & Murphy (1996)). HCS, TR & AH IEMS-25

4 2.2.2 The Swiss medical price indices Currenly he Swiss Federal Saisical Office (OFS) does no produce a producer price index for he medical secor. The Swiss CPI conains a hospial service componen. The principles underlying he consrucion of he hospial services componen of he CPI are similar o he American counerpar. Quoes are obained from hospials regarding average prices of a day in he hospial and prices of iems which can be regarded as inpus in he producion of healh care such as laboraory ess, x-rays, physioherapy, ec. I is herefore he perspecive of inpus o healhcare provision principle ha is adoped and no he cos-of-illness perspecive (see appendix 2 for more deails). There is however an imporan difference beween he American and Swiss hospial componens of he CPI. Wha is priced in he American index (since 1997 bu no previously) is he say in he hospial and no he day in he hospial. The change in mehodology in he American index was due o changes in he case mix of paiens in hospials over ime, and in paricular o he increase in average severiy of paiens due o shifs of paiens from inpaien o oupaien reamen. This led o an increase in he index when he iem considered was price per day bu his did no correspond o an effecive increase in price bu only o a shif in he composiion of he hospial populaion. The Swiss index prices he day in hospial and is herefore more sensiive o shifs in hospial case mix and case severiy mix. 3 The Swiss hospial sysem 3.1 The Swiss hospial RGs and coss Currenly in Swizerland here are sudies under way for he implemenaion of a prospecive paymen sysem in he hospial secor. This means ha hospials will be paid a fixed price per paien depending only on he classificaion of ha paien ino a diagnosic group. The main classificaion mehodology being considered in Swizerland is ha of APRG's (All Paien iagnosic Relaed Groups). This is in accordance wih many healh economiss belief ha he relevan uni of analysis for pricing decisions is he cos of a reamen episode. The main reason for his is ha echnological progress ends o vary widely from disease o disease. I seems appropriae herefore o sudy he evoluion of prices and coss in he medical care secor on diseases by diseases basis or for a cerain chosen panel of diseases and reamens and no he evoluion of prices of facors ha ener in he producion of healh care services. Furhermore from he perspecive of updaing paymens made o hospials in he prospecive paymen sysem, he relevan inflaion is he one measured on he cos of a reamen episode, which is he uni of paymen for he hospial. Also differen hospials are likely o face differen inflaion raes merely due o he composiion of heir paien populaion. The inflaion rae numbers for he Unied Saes calculaed using he producer price index for he hospial secor are exhibied in able 1. The able shows how widely prices can vary from one disease group o anoher. HCS, TR & AH IEMS-25

5 Table 1 : US Hospial PPI by Major iagnosic Caegories isease Group / Year General medical and surgical hospials 2.7% 3.% 3.6% iseases and disorders of he nervous sysem 3.1% 2.5% 2.5% iseases and disorders of he ear, nose, mouh, and hroa 3.6% -.2% 6.4% iseases and disorders of he respiraory sysem 2.5% 2.8% 4.4% iseases and disorders of he circulaory sysem 3.% 2.8% 4.2% iseases and disorders of he digesive sysem 4.2% 3.1% 6.1% iseases and disorders of he hepaobiliary sysem and pancreas 2.5% 3.4% 5.9% iseases and disorders of he musculoskeleal sysem and connecive issue 2.4% 6.% 4.% iseases and disorders of he skin, subcuaneous issue and breas 3.6% 4.5% 4.8% Endocrine, nuriional, and meabolic diseases and disorders 3.6% 3.% 3.9% iseases and disorders of he kidney and urinary rac 5.2% 6.1% 12.1% iseases and disorders of he male reproducive sysem 1.6% 15.1% 3.% iseases and disorders of he female reproducive sysem 2.7% 4.3% 9.2% Pregnancy, childbirh, and he puerperium 3.4% 6.2% 3.8% Newborns and oher neonaes wih condiions originaing in he perinaal period 4.3% 1.8% 1.5% iseases and disorders of he blood and blood forming organs and immun. diseases 2.6% 2.4% 9.3% Myeloproliferaive diseases and disorders, and poorly differeniaed neoplasms 4.8% 4.4% 4.% Infecious and parasiic diseases (sysemic or unspecified sies) 4.3% 2.8% 4.3% Alcohol/drug use and alcohol/drug induced organic menal disorders 1.3% 3.2% 5.5% Injuries, poisonings, and oxic effecs of drugs 4.7% 4.1% 7.4% Facors influencing healh saus and oher conacs wih healh services 3.2% 3.% 4.8% Source: US BLS, Producer Price Index 3.2 aa Available The Swiss prospecive paymen sysem by AP-RG The RGs (iagnosic Relaed Groups) consiue a sysem of paien classificaion based on primary and secondary diagnoses and procedures, age and lengh of say. These groups are defined such ha each caegory has a more or less a uniform cos. Therefore, reaing a paien in any given RG can be considered as a single medical service wih regards o coss. The RG sysem was firs developed in he early 8s in he US. In Swizerland, a similar classificaion sysem, Swiss APRG, has been developed since This sysem, adminisered by he Swiss Insiue of Healh and Economics (ISE), is used as a basis for cos reimbursemen of hospials in Swizerland. The RG-adjused number of cases is one of he bes available simple measures of oupu. In any case i is more represenaive of coss han he number of paien-days. In 26, one hospial ou of wo will be financed using he AP-RGs prospecive paymen sysem. Under his paymen sysem, hospials will be paid by RGs recorded, prospecively, i.e. on he basis of he previous year s aciviy. As a consequence, he paymens by RG given by he Canonal healh parners should be adjused by an inflaion rae, hence he imporance of esimaing an appropriae rae. The daase 1 The daa available for his work is he discharge daa from 4 hospials from 2 o 22 ( see able 3). The daa consis of paien level records conaining demographic informaion for he paien and he paien AP-RG code as well as deailed diagnosic and procedures 1 We hank he ISE insiue for making his daase available o our research. HCS, TR & AH IEMS-25

