physician payment mechanisms, hospital length of stay and risk of readmission: evidence from a...
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Journal of Health Economics 36 (2014) 112–124
Contents lists available at ScienceDirect
Journal of Health Economics
journa l h om epa ge: www.elsev ier .com/ locate /econbase
hysician payment mechanisms, hospital length of stay and risk ofeadmission: Evidence from a natural experiment�
amien Échevina,∗, Bernard Fortinb
Université de Sherbrooke, CRCELB and Cirpée, CanadaUniversité Laval, Cirpée and Cirano, Canada
r t i c l e i n f o
rticle history:eceived 19 November 2012eceived in revised form 19 March 2014ccepted 19 March 2014vailable online 12 April 2014
EL classification:10121841
a b s t r a c t
We provide an analysis of the effect of physician payment methods on their hospital patients’ length ofstay and risk of readmission. To do so, we exploit a major reform implemented in Quebec (Canada) in1999. The Quebec Government introduced an optional mixed compensation (MC) scheme for specialistphysicians working in hospital. This scheme combines a fixed per diem with a reduced fee for servicesprovided, as an alternative to the traditional fee-for-service system. We develop a model of a physician’sdecision to choose the MC scheme. We show that a physician who adopts this system will have incentivesto increase his time per clinical service provided. We demonstrate that as long as this effect does notimprove his patients’ health by more than a critical level, they will stay more days in hospital over theperiod. At the empirical level, we estimate a model of transition between spells in and out of hospitalanalog to a difference-in-differences approach. We find that the hospital length of stay of patients treatedin departments that opted for the MC system increased on average by 4.2% (0.28 days). However, the risk
eywords:hysician payment mechanismsixed compensationospital length of stayisk of re-hospitalisationuration model
of readmission to the same department with the same diagnosis does not appear to be overall affectedby the reform.
© 2014 Elsevier B.V. All rights reserved.
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atural experiment
. Introduction
Most empirical studies on physicians responses to various pay-ent mechanisms focus on their activities as measured by their
olume of services, their hours of work, or their productivity. Ineneral, this research does provide evidence that these choices are
nfluenced by physician remuneration schemes. See, among oth-rs, Gaynor and Pauly (1990), Hemenway et al. (1990), Hurley et al.1990), Ferrall et al. (1998), Barro and Beaulieu (2003), Hadley and� This article was partly written while Fortin was visiting the University Paris Panthéon-Sorbonne. We gratefully acknowledge Marie Connolley Pray, Davidaardt, Nicolas Jacquemet, Pierre-Thomas Léger, Daniel Parent, as well as partic-
pants at Journées Louis-André Gérard-Varet, CAE conference, SCSE meeting andttawa University Department of Economics seminar and two anonymous referees
or their useful comments and suggestions. We acknowledge research support fromhe Canada Research Chair in Economics of Social Policies and Human Resources athe Université Laval. Marc-André Morin provided valuable research assistance.∗ Corresponding author.
E-mail addresses: [email protected] (D. Échevin),[email protected] (B. Fortin).
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eschovsky (2006), Devlin and Sarma (2008), and Dumont et al.2008). However, very few studies have analyzed the impact oflternative methods of physician remuneration on their hospitalatients’ length of stay (LOS) and the risk of their re-hospitalisationost-discharge.1
This is unfortunate for at least three reasons. Firstly, for aiven diagnosis, outcomes such as LOS in hospital are potentiallyerifiable, albeit imperfect, measures of inputs that may affect spe-ialists’ quality of service (Chalkley and Malcomson, 2000). Fornstance, an increase in LOS in hospital may reflect more time spent
y a specialist to better identify the nature of his patient’s healthroblem and to improve the quality of treatment. Of course, anncrease in LOS in hospital may just reflect the fact that specialists
1 One exception is Hutchinson et al. (1996) who analyzed the impact of primaryare physician payment mechanisms on hospital utilization rates among patientsn Ontario. They found that capitation payment, with an additional incentive pay-
ent to encourage low hospital utilization rates, did not reduce hospital use. Oneimitation of the research is the small number of physicians (39) whose method ofayment was converted from fee-for-service to capitation over the period.
