An Analysis of the Length of Hospital Stay for Cataract Patients in Japan

Transcription

1 An Analyss of the Length of Hosptal Stay for Cataract Patents n Japan K. Nawata 1, M. I 2, A. Ishguro 3 and K. Kawabuch 4 1 Graduate School of Engneerng, Unversty of Tokyo, Tokyo , Japan, e-mal: nawata@geosys.t.u-tokyo.ac.jp 2 Graduate School of Internatonal Corporate Strategy, Htotsubash Unversty, Tokyo , Japan 3 Data Analyss Department, Mllenna Corporaton, Tokyo , Japan 4 Dvson of Health Care Economcs, Tokyo Medcal and Dental Unversty, Tokyo , Japan EXTENDED ABSTRACT The number of cataract patents n Japan has also been ncreasng rapdly wth the ageng of the populaton. Accordng to the surveys of the Mnstry of the Health, Labor and Welfare, the number of cataract patents was 1.29 mllon n 2002 and the number of cataract operatons n the month of June was 33,286 n 1995, 61,117 n 2000, and 65,864 n Ths mples that nearly 1 mllon cataract surgeres are performed annually. Cataract patents n Japan reman n the hosptal for a long perod after undergong an operaton. As a result, analyses of the length of hosptal stays have become very mportant. In ths paper, the length of hosptal stay s analyzed usng data pertanng to patents hosptalzed for cataract and related dseases (Dagnoss Related Groups (DRG) 2041) n Japan. DRG were developed n the Unted States n the 1970s. These groups categorze combnatons of dseases, operatons, and treatments nto groups based on Internatonal Classfcaton of Dseases (ICD) 9 or 10. We utlze the data pertanng to 4,151 patents on whom one-eye lens operatons were performed. The varables that may affect the length of stay are analyzed by the dscrete-type proportonal hazard model. Estmates of the Chld and Other Faclty Dummes are negatve and sgnfcant. These varables affect the leavng rate and the length of stay. Wth regard to the type of operatons and treatments, the estmates of dummy varables are negatve and sgnfcant at the 1% level, except for those of Mechancal phacofragmentaton and other aspraton of cataract (Internatonal Classfcaton of Dseases, 9 th Revson, Clncal Modfcaton (ICD-9-CM) 13.43) and Other extracapsular extracton of lens (ICD-9-CM13.59). It has been determned that the leavng rates reduce and the length of stay becomes longer for the abovementoned operatons as compared wth the case of (ICD-9-CM13.41). We also found large dfferences n the length of stay among hosptals despte elmnatng the nfluence of both the characterstcs of the patent and the types of operaton and treatment. The longest average length of stay s over 3 tmes as long as the shortest average length of stay. Fnally, we analyzed the factors pertanng to hosptals that may affect the lengths of stay. The estmates of Proft and Cold Regon are negatve and sgnfcant; n other words, the leavng rate reduces and the length of stay becomes longer f the hosptal becomes more proftable and s located n the cold regons of Hokkado and Tohoku. The results of analyss strongly suggest that n order to reduce the length of stay there s a necessty for mprovement n the Medcal Servce Fee Schedule, such as ntroducng the Prospectve Payment System (PPS), where a hosptal s pad a fxed fee regardless of the length of stay. For ths purpose, t s necessary for us to analyze the data after ntroducton of the Dagnoss Procedure Combnaton (DPC) system, system n a future study. The results of ths study also suggest the possblty of reducng the length of stay by provdng sutable means of transportaton to and from the hosptal n the wnter season n cold regons. 1014