6 informaion, he lengh of say of he paien in he hospial and he cos of he say. The coss per AP-RG do no include invesmen charges, research or eaching. Table 2 Episodes of care per Hospial Hospial Toal Universiy hospial Regional hospial Regional hospial Regional hospial Sub-oal for he 3 regional hospials Toal Noe: The 3 regional hospials belong o he same canon. The universiy hospial is locaed in one canon (canon A), and he 3 regional hospials in anoher canon (canon B). The 3 regional hospials are comparable o he Universiy hospial in erms of he number of paiens reaed for he hree years. However, hey do no necessarily rea he same pahologies, so hey do no have he same RG disribuion. The able below summarizes he number of RGs and he average lengh of say in each hospial. Table 3: number of RGs and average LOS by hospial Hospial Number of AP-RGs Average lengh of say Universiy hospial days Regional hospial days Regional hospial days Regional hospial days So as o obain a homogeneous daase, only AP-RGs in which he minimal number of hospial says regisered was a leas 3 across all hospials have been used. Only RGs ha are recorded each year have been included 2. In view o compue hospial inflaion, we have only worked on he inliers hospial says, ha are he says whose lengh is comprised beween wo bounds (in erms of number of days a hospial) defined by he AP-RGs Swiss sysem. The bounds for he lengh of say are available RG by RG. Abou 5% of he cases are defined as ouliers. Ouliers says are no reimbursed on he same basis as inliers says. For his kind of says he reimbursemen is modified relaing o he lengh of he say. So compuing he inflaion rae on inliers says only is relevan because inliers says are used as benchmark hospial says o compue he value of poins ha finances he hospial RGs says hrough Cos-Weighs. 2 We have dropped he RGs 469 and 477. HCS, TR & AH IEMS-25

7 4 Esimaing hospial inflaion raes 4.1 Mehod of invesigaion We will use panel daa mehods and he informaion obained from he reviews menioned above o analyze he evoluion of hospial coss. In paricular we will sudy models of he ype: y ni = α + δ + x β + ε i ni i ni where y ni is he logarihm of he cos of he say of paien n in RG group i in period, α i is an average cos by RG, δ is he average difference in he cos (log of) beween he base period and period, x ni are paien characerisics such as age, degree of severiy of disease, lengh of say in he hospial, ec. and ε ni is a perurbaion erm. The hospial PPI is rerieved from he esimaed value of δ. Mehod of esimaion The specific conrol variables o include in he model will depend on he ype of disease group as well as on consideraion of he desired meaning of he final index. In paricular, including lengh of say as a conrol variable implies ha one considers decreases in he average lengh of say as a change in he qualiy/echnology of delivering a reamen, so any decrease in cos associaed wih a decrease in he lengh of say is no refleced in he price index. The fixed effec (FE) specificaion implicily assumes ha paiens (for he purpose of calculaing he cos of heir say) differ only in he RG hey have been classified ino and in he lengh of heir say. Afer hese effecs have been removed paiens are considered homogeneous from he poin of view of heir cos. Esimaion proceeds by OLS. As he number of coefficiens is very large (reaching close o 1) we use an ieraive backfiing procedure which reduces significanly he memory requiremens as well as compuaion ime. In his se-up he inflaion rae from period 1 o period is given by exp ( δ δ 1 ) 1 δ δ 1. HCS, TR & AH IEMS-25