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pend more time on nonclinical activities (e.g., teaching, adminis-rative tasks and research) and less time on clinical activities. In thisase, one should not expect an increase in the quality of treatmentt least in the short run, ceteris paribus. Secondly, the risk of re-ospitalisation post-discharge to the same department is a naturaleasure of adverse outcome and is often used as a proxy for mor-
idity (e.g., Cutler, 1995). Therefore, one may expect that a longerOS in hospital, as long as it leads to better service quality in hospi-al, will reduce the risk of re-hospitalisation post-discharge. Finally,OS in hospital is generally considered as a major determinant ofospital costs per patient, while hospitalisations account for a largeortion of total health care costs, even if they are a relatively rareccurrence.2 Note however that an increase in LOS in hospital isikely to reduce alternative care costs, given the potential substi-ution between hospital and post-hospital care (e.g., convalescentome, home care).
This paper attempts to partly open the black box of the impactf physician payment mechanisms on LOS in hospital and theisk of re-hospitalisation post-discharge to the same departmentith the same diagnosis. To do so, we exploit a major reform ofhysician-payment mechanisms implemented in the Province ofuebec (Canada) by the Quebec Government. This reform intro-uced an optional mixed compensation system (MC) for specialistsorking in hospital, as an alternative to the traditional fee-for-
ervice (FFS) system.3 The MC system combines a fixed per diemith a discounted (relative to the FFS system) fee for services pro-
ided. Upon the introduction of the MC system, each departmentoted on its adoption, switching to the MC system only if the voteassed unanimously.4 In 2008, close to 50% of all specialists hadpted for this system in Quebec.
In economic terms, the two main objectives of the governmentn introducing this reform can be stated as follows. Firstly, it wasimed at reaching a more efficient quantity–quality trade-off inealth care provided by specialists. Since the MC system intro-uces a per diem independent of the number of clinical servicesrovided and strongly reduces the fees per service (at about 41%f the average fee), specialists who opt for MC may have incen-ives to reduce their supply of clinical services. This effect maymprove the efficiency in health-care allocation of resources as longs the volume of clinical services provided under FFS is excessive.or instance, a FFS specialist may have incentives to abuse his roles a medical adviser and multiply the number of non-necessaryervices in hospital to advance his own economic self-interests.
his phenomenon of physician-induced-demand (PID) may occurhen an asymmetry of information exists between provider andonsumer in the physicians service market. Note however that
2 This is one reason why the prospective payment system (PPS) was introduced foredicare in 1983 in the U.S. Under the PPS, the federal government reimbursed
ospitals a fixed price for each patient treated (based on his diagnosis) that isndependent of the actual costs of treatment (in contrast with the previous costeimbursement method). It was expected that the PPS system would introducetrong incentives on hospitals to keep costs down by reducing, among others, LOS inospital. However, there was also fear that such a system could reduce the qualityf services in hospital and may result in worse outcomes (e.g., Cutler, 1995).3 In Quebec, as in each of the Canadian provinces and territories, all physiciansork within a universal public Health Care System.4 The MC system is available only for activities completed in health establish-ents (mainly hospitals). Services provided within private clinics continue to be
enerally paid under the FFS system. Also, there are restrictions on the number ofer diems a physician can claim and the time-period during which he can claimhem. Half per diems are claimed on a 3.5-h basis. The maximum number of halfer diems that a physician can claim during a two-week period is 28 and these cannly be claimed Monday to Friday between 7AM and 5PM. Once the maximumumber of per diems is reached, or when a physician works outside the per-diemlaimable hours, he is paid on the FFS basis. See Dumont et al. (2008) for moreetailed description of the reform.