2 1. Introducton Wth medcal care expenses havng rapdly expanded, shortenng the average length of stay n hosptals by reducng ncdences of long-term hosptalzaton has become an mportant poltcal ssue n Japan. The requste average length of stay n general hosptals was shortened by the Revson of Medcal Servce Fee Schedule, whch was mplemented n Aprl It was mportant to evaluate the length of hosptal stay n order to consder future medcal polces, such as medcal-care payments. Recently, numerous eye surgeres, such as those for cataract, have been performed worldwde. For example, approxmately 1.5 mllon cataract surgeres have been performed annually n the Unted States (Schen et al. 2000). It has also been reported that wth the ageng of the populaton the number of such surgeres has been ncreasng n Sweden and other countres (Lundström et al and 2002). The number of cataract patents n Japan has also been ncreasng rapdly wth the ageng of the populaton. Accordng to the surveys of the Mnstry of the Health, Labor and Welfare, the number of cataract patents was 1.29 mllon n 2002 and the number of cataract operatons n the month of June was 33,286 n 1995, 61,117 n 2000, and 65,864 n Ths mples that nearly 1 mllon cataract surgeres are performed annually. In the Unted States and Europe, a majorty of the cataract surgeres are outpatent; n other words, patents are dscharged from the hosptal n 1 day. On the other hand, cataract patents n Japan reman n the hosptal for a long perod after undergong an operaton. As a result, analyses of the length of hosptal stays have become very mportant. Under the Dagnoss Procedure Combnaton (DPC) system, the daly payment to the hosptal s 2,661 ponts for up to 2 days, 2,140 ponts for between 3 to 6 days, 1,819 ponts for between 7 to 12 days, and for over 12 days t s based on the actual expense (the medcal care fee s measured by ponts n Japan; ths system was ntroduced n 1943, and 10 yen per pont has been pad to hosptals snce 1958). A longer length of stay causes the medcal expense to ncrease. If the average length of stay for cataract patents can be reduced by 1 day, the total medcal expense of the country could decrease by as much as 20 bllon yen. However, a suffcent number of analyses on the length of stay have not been conducted thus far. In ths paper, the length of hosptal stay s analyzed usng data pertanng to patents that have been hosptalzed for cataract. We utlze the data pertanng to 4,151 patents hosptalzed for cataract and related dseases on whom one-eye lens operatons were performed. The dscrete-type proportonal hazard model s used n the analyss. 2. Data 2.1 Surveyed Hosptals In ths paper, we utlzed the data set collected from 36 general hosptals (Hp1 36) n Japan. These hosptals were part of The Project for Informaton Standardzaton and System Developments for Effcent Hosptal Management. The tems surveyed for hosptals are number of beds, fnancal data, number of doctors and nurses, lease, prces and deprecaton costs of medcal applances, and the number of new and total patents. The dates of admsson and dscharge from the hosptal, dates of brth, sex, placement after hosptalzaton, names of prncple and secondary dseases, and types of medcal operaton and treatment are reported for patents. In order to protect the prvacy of ndvdual patents, we utlzed only a general data set. The names of prncple and secondary dseases are based on the Internatonal Classfcaton of Dseases 9 (ICD-9) or ICD-10 and the type of operatons and treatment s based on the Internatonal Classfcaton of Dseases, 9 th Revson, Clncal Modfcaton (ICD-9-CM). In ths study, we analyzed the data pertanng to patents classfed n the 2041 category of the Dagnoss Related Groups (DRG 2041) - those patents that underwent lens operaton wthout complcaton. DRG were developed n the Unted States n the 1970s. These groups categorze combnatons of dseases, operatons, and treatments nto groups based on ICD-9 or ICD-10. In ths survey, the Internatonal Refned Dagnoss Related Groups (IR-DRG) s used (hereafter referred to smply as DRG.). The patents belongng to ths group were hosptalzed for cataract (and related dseases) and underwent lens operatons from Aprl 2000 to March The type of operaton and treatment was reported usng the ICD-9-CM. In order to elmnate patents who were hosptalzed for other dseases and also underwent lens operatons, we only utlzed the data of patents