8 The use of he cos variable in log form requires furher explanaion. I is commonly observed ha coss per case have highly skewed disribuions wih a small number of very large ouliers, which is o say ha he disribuion of ε ni if one considers he cos variable in levels will be far from a normal disribuion. The ransformaion of levels ino logarihms has he objecive of making he ransformed variable closer o a normal and hence he OLS esimaes based on he ransformed variable will be efficien. This ype of ransformaion, usually referred o as variance sabilizing ransformaions, has a long hisory in saisics (see for example Barle (1947), Box & Cox (1964,1982), Bickel & oksum (1981) and Hinkley & Runger (1984)). I amouns o a change of scale so ha in he new scale our model has desirable properies, i.e. he properies ha make OLS opimal in some sense. Anoher issue of relevance is he inerpreaion of he coefficiens on his ransformed scale. Wih he logarihmic ransformaion our coefficiens are easily inerpreable bu his does no mean he logarihm is he appropriae scale. An alernaive approach is o follow Holly and Pensak (24), which insead develop esimaion procedures based on maximum likelihood ha ake ino accoun he skewness and kurosis of he observed variable and where here is no need for ransforming he dependen variable. We leave he exension of his work o he laer mehods for fuure sudy. Weighing coss daa As we aim o consruc a hospial price index, in he spiri of price index heory, we will use weighs so ha our regression procedures replicae as closely as possible known indices. In Laspeyres price index, he quaniy is fixed o he one observed in he baseline period. Here an observaion of RG i in year will have a weigh equal o he share of ha RG s coss on oal coss in he baseline year (2) divided by he number of inpaien days for RG i in year. As a consequence, in a given year, he sum of he weighs for he observaions of a cerain RG will always be equal o ha RG s share of oal cos in he baseline year. We presen a formal jusificaion and furher discussion of his choice of weighs in Appendix 3. Alernaively one could sample paiens in RG s wih probabiliy equal o he weighs jus defined. 4.2 Resuls: hospial inflaion raes We have esimaed differen price indices and inflaion raes. We have compued monhly inflaion raes for all he hospials ogeher, hen for he hospials wihin canons A and B respecively. We have hen conrolled for he higher RG coss of he universiy hospial by inroducing a dummy variable for his hospial when compuing overall inflaion. The effec of he lengh of say on he cos of hospializaion is hen wihdrawn by inroducing he LOS in our esimaion. Thus, he inflaion rae compued is conrolled for he impac of changing lengh of says on hospial coss. Following, as he coss are regisered and disribued o paien says according o hospial aciviies once a year, we have also compued an annual inflaion rae ha we can compare direcly wih he Swiss hospial inflaion. Finally we have also provided PPI by Major iagnosics Caegories (MC). HCS, TR & AH IEMS-25

9 I is imporan here o make several remarks concerning he monhly inflaion esimaes repored below: he accouning procedures in hospials mean ha a significan porion of he cos of a paien in a cerain RG is obained only a he end of he year afer cos accouning procedures deermine he amoun of fixed coss. Hence monhly variaion wihin a year can be a reflecion of accouning pracices; our sample consiss of only 4 hospials and is mean as illusraive - an inerpreaion of a Swiss price index should be given if one could have a represenaive sample of paiens from all hospials - bu i is neverheless enough o show ha here can be significan and disparae inflaion for differen hospials and ha his inflaion can be very differen from he hospial componen in he Swiss CPI; he excessive monhly variaion found is mos of he imes no saisically significan and should no be inerpreed as real price variaion; here is however a significan shif from one year o he nex and his can be righly considered as a change in he price level; monhly esimaes are relevan in pracice if one could obain real ime informaion of paien coss, which is no he case for he presen sample where monhly coss are obained ex-pos, a he end of he year, for each hospial. I is neverheless relevan from an illusraive poin of view, o show how he mehodologies discussed can be applied o an exended period of ime Wih he previous commens in mind we urn o he discussion of our findings. HCS, TR & AH IEMS-25