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Economics 36 (2014) 112–124 113
ompetition among physicians, constraints imposed by hospitals,nd non-financial motives such as physicians’ altruism are forceshat may limit PID. Note also that waiting lists to see specialistsre very long in Quebec. Under these circumstances, FFS specialists’ncentives to induce demand are likely to be reduced.5 On the otherand, physicians who choose the MC system are expected to spendore time per clinical service provided, as they are paid more in
ime and less in clinical services. This effect may improve the qual-ty of clinical services.6 All in all, these predictions are consistent
ith Dumont et al. (2008) according to which the 1999 Quebeceform induced specialists who switched to MC to reduce theirolume of clinical services by 6.15% while increasing their aver-ge time spent per clinical service by 3.81%. These results suggest
potential quality–quantity substitution.A second objective of the reform was to improve efficiency in
he allocation of time between clinical and nonclinical activities.ince the latter are not remunerated under the FFS system, theyre likely to be neglected. As long as they are included in the periem under MC, 7 this system is likely to stimulate these activi-ies. Results from Dumont et al. (2008) also confirm this prediction.pecialists who adopted MC increased their time spent on admin-strative and teaching tasks (activities not remunerated under FFS)y 7.92% while they reduced time spent on clinical activities by.57%. Thus, the reform may favour a more efficient allocation ofasks within departments that adopted a MC system.8
We assess the effects of the introduction of the 1999 Quebeceform on both LOS in hospital and the risk of re-hospitalisationf patients treated in departments that opted for the MC sys-em (average treatment effects on the treated). Our contributions both theoretical and empirical. At the theoretical level, we pro-ide a static model that shows that, under realistic assumptions,he reform induces a physician who opts for the MC system to per-orm less clinical services per unit of time. Therefore, he will spend
ore time per clinical service. Assuming for simplicity fixed on-he-job leisure and nonclinical activities, this is likely to increasehe quality of services. However, as long as this effect does noteduce the required volume of services to treat a patient by lesshan a critical level, his time spent in hospital will increase overhe period. Our static model thus allows us to predict the impact ofhe reform on the product (or on the sum of log) of the two basicutcomes of interest: a MC patient’s LOS in hospital and his risk ofe-hospitalisation per unit of time. Note that while the static naturef our model does not allow us to make predictions on each of theseutcomes, it is still useful in order to predict the effect of the reformn the total MC patient’s hospitalization cost over the period. Also,ur model allows us to make conditional predictions. For instance,onditional on a zero or negative impact of the reform on the risk ofe-hospitalization, our model will predict that the reform will pos-
tively affect an MC patient’s LOS in hospital. Besides, if the reformas an effect on the reallocation of tasks toward less clinical andore nonclinical activities in MC departments, our model predicts5 Literature on PID is plentiful but empirical evidence is mixed. See McGuire2000) and Léger (2008) for recent surveys.
6 Ma and McGuire (1997) suggest the use of average time spent per service as aroxy for the intensity or quality of treatment provided by the physician. Of course,ime spent per service is an imperfect measure of quality – physicians may simply beaking longer breaks between services, or spending more time with patients withoutffecting health outcomes.7 The per diem only applies to certain activities, principally time spent on admin-
stration, teaching and seeing patients.8 A third objective of the reform was to improve horizontal equity between spe-
ialists with different behaviours in terms of clinical and nonclinical activities. Fornstance, the pay gap between specialists who mainly do clinical tasks and those whoo a higher proportion of administrative tasks is likely to be reduced in departmentshat opted for MC.
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hat the effect of the reform of a MC patient’s time spent in hospitalill increase over the period, as long as it is positive. This result is
ntuitive as the MC physician spends less time to treat his patients.As we cannot exploit a randomized experiment, our empir-
cal methodology uses a quasi-experimental design based on awo-state mixed proportional hazard model analog to a difference-n-differences approach. The control groups are defined byepartments that remained within the FFS system. We make clearhe assumptions we adopt to allow our empirical approach todentify the impact of the reform, given that the decision of aepartment to move to the MC system is endogenous. To estimatehe model, we take advantage of a unique administrative patient-evel dataset from a major teaching hospital in Quebec (Sherbrookeniversity Hospital Center).9 The number of observations includes many as 144,510 spells in hospital and 125,291 spells outsideospital.
An originality of our approach lies in the fact that our estimatesake into account the heterogeneity of patients through the diver-ity of diagnoses. Indeed, a variation in the average length of stay in
given department can reflect changes in the sickness distributionf patients due to supply or demand factors. For instance, the facthat a department is flexible enough to choose the distribution ofatients before and after a change in the physician compensationcheme can bias our estimates of the impact of the reform. Hence,sing diagnostic-related group dummies can correct part of theelection bias since fixed effects can adjust for baseline differencesn levels.
Overall, our empirical results suggest that the length of stayncreased on average by 4.2% (0.28 days) in departments that
oved to a MC system (average treatment effect on the treated).owever, the risk of re-hospitalisation does not appear to beffected by the reform, at least not at the global level. The positivempact of the reform on time spent in hospital by patients treatedn MC departments is consistent with our static model. The absencef effect on the probability of re-hospitalisation at the global levelay be partly explained by the fact that the reform does not influ-
nce patients’ health in hospital. The reform may also induce MChysicians to reallocate their time toward more nonclinical activ-
ties (teaching and administration) but less clinical activities, thusncreasing the length of stay of patients in hospital but with littleffect on the risk of re-hospitalisation.
The paper is structured as follows. Section 2 presents a theoret-cal model of the impact of a mixed payment system on the lengthf stay. Data are presented in Section 3. Section 4 introduces theconometric framework. Section 5 presents the results. Section 6oncludes.