who underwent the operaton and treatment classfed n categores 13 (operatons on lens) and 14 (operatons on retna, chorod, vtreous, and posteror chamber). We dd not utlze data pertanng to patents who underwent any operaton and treatment n other categores. Unlke n other countres, n Japan, n addton to the one-eye operaton (a sngle eye of the patent s operated n a sngle perod of hosptalzaton) the two-eye operaton (both eyes of the patent are operated n a sngle perod of hosptalzaton) s also performed. It s natural that the two-eye operaton requres a patent to reman hosptalzed for a longer perod of tme. Therefore, we utlzed data pertanng to only those patents who underwent one-eye operatons. Snce 11 hosptals from among 1015

3 36 dd not perform these operatons, we analyzed the data pertanng to 25 general hosptals (Hp1 3, 5 8, 13, 15, 17 24, 26 32, and 36). The average number of beds, doctors, and total patents durng the perod were 575, 90, and 190,417, respectvely. The hosptals were located as follows: 7 n the Hokkado and Tohoku regon, 2 n the Kanto regon, 7 n the Hokurku and Toka regon, 5 n the Knk regon, 1 n the Chugoku regon, 1 n the Shkoku regon, 1 n the Kyushu regon, and 1 n Oknawa. The manageral organzatons related to the hosptals are as follows: 5 local governments; 4 mutual-ad assocatons; 3 Red Cross; and 13 medcal assocatons, corporatons, and other organzatons. The total number of patents who underwent the one-eye operaton was 4, Length of Stay The summares of the length of hosptal stay (number of days stayed) s presented n Fgure 1. For all patents, the average length of stay s 7.29, the standard devaton s 8.10, the skewness s 21.72, the kurtoss s , the mnmum s 1, the medan s 4.0, and the maxmum s 357. The maxmum average length of stay by hosptal s (Hp18) and the mnmum s 3.52 (Hp20). The skewness and kurtoss values are large. In other words, the dstrbutons are rather dfferent from the normal dstrbuton, and the large skewness values mply that there are patents that are stayng n the hosptal for long perods of tme. 2.3 Explanatory Varables In ths paper, we select varables that represent ) characterstcs of patents, ) types of operaton and treatment, and ) nfluence of hosptals as explanatory varables. The varables that represent the characterstcs of the patent are age, sex, and place of stay after hosptalzaton. Wth regard to the age, the average s 72.03, the standard devaton s 10.64, the skewness s 1.278, the kurtoss s 3.903, the mnmum s 2, the medan s 73, and the maxmum s 96 for all patents. The mnmum average age by hosptal s and the maxmum s Females represent 60.1% of all patents; n ths respect, the mnmum s 36.9% and the maxmum s 80.0% by hosptal % of the patents returned home, 1.40% went to other hosptals, and 0.55% went to other (non-hosptal) facltes post-hosptalzaton. All patents that were dscharged from 18 hosptals returned home. The type of operaton and medcal treatment s classfed accordng to the ICD-9-CM. The ICD-9-CM classfes the operaton and treatment by codes up to 4 dgts from general to detaled categores. For example, 13 represents Operatons on lens, 13.1 s Intracapsular extracton of lens, and more specfcally represents Intracapsular extracton of lens by temporal nferor route. In ths paper, we select Intracapsular extracton of lens by temporal nferor route (ICD-9-CM13.1), (ICD-9-CM13.41), Mechancal phacofragmentaton and other aspraton of cataract (ICD-9-CM13.43), Other extracapsular extracton of lens (ICD-9-CM13.59), and other lens operatons and treatments as the prmary operatons and treatments. Further, Inserton of prosthetc lens (pseudophakos) (ICD-9-CM13.7, ncludng ), Operatons on vtreous (ICD-9-CM14.7, ncludng ), and other afflated operatons and treatments were selected as the afflated operatons and treatments. Among the prmary operatons and treatments, the proporton of Intracapsular extracton of lens by temporal nferor route (ICD-9-CM13.1) s 5.88%, (ICD-9-CM13.41) s 84.20%, Mechancal phacofragmentaton and other aspraton of cataract (ICD-9-CM13.43)s 6.19%, Other extracapsular extracton of lens (ICD-9-CM1359) s 3.73%, and other lens operatons and treatments s 1.42%. Among the afflated operatons and treatments, the proporton of Inserton of prosthetc lens (pseudophakos) (ICD-9-CM13.7) s 76.42%, Operatons on vtreous (ICD-9-CM14.7) s 3.52%, and other afflated operatons and treatments s 0.75%. varables are used to represent the nfluence of hosptals. The base of these varables s Hp18, where the average length of stay was the longest. 