10 Figure 1: Monhly inflaion raes and price indices from January 2 o ecember 22 The monhly inflaion raes range from 3.2% o 3.3%, wih a major conribuion of he Universiy hospial o he exremes. Alhough monhly variaion is permanen hroughou he period we observe a clear shif in he index in he las year. HCS, TR & AH IEMS-25

11 Figure 2: Monhly inflaion raes and price indices wih and wihou LOS adjusmen (2-22) Accouning for he effec of lengh of say on hospial coss has lile impac on he monhly inflaion raes and price levels, alhough below we noe hea a he year level he are differences when comparing he differen ypes of hospials. HCS, TR & AH IEMS-25

12 Figure 3: Monhly inflaion and price indices, wih and wihou universiy hospial impac conrol When accouning for he impac of he universiy hospial on he RG coss, he hospial PPI is higher a he end of he ime period (for he year 22). HCS, TR & AH IEMS-25

13 Figure 4: Monhly inflaion and price indices for Universiy hospial In general and as expeced, removing he effec of LOS ends o smooh he variaions in he monhly inflaion raes. For he case of he universiy hospial his occurs mainly in he firs year of observaions. There is also a clear upward rend in he price index for he universiy hospial in he las year. HCS, TR & AH IEMS-25

14 Figure 5: Monhly inflaion and price indices for he hree regional hospials From 2 o 22, he inflaion measure for he hree regional hospials oscillaes significanly more in he firs year han in subsequen years. There is also a clear upward rend in he price level over he period under consideraion. As poined ou earlier he monhly esimaes of inflaion are quie variable, bu mos of hese oscillaions jus reflecs he fac ha esimaes are no precise and hence many of hem are no saisically differen from zero, So one should no consider his variaion as an underlying variaion in coss. Neverheless here in an upward rend in he price index which is quie noiceable in all he scenarios considered and is more appropriaely described by inflaion raes compued on an annual basis o which we now urn. HCS, TR & AH IEMS-25

15 TP TP TP PT Source PT The PT Which PT.7% Price index Table 4: Annual inflaion raes LOS model All RGs All hospials.16% 3.2% 1.8% 2.32% Universiy hospial (canon A) -1.29% 5.21% -.22% 3.84% 3 regional hospials (canon B) 1.96% 1.84% 2.64% 2.6% All hospials Wih universiy hospial dummy.1% 3.83%.93% 3.13% 3 Swiss Healh CPITP PT.6% Swiss hospial CPITP 4.4% 1.7% Concerning he overall inflaion rae, here is barely any change in prices in 21 (.16%) and a posiive inflaion rae abou 3% in 22. The Swiss hospial CPI also poins o a zero inflaion in 21 bu is below our compued inflaion by 1.5% in 22. The Universiy hospial has a general level of coss ha is lower in 21 when compared wih 2 and a significan higher one in 22. This wide variaion of inflaion from 21 o 22 comes from changing accouning principles used in he Universiy hospial during he period. Taking a closer look a changes in he budge of he universiy hospial beween 21 and 22 we noice ha wo facors were responsible for he growh in producion coss up. In 22, a new Canonal Law on public employees and he reclassificaion of medical saff increased coss by abou 2.5%. Also he applicaion of a new Federal Law on herapeuic producs pushed coss up by abou 1%. In he hree regional hospials he coss grew seadily over he period considered. Esimaed inflaion is abou 2% in 21 and 1.8% in 22. We again have a divergence wih inflaion measured in he hospial CPI in 21. When accouning for he impac of he lengh of hospial says on hospial coss, he inflaion rae is higher in 21 (1.1%), and smaller in 22 (3.8%). Taking ino accoun of he impac of he lengh of hospial say on RG coss reveals ha he cos decrease in universiy 5 hospials (in 21) was mosly caused by a decrease in he lengh of saytp PT. This effec is also visible in regional hospials where inflaion is higher when changes in lengh of say are aken ino accoun. We have also aken ino accoun he fac ha he universiy hospial has poenially higher hospial coss han he regional hospials for wo main reasons: i provides a wider range of medical reamens han regional hospials (such as reamens for burned paiens, cardiac ransplans), and by law, he universiy hospial is in charge of raining and medical research, aciviies ha increase is producion cos. Even if coss per RG should no ake ino accoun such aciviies, he mehod of accouning for medical research and raining has only become more precise in : OFS (Federal Saisical Office), baseline: 1 Swiss francs in 2. 4 hospial CPI conains healh care iems from saionary AN ambulaory hospial admissions. 5 decreased 1.4% on average from 2 o 21 for all hospials and 2.1% from 21 o 22 in he regional hospials only. HCS, TR & AH IEMS-25