. Theoretical model
The determination of the average duration and frequency of hos-italisation is a result of a complex process of interaction betweenatient characteristics, social environment, hospital characteris-ics, firms offering covered post-hospital care, (public and private)
nsurers, and medical practice (see Picone et al., 2003). However,iven the aims of this study and the nature of our data, we focusn medical practice, assuming the characteristics and behaviourf all the other agents to be constant.10 In particular, the patients9 Sherbrooke is the 6th largest city in Quebec with a population of 155,583 peoplen 2010. Sherbrooke University Hospital Center, a 682-bed multi-facility hospital, ishe only university and regional hospital in that region of Quebec.10 Most studies on length of stay have focused primarily on the effects of patientnd hospital characteristics. See Ellis and Ruhm (1988) for a theoretical model ofospital length of stay along these lines.
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Economics 36 (2014) 112–124
re assumed to be passive and to have no influence on their num-er of days spent in hospital over the period. In the context ofxcess health care demand observed in Quebec, it is indeed plau-ible to suppose that the patients have no power to negotiate forealth services in the hospital. Moreover, following our discussion
n the introduction, physician-induced demand (PID) is ignored,ince long waiting lists in Quebec are likely to be used as a substituteor generating non-necessary services. To motivate our empiricalpproach, we present a simple static model of the impact of thentroduction of an optional MC system on a physician’s medicalractice and, as a consequence, on the average number of dayspent by his patients in hospital over the period.
Consider a representative physician who works in a hospi-al department and spends his working time performing clinicalervices.11 His preferences are represented by a standard utilityunction given by
= U(X, e, D), (1)
here X represents his total consumption, e his effort at work, and his number of working days. The utility is twice-differentiable,trictly quasi-concave, increasing with X and decreasing with e and. The physician faces the following simple budget constraint:
= pS + wD + y, (2)
here S is a Hicksian aggregate of clinical services (i.e., a group oflinical services which relative prices do not vary and can thus bereated as one single clinical service), p is the corresponding feeer service, w is the per diem and y is his nonlabour income. Inhis model, there are two prices, one for the services performed,nd one for the days worked. Under a FFS system, p > 0 and w = 0;nder a wage compensation system, p = 0 and w > 0; and under aixed compensation (MC) system, p > 0 and w > 0. Under a public
ealth system such as the one prevailing in each Canadian province,rices are exogenous to the physician as they are determined by theovernment. The physician’s effort, e, is approximated by the vol-me of his (clinical) services per working day. Inversely, time spenter service, 1/e, can be taken as a proxy for the quality of services
changes in which are a valid measure of changes in time spentroviding services as long as on-the-job leisure is fixed. The (Cobb-ouglas) production function for clinical services is thus given by
= eD. Substituting in (2), the budget constraint becomes:
= peD + wD + y (3)
The physician is assumed to choose his effort e (or, equivalently,he quality of his services, 1/e), his number of working days D; as aonsequence, his consumption X maximizes his utility function (1)ubject to his budget constraint (3).
The optimization program to be solved is not standard since theudget constraint is nonlinear in effort e, but linear in the number ofays D (given e). The standard approach to solve this problem (e.g.,ecker and Lewis, 1973; Blomquist, 1989) is to linearize the budgetonstraint at the optimum. From this linearization, one can definehe virtual (or local) price of effort as pv
e = pD, the virtual price oforking days as pv
D = pe + w, and the virtual nonlabour income asv = y − peD. A key feature of this analysis is that the virtual pricef effort increases with the number of working days, the virtualrice of working days increases with effort, and the virtual non-
abour income decreases with effort and working days. Therefore change in p or in w will in general affect both virtual prices andhe virtual nonlabour income, since e and D are choice variables.ssuming a unique interior solution to the program, the structural
11 To simplify the presentation, we ignore nonclinical services.
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Marshallian) equations for effort and working days supplied areiven by:
= e(pD, pe + w, y − peD) (4)
nd
= D(pD, pe + w, y − peD). (5)
Now let us first assume that the compensation system in placet the start is a FFS. The impact of the introduction of an optional MChat reduces the FFS by �p and introduces a per diem, w, on physi-ian’s effort, can be approximated by differentiating the structuralqs. (4) and (5), and by using Slutsky equations that decompose vir-ual price effects into substitution and income effects.12 Note thatymmetry and positive semidefinitiveness of the Slutsky matrixmpose standard restrictions on substitution effects.13An impor-ant point here is that since the MC is optional, the physician willpt for the MC system only if it increases his earnings at constantehaviour, i.e., only if e0�p + w > 0, where the subscript 0 denoteshe FFS initial situation.14 This means that a physician will adopt
C if his effort e0 is smaller than w/(−�p).One obtains:
�e ≈ ˝−1[A�p + Bw + CD(e0�p + w)] if e0�p + w > 0
= 0 otherwise(6)
here
= 1 − (e1D2 − e22) − 2e2p,
A = (e1D2 − e22)ep + e1D + e2e,
B = (e1D2 − e22)p + e2, and
C = (e1D3 − e2e3)p + e3.