3. Dscrete-Type Proportonal Hazard Model To analyze the length of stay at the hosptal correctly, t s not enough to compare the ALOSs of hosptals. It s necessary to consder dfferent characterstcs of the patents, such as age and sex, by hosptals. The length of stay s a dscrete-type varable takng postve ntegers (1,2,3, ). Therefore, the analyses usng ordnary methods such as the least squares methods are not proper for the length of stay and we analyze the length of stay by the dscrete-type proportonal hazard model. Let h be a condtonal probablty such that the -th patent stayng at the hosptal on the t-th day wll leave the hosptal on that day. We call h as the leavng rate. (Although t s the same as the hazard rate of survval analyss models, we call t leavng rate to clarfy the fact that the patent leaves the hosptal.) For the -th patent to leave hosptal on the t-th day, t s necessary for the patent to stay untl t-th day and leave on that day. Therefore, the probablty of the -th patent to leave the hosptal on the t-th day s a functon of h and gven by h, t = 1, (1) ( t) = { p 1016

4 = 1,2,...,n. t s= [ 1 h ( s)}] h ( t), t 2, 1{1 where n s the number of patents. To remove nfluences of a small number of patents who stay at the hosptal over a long perod of tme, we choose T as the maxmum number of days stayng n the hosptal. For patents stayng more than T days, we just use the nformaton such that they stay n the hosptal more than T days. Let p ( T +1) be the probablty such that the -th patent stays n the hosptal more than T days. p ( T +1) s gven by p T ( T + 1) = {1 h ( s)}. (2) s= 1 Let x be a vector of explanatory varables whch represent the characterstcs of the -th patent. As usual contnuous proportonal hazard models (Cox 1973), we assume that h s gven by h ( t) = dt exp( x ' β ), t = 1,2,3,..., T (3) Although d t represents the leavng rate of the t-th day, a proper functonal form s unknown. Hence, we do not assume a functonal form as the usual contnuous proportonal hazard model, and estmate d 1, d2,..., dt ndvdually. Ths means that the model s a non-parametrc form regardng t. It s one of the advantages of the model snce we do not assume any functonal form. From equatons (1)-(3), we get the lkelhood functon. By maxmzng the lkelhood functon, we get the maxmum lkelhood estmator (MLE). Note that x does not contan a constant term for dentfcaton of the model. 4. Results of Estmaton 4.1 Estmaton of β In ths paper, we used varables representng characterstcs of the patent, types of operaton and treatment, and nfluence of hosptals; these varables are represented as x - a vector of explanatory varables. The varables representng the characterstcs of a patent - age, sex, and place of stay after hosptalzaton - were readly avalable. Wth regard to age, the treatment method and calculaton of medcal fee are dfferent f the age of the patent s under 7. Moreover, the length of hosptal stay s longest f patents are n ther 40s. Therefore, n addton to the Age of the patent, we used the Chld (1 f the patent s under 7 and 0 otherwse) and the Age 40 dummy (1 f the patent s under 40 and 0 otherwse). Wth regard to other varables, we used the Female (1 f the patent s female and 0 otherwse), the Other Hosptal (1 f the patent goes to another hosptal after hosptalzaton and 0 otherwse), and the Other Faclty (1 f the patent goes to another faclty after hosptalzaton and 0 otherwse). Wth regard to the type of