16 In order o ake ino accoun higher producion coss of he universiy hospial, we have inroduced in our model a dummy variable for all he hospial says recorded a he universiy hospial. This variable is highly significan indicaing ha he level of coss in he universiy hospial is higher. However he impac on inflaion is negligible.. Following he BLS, we have compued Swiss hospial producer price indices by Major iagnosic Caegories (see able 5, below). As expeced, he inflaion raes are quie differen from one MC o anoher, as well as when compared o he general hospial inflaion, and o he Swiss hospial CPI. Table 5: Swiss hospial inflaion by Major iagnosic Caegories (MC) isease group - Major iagnosic Caegories Base model LOS model iseases and disorders of he nervous sysem -2.49%.9% -1.2% -.28% 2-iseases and disorders of he eye -.49% 19.91%.8% 19.1% 3-iseases and disorders of he ear, nose, mouh, and hroa 1.82%.6% 3.55%.31% 4-iseases and disorders of he respiraory sysem -.41% 1.6% -.73% 1.54% 5-iseases and disorders of he circulaory sysem 5.%.2% 4.48% -.85% 6-iseases and disorders of he digesive sysem -.12% 2.93% 2.22% 2.7% 7-iseases and disorders of he hepaobiliary sysem and pancreas -3.2% 1.7% 1.4% -.22% 8-iseases and disorders of he musculoskeleal sysem and connecive issue -2.87% 4.17% -1.26% 3.97% 9-iseases and disorders of he skin, subcuaneous issue and breas -7.37% 6.42% -5.69% 6.3% 1-Endocrine, nuriional, and meabolic diseases and disorders 1.3% 7.61%.14% 7.43% 11-iseases and disorders of he kidney and urinary rac -1.44% 5.55% -1.33% 4.53% 12-iseases and disorders of he male reproducive sysem -2.4% -.61% -2.49%.89% 13-iseases and disorders of he female reproducive sysem -9.65% -4.95% -8.19% -4.87% 14-Pregnancy, childbirh, and he puerperium -1.91% 13.73% -1.27% 13.27% 15-Newborns and oher neonaes wih condiions originaing in he perinaal period 1.97% 5.88% 1.54% 3.69% 16-iseases and disorders of he blood and blood forming organs and immun. diseases -4.97% 2.54% -1.35%.35% 17-Myeloproliferaive diseases and disorders, and poorly differeniaed neoplasms % 7.34% -9.44% 4.47% 18-Infecious and parasiic diseases (sysemic or unspecified sies) -1.18% 3.49% -5.21% 4.7% 19-Menal diseases and disorders 9.14% % 2.89% -6.71% 2-Alcohol/drug use and alcohol/drug induced organic menal disorders 9.34% % 11.24% -14.3% 21-Injuries, poisonings, and oxic effecs of drugs 1.75% -8.68% 1.43% -6.83% 22-Burns % 29.72% -24.7% 2.41% 23-Facors influencing healh saus and oher conacs wih healh services.72% 3.29%.3% 4.25% 24-Muliple significan rauma 35.93% -6.9% 34.71% -24.7% 25-Human immunodefiency virus infecions -8.95% 9.33% -4.91% 9.9% We noe ha he exreme values found in some caegories and he shifs in inflaion from one year o he nex reflec he small number of observaions in our sample. One of he main purposes of compuing inflaion by groups of represenaive condiions is o be able o compue differen inflaion raes by hospial ha can legiimaely be used in a prospecive paymen sysem. By he previous saemen we mean ha he hospial should be compensaed for increases in cos which do no resul from is own direc acions. A hospial ha has a disproporionae share of paiens classified in a disease group whose coss rise faser han average should be compensaed for his fac by having is paymens rise by a rae higher han ha used for oher hospials. On he oher hand i would be conrary o he spiri of he prospecive paymen sysem o allow he paymens o a cerain hospial o rise faser HCS, TR & AH IEMS-25