In (6), ˝−1 is the fundamental non-linearity scalar. It transformsinear income and substitution effects into nonlinear ones (seelomquist, 1989, p. 282). It is easily shown that is positive if theroduct of the own compensated elasticities of effort and workingays supplied is smaller than 1 + w/e0p, which is greater than 1.
n the following, we will assume that this is the case since almostll estimated (compensated) labour supply elasticities are smallerhan 1 (e.g., Blundell and MaCurdy, 1999).
The first two expressions within the brackets on the right-handide of (6) represents the substitution effects respectively associ-ted with the change �p in the fee and the introduction of theer diem w, and the third expression represents the income effect.ithout additional assumptions, the impact of the MC on the
hysician’s effort is ambiguous. However under plausible sufficientssumptions, it is possible to sign it.
Firstly, assume that effort and working days are net substitutesn the physician’s preferences (e2 ≤ 0) and that leisure at work andeisure outside work are normal goods (i.e., e3 ≤ 0 and D3 ≤ 0). In thisase, the income effect of the reform is negative (since C ≤ 0). Thisesult is intuitive: the physician who opts for MC benefits from an
ncrease in his income (at constant behaviour) which induces himo reduce his effort at work. Second, under the assumption thathe own compensated elasticity of effort exceeds its correspondingross elasticity (in absolute value), one has A ≥ 0. Therefore, the12 The Slutsky decompositions are: e1 = e1 + ee3, e2 = e2 + De3, D1 = D1 + eD3,
nd D2 = D2 + DD3, where ∼ stands for a compensated effect.13 The Slutsky restrictions are: e1 ≥ 0, D2 ≥ 0, e2 = D1, and e1D2 − e2
2 ≥ 0.14 This is strictly correct when changes in p and w are infinitesimal. With finitehanges, one must compare the physician’s (indirect) utility levels under MC andFS systems.
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Economics 36 (2014) 112–124 115
ubstitution effect of the reduction in the fee (�p ≤ 0) induces thehysician to reduce his effort. Again, this result is intuitive: with aecrease in the piece rate per service, the physician will perform
ess services per day.The substitution effect of the introduction of the per diem is more
ifficult to sign. However, one can easily show that if the cross com-ensated elasticity of effort (in absolute value) exceeds the productf the own compensated elasticities of effort and working days,hich is not an implausible assumption, one has B ≤ 0. In this case,
he substitution effect of the per diem on effort will be negative.he intuition of this result is also clear: the per diem induces thehysician to substitute working days for effort. In short, under plau-ible assumptions, both income and substitution effects induce thehysician to reduce his effort at work under MC.
We should now examine the following question: what is theelationship between the physician’s effort and the average numberf days spent by his patients in hospital? To provide an answer tohis question, let us first define the following variables:
≡ S
N, the average volume of services per patient (7)
nd
≡ D
N, the average number of days in hospital per patient, (8)
here N is the number of patients treated by the physician over theeriod. Therefore, one has d = (S/N)/(S/D) = a/e. Now, we assume thathe patient’s health improves when a physician spends more timeo perform clinical services. In that case, the average volume of ser-ices per patient necessary to treat health problems will increaseith e, the volume of services performed by the physician per work-
ng day.15 Since we assume no PID, it is realistic to assume that thehysician provides the number of services just necessary to treatis patients. We thus have:
= f (e), with f ′(e) ≥ 0. (9)
Substituting (9) in d = a/e, one obtains:
= f (e)e
. (10)
Differentiating (10), the average change in time spent in hos-ital by patients treated by a physician who opts for MC can bepproximated by:
�d
d0≈ −�e
e0+ �a,e
�e
e0= (�a,e − 1)
�e
e0, (11)
here �a,e is the elasticity of a with respect to e evaluated at thenitial FFS situation, 0.16
The right-hand side of (11) makes clear that the introductionf a MC system yields two opposite effects on d, the average timepent in hospital by patients. On the one hand, a physician whodopts the MC system reduces his volume of services per workingay (�e/e0 < 0). This effect tends to increase d, ceteris paribus. Onhe other hand, since e decreases and �a,e > 0, the patient’s healthends to increase for a given level of services and therefore less ser-ices are needed to treat patients. This effect tends to reduce d. Theecond right-hand side of (11) shows that the net effect depends
n whether the elasticity of a with respect to e, �a,e, is smaller orreater than one. As long as the negative effect of the reform onhe volume of services required by patient is not too strong (i.e.,15 We assume that the volume of beds attributed to a physician per working days exogenous as it is determined by the hospital. Therefore e is proportional to theolume of services per bed per working day.16 Using (8) and (10), the number of patients N is given by N = (D/d) = (De/f(e)).