prmary and afflated operatons and treatments, we used the Operaton and Treatment Dummes. The base of these dummy varables was (ICD-9-CM13.41), whch s currently the standard operatonal method. The nfluence of hosptals was measured by the Hosptal Dummes, based on Hp18, where the average length of stay was the longest. x ' β of Equaton (3) becomes x ' β = β 1 Female (4) + β 2 (Age Average Age) + β 3 Chld + β 4 Age 40 dummy (Age 40) + β 5 Other Hosptal + β 6 Other Faclty + β j j-th Operaton and Treatment j + β k k-th Hosptal. k Snce two or more patents left the hosptal wthn 27 days, we selected T = 27 and calculated the net leavng rate, d t, for up to 27 days. Four thousand one hundred patents - 99% of all patents - left the hosptal wthn 27 days. It must be noted that we also estmated models usng dfferent values of T, and consdered the possblty that values of T may affect the results of estmaton. However, the results were rather smlar to those presented n ths paper. Table 1 presents the estmates of β. Havng evaluated the leavng rates, t can be stated that a larger value of x ' β mples a shorter length of hosptal stay. The estmate of Age s postve but not sgnfcant at the 5% level. The estmate of the Chld s negatve and sgnfcant at the 5% level. Ths mples that the leavng rate of chldren s low and that they stay n the hosptal for a long perod; ths s reasonable snce examnaton by a pedatrcan s often requred and self-control s dffcult for chldren. The estmate of the Age 40 (Age 40) s negatve but not sgnfcant at the 5% level. We cannot state that the length of stay changes at age 40. The estmate of the Female s postve but not sgnfcant at the 5% level. Wth regard to the Other Hosptal and Other Faclty Dummes, the estmate of the Other Faclty s negatve and sgnfcant at the 1% level, and strongly affected the leavng rates. Wth regard to the types of operaton and treatment, the estmates of dummy varables are negatve and sgnfcant at the 1% level, except Mechancal phacofragmentaton and other aspraton of cataract (ICD-9-CM1343) and Other extracapsular extracton of lens (ICD-9-CM1359); n other words, the leavng rate reduces and the length of stay ncreases as compared wth the case of 1017

5 (ICD-9-CM1341). In partcular, the estmate of Operatons on vtreous (ICD-9-CM147) s and ts t-value s The length of hosptal stay ncreases to a large extent f ths operaton s performed. Wth regard to the estmates of the Hosptal Dummes, the maxmum s 1.515, the mnmum s 0.471, and the dfference between the maxmum and mnmum values s There are large dfferences among hosptals, despte elmnatng the nfluence of characterstcs of patents and types of operaton and treatment. For example, let us consder a patent of age 72, male, who returns home post-hosptalzaton after undergong (ICD-9-CM13.41) and Inserton of prosthetc lens (pseudophakos) (ICD-9-CM13.7). In Hp15, where the leavng rate was the hghest and the length of stay was the shortest, The average length of stay was only 3.92 days. On the other hand, n Hp31, where the leavng rate was the lowest and the length of stay was the longest, the average length of stay becomes days (the real value s larger than ths number), whch s 3.1 tmes as large as that of the hosptal wth the shortest length of stay. 4.2 Dstrbuton of d t The dstrbuton of d t, the net leavng rate, s provded n Fgure 2. The dstrbuton of d t s mportant for analyzng the effcency of treatments. There are two clear peaks on the eghth and ffteenth days. Furthermore, the value of the twenty-second day s clearly hgher than the neghborng values; ths mples that there s a one-week cycle n the net leavng rates. Ths fact mples wth hgh probablty that the patent leaves the hosptal on the same day of the week as beng admtted to the hosptal. Consderng the effcency of treatments s an nterestng subject for future study. 