17 han he ones o oher hospials simply because is coss have risen faser wihou paying aenion o he cause of he underlying cos increase. The previously compued hospial specific inflaion does no discriminae beween he possible causes of inflaion in a given hospial. In able 6 below we compue he inflaion rae of each hospial by a weighed average of he MC raes where he weighs are each hospial s share of ha MC in oal cos. The raes reflec differenials due only o case mix composiions. For his o be an accurae exercise one would have o have MC inflaion raes compued for he counry as a whole so ha he impac of a single hospial on he naional rae could only be minor. This is unlikely o be he case here given ha we only have 4 hospials in our sample. Table 6: Inflaion due o differen case-mix(mc) LOS model All RGs Universiy hospial (canon A).52% 2.85% 1.38% 1.8% 3 regional hospials (canon B) -.5% 3.35%.55% 2.82% There is a considerable difference when comparing wih he raes in able 4. eparures of specific hospials form he overall inflaion are much less pronounced here indicaing ha here could be hospial specific componens of he changes in cos ha are no due o a differen case mix. HCS, TR & AH IEMS-25

18 5 Sequenial esimaion of inflaion One problem wih he general approach jus described is ha i is no pracical o use from he perspecive of consrucing an index series, since by definiion i implies ha he models should be re-esimaed every ime new daa becomes available. This would necessarily imply ha all he values of he price index in previous periods would change, which is no in accordance wih wha is generally undersood by a price index series. This is one of he criicisms ha iewer (1995) makes of he approaches ha go under he general classificaion of sochasic approaches o index heory as described in previous secions. We now presen alernaive mehods ha circumven his problem. 5.1 Kalman filer algorihm The proposiion presened here is o develop price indices ha can be calculaed in real ime and can be seen as sligh modificaions of he models in he previous secion. The general principle is o combine he models above wih updaing algorihms generally known as Kalman Filers. To be more specific we have he following class of models: δ =δ 1 +σ ν ν y ni =α i +δ +x ni β i +σ ε ε ni where δ is now a random coefficien and he perurbaions ν and ε ni are joinly normally disribued and uncorrelaed. Our esimae of δ is now given by E( δ Ω ) where Ω represens all he informaion available a ime, ha is ( ynis, α i, xnis, β i, i, n, s = 1,... ). This quaniy can be readily calculaed from he Kalman filering recursions. To beer clarify he connecion beween hese models and he ones in he previous secion one can view he laer as exreme cases of he former. If one inerpres he raio σ ν σ ε as a smoohing parameer hen he models of he previous case correspond «loosely speaking» o he case σ ν σ ε. The oher exreme, where σ ν σ ε corresponds o he case where δ does no change (in fac δ δ as ) and δ can be inerpreed as he inercep of he equaion above (afer suiable normalizaion of he parameers α i ). In he noaion of he model and in he descripion jus made, he remaining parameers of he model are esimaed using an iniial period and hen used as fixed o calculae he inflaion rae in subsequen periods. This does no need o be he case. The remaining parameers can be given he same reamen as δ and can be sequenially updaed as new informaion becomes available. HCS, TR & AH IEMS-25

19 5.2 Resuls: sequenial esimaion of hospial inflaion To compue hospial inflaion by he proposed mehod we need preliminary esimaes of he parameers α i and β i. We use he sample from year 2 o obain hese values, and apply he mehod described for he years 21 and 22. We hen compare he price index obained using his sequenial mehod o he one previously obained using an OLS procedure. As noed above, one needs o choose he parameer σ ν σ ε, which will ac as a smoohing parameer. Guidance for he choice of σ ν σ ε is provided in appendix 4. Essenially he sequenial procedure described will generae a price index ha is a closely relaed o a moving-average of he price index generaed in he OLS seing. A cerain value for σ ν σ ε will imply ha he moving average will be mosly based on a cerain number of periods. Figure 5: Monhly price index sequenial procedures. Each line corresponds o he approximae number of periods ha ener he weighed average of he price index and provides guidance o he choice of he variance of he price equaion. I is noiceable ha he shorer he period used for he price predicion, he closer he sequenial esimae is o he OLS esimae, reflecing he heoreical calculaions made. I is worhwhile o poin ou ha he sequenial esimaes use values for α i and β i compued using only one year of daa and ha he OLS esimaes use all he sample o esimae hese parameers. The resuls sugges ha if he goal is o use he OLS esimaes hen i is possible o do so in a sequenial and implemenable way. We noe also when choosing parameers ha imply a higher degree of smoohing one obains price indices ha are much less vulnerable o he excessive monhly variaion. If one believes ha his variaion derives HCS, TR & AH IEMS-25