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he volume of services required to treat a patient is inelastic tohe time spent per treatment, �a,e < 1), the average time spent byreated patient by MC physicians will increase over the period.
Now we can decompose the average number of days spent inospital by patients over the period into the product of their aver-ge length of stay in hospital, l, and their average frequency ofospitalisation, g, the two variables of interest in our analysis. Oneas: d = lg . Given that the size of �a,e is smaller than one, our staticodel can sign the impact of the reform on the product of these
wo variables (or the sum of their log) but not on each variablendividually. However, our model is still useful since it can be usedor instance to evaluate the impact of the reform on the total costf a MC patient’s hospitalization over the period, or to make con-itional predictions. Thus, one can use our theoretical frameworko predict that the impact of the reform will be positive on a MCatient’s LOS in hospital, given that the reform involves no effectr a negative one on the frequency of readmission (which is testedn the empirical section of the paper).
The impact of the reform on the reallocation of tasks betweenlinical and nonclinical activities in MC departments (ignored upo now for simplicity) must also be taken into account. One shouldxpect that MC physicians will spend less time in clinical activ-ties and more time in nonclinical activities per working day, ashe fee for clinical services is smaller than under the FFS schemehile non-clinical services are now remunerated by the per diem
substitution effect). This suggests that this effect will amplify theegative impact of the reform on the volume of a MC physician’slinical services per working day, and therefore its positive impactn the number of days in hospital a MC patient will spend over theeriod (see Eq. (11)).
All in all, our model predicts that the reform will increase theime spent by a MC patient in hospital (as long as �a,e < 1) overhe period. Moreover, the reform will increase LOS in hospital, ateast as long as it has a zero or negative effect on the risk of read-
ission. Our empirical analysis attempts to test these predictionsy estimating a reduced form transition model of hospitalisationnd re-hospitalisation analog to a difference-in-differences (DD)pproach. This model allows us to evaluate the impact of the reformn the average LOS in hospital and the risk of re-hospitalisation ofatients treated in MC departments.
. Data description
The data concerns patients’ hospitalisations in a teaching hos-ital (Sherbrooke University Hospital Center). Only patients whotayed in hospital one day or more are observed in the database.ach patient discharged from hospital was registered in theatabase over a period of 9 years (1999–2007) with their pre-ise time of admission to hospital, age, gender and department ofdmission, as well as the time when the patient left the hospital,epartment, Diagnosis-Related-Group (DRG)17 and Major Diagno-
is Category (MDC)18 when leaving.Due to problems of access to data, we could not use a sam-le period starting before 1999. One could argue that this reduces
17 The DRG system classifies hospital cases expected to have similar hospitalesources use into approximately 500 groups DRGs are assigned by an algorithmased on the International Statistical Classification of Diseases and Related Healthroblems (ICD) diagnosis codes, Current Procedural Terminology (CPT) codes, age,ender, and the presence of complications or co-morbidities. An example might behe group of females aged 55 and older with a Breast Cancer diagnosis, a Mastectomyrocedure code and an osteoporosis diagnosis (comorbidity).18 The MDC are formed by dividing all principal diagnoses into 25 mutually exclu-ive diagnosis areas. DRG codes also are mapped, or grouped, into MDC codes.Table 4) displays the list of them.