5. Factors Pertanng to Hosptals that May Affect the Net Leavng Rates There exst large dfferences n the leavng rates and lengths of stay among hosptals despte elmnatng the nfluences of characterstcs of patents and types of operaton and treatment. In the prevous secton, dummy varables were used to evaluate the nfluence of hosptals. The values of the dummy varables represented the net effects of hosptals on the length of stay. In ths secton, we analyze the estmates of the Hosptal Dummes by regresson analyss (the value of Hp18 s set to 0.) Sze, profts, manageral organzatons, and regons where hosptals are located are used as explanatory varables of the regresson model. The varables representng the szes of hosptals, namely, the number of beds, number of doctors and nurses, number of patents, and ncomes and expenses are readly avalable. Snce these varables are hghly correlated, we use Number of Beds as an explanatory varable. We also use the number of patents n the ophthalmology departments (Number of Patents) to evaluate the szes of these departments. Manageral organzatons are local governments, mutual ad assocatons, Red Cross, medcal assocatons, corporatons, and other organzatons. Snce hosptals managed by local governments, mutual ad assocatons, and the Red Cross are consdered to have publc functons, we use the Publc for these hosptals. Profts accrung to hosptals represent busness stuatons and polces of hosptals. We use proft rates (Proft) n order to remove the effects of the sze of hosptals. For the varables representng regonal effects, we use the Cold Regon (Hokkado and Tohoku regons) and West Japan (Knk, Chugoku, Shkoku, and Kyushu regons) Dummes. The estmates of βˆ k, coeffcent of Hosptal Dummes, are analyzed by βˆ k = b + b 1 log(number of Beds) (5) b log(number of Patents) b Publc + b 4 Proft b Cold Regon b West Japan + ε k. The standard errors of bˆ j are estmated by the robust estmaton method. The results of estmaton are provded n Table 2. The estmate of Proft s negatve and sgnfcant at the 5% level. The estmate of the Cold Regon s negatve and sgnfcant at the 1% level wth a one-sded test. Ths mples that the leavng rate becomes smaller and the length of stay becomes longer f the hosptal becomes more proftable and s located n the cold regons of Hokkado and Tohoku. It s consdered that the proft rates are related to the occupaton rate of beds. Reducng open beds and keepng the occupaton rate hgh may prove to be advantageous for hosptal managers. The possblty that the length of hosptal stay becomes longer because of the busness perspectve must be consdered. Ths s an mportant problem when consderng the future medcal fee payment system. (The dseases analyzed n ths paper are only a small percentage of the entre gamut of medcal treatments provded by hosptals. The patents wth these dseases represent 0.1% of the total patents. The occupaton rate of beds for these dseases s 2% at most and less than 1% n a majorty of the hosptals. Therefore, t s extremely unlkely that a longer length of stay for these dseases (solely due to medcal reasons) causes a hosptal to become 1018

6 more proftable. It s reasonable to consder that busness stuatons and polces of hosptals affect the length of stay.) In cold regons, t s consdered that patents stay n the hosptal untl they have recovered completely because commutng to the hosptal durng the wnter s dffcult. If ths s a vald reason, t may be possble to reduce the length of stay by provdng sutable commutng methods to and from the hosptal durng the wnter season. Although the other varables are not sgnfcant at the 5% level, estmates of the Number of Beds, Number of Patents, Publc, and West Japan Dummes are negatve. The t-values of the Number of Beds, Number of Patents, and West Japan Dummes are 1.03~1.28, and are relatvely large. Wth regard to these varables, the number of hosptals may be a reason for beng unable to obtan statstcally sgnfcant results. It may be necessary to nvestgate addtonal hosptals n order to precsely evaluate the effects of these varables. 