20 from insufficien sample sizes (a he RG/monh level) and from accouning pracices hen such filering is advised. The opimal level of filering will necessarily depend on our judgmen abou he daase and on he periodiciy of he calculaion. Even if we do no find i jusified o compue inflaion on a monhly basis, he smoohing procedures ha imply a one year or more averaging period consiue an alernaive o simple year averages of prices. Naurally wha was exemplified here wih monhly daa can be reproduced wih annual daa as coninued daa collecion procedures make such daa available. 6 iscussion We have proposed a way o compue hospial PPI and inflaion raes from rouinely colleced RG and coss daa. This approach is relaed o he hedonis price regression mehod, which capures price inflaion afer wihdrawing he impac of he good s characerisics on is price. Here we conrol for he impac of he feaures of he hospial says is RG classificaion and he lengh of say. As expeced our hospial inflaion rae is quie differen from he Swiss hospial CPI, suggesing ha due aenion should be paid o hospial specific PPI ha akes ino accoun he feaures of he healh care indusry. The mehods proposed are flexible enough o be made do mimic sandard index conceps such as he Laspeyres index as well as o ake ino accoun shifing composiions of casemix boh a he naional level and a he hospial specific level by appropriae choice of weighs. So we can accommodae he changing composiion of hospial healh care over ime. The indices proposed are based on an illness episode approach, and i ake ino accoun qualiy changes of healh care provided measures of qualiy are available. The hospial PPI discussed is closer o hospials producion coss han he one compued by he US Bureau of Labor Saisics (BLS) as i is based on cos accouning daa whereas he BLS index is based on price quoes for paricular clien bills and herefore includes h hospial desired margin. A sep furher of he work presened here would be o compue hospial PPI for all hospials in Swizerland and verify unil wha exen he resuls presened here are mainained all Swiss hospials. HCS, TR & AH IEMS-25

21 APPENIX 3: WEIGHT EFINITION Consider he sandard Laspeyres price index formula in a wo period seing: P = d =1 d =1 d =1 q d p d 1 q d p d = d =1 q d p d p d 1 d =1 q d p d q d p d 1+ log p 1 d p d d =1 q d p d =1+ w d log p 1 d p d d =1 where q d d is he quaniy of paiens in RG d in year, p d is he price(cos) of a paiens in RG d in year and w d is he share of he oal cos of RG d in year. Hence we have he calculaed inflaion o be: w d log p 1 d p d =1 d In order o replicae he previous expression in a regression seing consider he following simple model: log( c id )= α + βt id where =, 1 is a ime index, i is a paien index, d a RG index, c id is he cos of paien i in RG d and period and T id is a ime dummy equal o 1 if = 1 and zero oherwise. Consider a WLS procedure wih weighs id. The esimaor for α is: + ε id p d HCS, TR & AH IEMS-25

22 PBdB is Price index ˆ α = = N d d = 1 i= 1 d N d i= 1 Nd d = 1 d = 1 i= 1 id N d = 1 i= 1 id id log id N o ( c ) id d Nd i= 1 i= 1 id id log o ( c ) id = d = 1 Nd. d.. i= 1 id. d log( c id ) = d = 1. d.. log( c. d ) where NP he number of paiens in RG d in year,. d = i = 1 id is he sum of weighs for RG d in year, N d = is he oal sum of weighs and c is he.. d = 1 i = 1 (geomeric) average cos of RG d in year. Likewise he esimaor of β is: id N d.d ˆ β = d = 1. d 1.. log( c 1. d ) d = 1. d.. log( c. d ) 1 If we se = = q p. d. d d d oal cos of RG d in period hen we have:, i.e. he sum of weighs for RG d in boh periods equal o he ˆ β =.d log c 1.d.. c.d d =1 ˆ β = w d log c 1.d c.d d =1 ha is we have he price index defined iniially. The condiion achieved by seing: = = q p can be 1. d. d d d id Nd i = c 1 id N d = An analogous choice of weighs can be made do obain a Paasche index or a chain index. Insead of using weighs one could also sample paiens from all hospials wih paiens in a. d cerain RG in a given year having he probabiliy.. of being sampled. HCS, TR & AH IEMS-25

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