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Economics 36 (2014) 112–124
he period of observation to a small number of months before theeform, since the latter was implemented on September 1st 1999,hile our sample period starts on January 1st 1999. Note however
hat the average LOS in hospital is 6.3 days. Therefore, there is still large number of spells in hospital (13,445 visits) within this timenterval. Also, not all treated departments moved to the MC systemn September 1999. The first move to MC occurred on September7th 1999 and the last on April 18th 2005 (see column 3, Table 1).
n fact, most treated departments (12 over 19) chose to opt forC in 2000 or later. This corresponds to two thirds of all spells in
reated departments. One reason why they did not make the movet the start of the reform is that the applicable date at which a spe-iality could adopt MC (see column 3, Table 1) was negotiated athe provincial level by the government and each medical specialistssociation. A second reason is that departments were waiting fornformation or recommendations from their own association. Theotential endogeneity of the date at which a department moved toC and how we deal with this problem in our econometric model
s discussed in Section 4.Each patient leaving the hospital was registered over a 9-year
eriod, from January 1st 1999 to December 31st 2007. Hence, thisata set allows us to calculate the complete LOS in hospital and the
ength of stay out of hospital for each patient over this period. Asegards spells in hospital, there is no left-censoring since the timef admission is available for all patients. However, right-censoringxists since we do not have information on the duration of hospi-al spells in the case of individuals who were still hospitalised onecember 31st, 2007. Moreover, 2.5% of patients (see last column ofable 1) died in hospital and their spells are therefore censored.19
lso, there is no left-censoring for spells outside of hospital after first period of hospitalisation within the sample period. Never-heless, right-censoring is present for two reasons. Firstly, somendividuals were out of the hospital at the end of the sample period.econdly, since we focus on returns to hospital in the same depart-ent with the same DRG, spells ending in hospital but in another
epartment or DRG are considered censored.20 Our econometricodel takes these right-censored spells into account.Table 2 summarizes descriptive statistics over the sample
eriod. As mentioned above, the LOS in hospital is 6.3 days on aver-ge (ignoring right-censoring). Its median value is 3 days; the 25thercentile is 2 days while the 75th percentile is 7 days. The lengthf stay outside of hospital is 455.9 days on average (ignoring right-ensoring), with 80% of the population going back to hospital aftertaying 10 (10th percentile) to 1262 days (90th percentile) out ofospital. The number of spells in hospital per patient is on aver-ge 1.6, with a 25th percentile of 1 and a 75th percentile of 2. 90%f the population return to the hospital 3 times or less over theeriod considered. If we consider patients returning to hospital,he average number of spells in hospital is 2.9, whereas this aver-ge is 1.7 when considering individuals coming back to the sameepartment. The average number of spells in hospital falls to 1.3or individuals returning to the same DRG. The age of patients isn average 40.9, with 75% being less than 66 years old, and theercentage of males being 45.1%.
Since the last move to the MC system occurred in April 2005,e chose to restrict our observation window to the period from
anuary 1999 to April 2006. Given this choice, spells in hospital areo longer right-censored, except for episodes lasting more than 8
19 Later on we discuss the possibility of considering this destination within a com-eting risks model.20 Note that estimates considering patients returning to hospital in the otherepartments with other DRG would be difficult to interpret.
D. Échevin, B. Fortin / Journal of Health Economics 36 (2014) 112–124 117
Table 1Department characteristics.
Speciality Remuneration scheme Applicable date Date of change Percent of patients Percent death at hospital
All – – – 100.00 2.50Cardiac surgery MC 11.13.2000 01.05.2004 1.15 5.21Cardiology FFS 09.01.1999 n/a 11.23 3.40Diagnostic radiology FFS 09.01.1999 n/a 0.12 0.00ENT MC 09.01.1999 11.27.2000 1.35 1.28Endocrinology MC 09.01.1999 11.08.1999 0.42 0.13Gastroenterology MC 09.01.1999 04.15.2002 0.51 0.55General pediatrics MC 09.01.1999 09.27.1999 8.82 0.25General surgery MC 09.01.1999 10.23.2000 6.23 2.34Hematology MC 01.01.2002 11.18.2002 2.04 5.32Internal medicine MC 09.01.1999 01.08.2001 4.35 8.29Microbiology–infectiology FFS n/a n/a 0.10 0.00Neonatology MC 09.01.1999 06.26.2000 13.26 0.38Nephrology MC 09.01.1999 10.09.2001 2.49 6.14Neurology FFS 09.01.1999 n/a 3.57 6.03Neuropediatrics MC 09.01.1999 10.10.2001 0.09 0.00Neurosurgery MC 09.01.1999 11.08.1999 4.52 4.32Obstetrics–gynecology FFS 09.01.1999 n/a 20.51 0.21Orthopedic surgery MC 09.01.1999 11.08.1999 4.37 1.33Pedopsychiatry MC 09.01.1999 06.12.2000 0.19 0.00Pneumology FFS 09.01.1999 n/a 4.03 8.38Pneumopediatrics MC 09.01.1999 11.08.1999 0.01 0.00Radio-oncology MC 09.01.1999 03.12.2001 1.03 8.55Rheumatology MC 09.01.1999 11.29.1999 0.52 1.27Thoracic surgery MC 11.13.2000 a 0.55 2.31Urology FFS 09.01.1999 n/a 3.79 0.73Vascular surgery MC 11.13.2000 04.18.2005 4.76 3.45
Source: Authors’ computations using hospital health record database.