6. Concluson In ths paper, we have analyzed the length of hosptal stay for ophthalmology treatment. Data pertanng to 4,151 patents who have been hosptalzed for cataract and related dseases (DRG 2041) have been analyzed usng the dscrete-type proportonal hazard model. We have also analyzed those factors pertanng to hosptals that may affect the length of stay. Although cataract s an mportant dsease and a large number of operatons have been performed to remove t, the length of hosptal stay has not been suffcently studed. Estmates of the Chld and Other Faclty Dummes are negatve and sgnfcant. These varables affect the leavng rate and the length of stay. Wth regard to the type of operatons and treatments, the estmates of dummy varables are negatve and sgnfcant at the 1% level, except for those of Mechancal phacofragmentaton and other aspraton of cataract (ICD-9-CM13.43) and Other extracapsular extracton of lens (ICD-9-CM13.59). It has been determned that the leavng rates reduce and the length of stay becomes longer for the abovementoned operatons as compared wth the case of Phacoemulsfcaton and aspraton of cataract (ICD-9-CM13.41). Wth regard to the estmates of the Hosptal Dummes, the maxmum s 1.515, the mnmum s 0.471, and the dfference between the maxmum and mnmum values s There are large dfferences among hosptals despte elmnatng the nfluence of both the characterstcs of the patent and the types of operaton and treatment. The longest average length of stay s over 3 tmes as long as the shortest average length of stay. The operaton and treatment methods for cataract are standardzed and ther dffculty level s not hgh. It s surprsng that such large dfferences exst among hosptals wth regard to the length of stay. Fnally, we analyzed the factors pertanng to hosptals that may affect the lengths of stay. The estmates of Proft and Cold Regon are negatve and sgnfcant; n other words, the leavng rate reduces and the length of stay becomes longer f the hosptal becomes more proftable and s located n the cold regons of Hokkado and Tohoku. The results of analyss strongly suggest that n order to reduce the length of stay there s a necessty for mprovement n the Medcal Servce Fee Schedule, such as ntroducng the Prospectve Payment System (PPS), where a hosptal s pad a fxed fee regardless of the length of stay. References [1] Cox D. R Regresson Models and Lfe Tables. Journal of Royal Statstcal Socety B 34: [2] Lundström, M., U. Stenev, and W. Thorburn Age-Related Utlzaton of Cataract Surgery n Sweden durng A Retrospectve Study of Cataract Surgery Rate n One-Year Age Groups Based on the Swedsh Natonal Cataract Regster. Acta Ophthalmologca Scandnavca 79: (4) [3] Lundström, M., U. Stenev, and W. Thorburn The Swedsh Natonal Cataract Regster: a 9-year Revew. Acta Ophthalmologca Scandnavca 80 (3): [4] Metcalfe, J. S., A. James, and A. Mna Emergent Innovaton Systems and the Delvery of Clncal Servces: The Case of Intra-Ocular Lenses. Research Polcy 34 (9): [5] Schen O. D., J. Katz., E. B. Bass, J. M. Telsch, L. H. Lubomsk, M. A. Feldman, B. G. Petty, and E. P. Stenberg, The Value of Routne Preoperatve Medcal Testng before Cataract Surgery. New England Journal of Medcne 342 (3): [6]Yuzawa, S San Nssu karanta Roujnnse-Hakunashou Shujutsu no Byounn kan Hkaku n Kansuru Kenkyuu. ( An Analyss of the Length of Stay at the Hosptal by Hosptals for Senle Cataract Surgeres ) Byoun Kannr (Hosptal Management) 319: (n Japanese). 1019

7 Table 1. Estmates of β Varable Estmate Standard Error t-value Age Chld (Age 40)*Age Female Other Hosptal Other Faclty Major Operaton and Treatment Dummes Other Major Operatons Type of Afflated Operatons and Treatments Other Afflated Operatons Hosptal Dummes Hp Hp Hp Hp Hp Hp Hp Hp Hp Hp Hp Hp Hp Hp Hp Hp Hp Hp Hp Hp Hp Hp Hp Hp Table 2. Results of the Analyss of Hosptal Factors Affectng the Length of Stay Varable Estmate Standard Error t-value Constant log(number of Beds) log(number of Patents) Proft Publc Cold Regon West Japan R * Standard errors are calculated by robust estmaton. 1020