m(
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a Payment scheme has not changed since this department was created.
onths (they are very few) or censored by the death of the patientthey represent 2.5% of the sample; see Table 1).
. Empirical framework
In this section, we present the basic two-state transition modele use to identify the impact of the reform on two outcomes forospital departments that opted for the MC system (the treatmentroups): patients’ exit rates from hospital and their risk of re-ospitalisation to the same department and the same DRG. Theseutcomes can also be expressed in terms of the corresponding aver-ge duration in and out of the hospital. Our approach extends the
odel developed by Fortin et al. (2004) to account for the presencef many treatment and control groups.We assume that two states are possible for a patient: (i) in
ospital (s = 1) and (ii) out of hospital (s = 2). Here, two remarks
oa
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able 2atient characteristics.
Mean Std Min
Length of stay in hospital (days) 6.3 11.3 1
Length of stay out of hospital (days)Returning patients 455.9 570.8 0
Returning in same department 397.0 517.5 0
Returning in same DRG 602.0 545.5 1
Number of spells in hospitalAll patients 1.6 1.4 1
Returning patients 2.9 1.8 2
Returning in same department 1.7 1.5 1
Returning in same DRG 1.3 0.9 1
Age 40.9 28.3 0
Percent male 45.1 – –
ource: Authors’ computations using hospital health record database.
re in order. Firstly, as suggested by Picone et al. (2003), we alsomplemented a competing risks model with several post-hospitalestinations for a patient in hospital. Given the administrativeature of our data, we could consider only two mutually exclu-ive destinations: (a) death in the hospital and (b) other out of theospital destinations. However, in no specification did the reformave any overall effect on death in the hospital destination. There-
ore, we have decided to restrict our analysis to a two-state modelith spells with death in the hospital assumed to be censored.
econdly, with regards to spells out of hospital, we considered aompeting risk approach to deal with destination in hospital butot in the same department or DRG. However, this did not change
ur results in any significant way. Therefore, these destinations arelso considered censored.Our model contains many treatment groups and the time athich they are treated varies across groups. A department is a
P10 P25 P50 P75 P90 Max
1 2 3 7 14 1192
10 40 204 693 1262 32328 32 147 628.5 1104 3205
40 110 519.5 896 1324 3190
1 1 1 2 3 532 2 2 3 5 531 1 1 2 3 251 1 1 1 2 17
0 18 43 66 77 102– – – – – –
1 Health
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18 D. Échevin, B. Fortin / Journal of
reatment group if it moves to the MC system within the sampleeriod.21 Otherwise, it is a control group. There are Ks (with K1 = 23nd K2 = 22)22 departments considered in the hospital (k = 1, . . .,s), of whom the first Rs’s (with R1 = 15 and R2 = 14) opted for theC scheme within the sample period.Consider a patient i, who has occupied a state s for a duration t,
n his spell j, in the department kij (it refers to the last departmenthere he was hospitalised if he is out of the hospital), at calen-ar time �ij (= �ij(t)), with a health problem belonging to the Majoriagnosis Category MDCij (it refers to his MDC at the end of his
ast stay in hospital if he is out of hospital), and with xij (= xij(t))ime-varying observed characteristics. The calendar time at which
treated department k switched to MC is given by ck. We assume flexible mixed proportional hazard (MPH) model based on therentice-Gloeckler approach generalized by Meyer (1990) to allowor unobservable heterogeneity. The model is time-continuous butnterval-censored, that is, not directly observed, but observed to fall
ithin a known interval (e.g., one day). The individual’s conditionalazard (or exit rate) function for each state s is given by:
s(t|zsij(t), �s
ij) = exp(zsij(t))�s
0(t)�sij, s = 1, 2, (12)
ith
sij(t) =
Ks∑k=1
˛s1kI(k = kij) + P(�ij; �s) +
25∑MDC=1
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+Rs∑
k=1
ˇskI(k = kij)I(�ij ≥ ck) + x′
ijıs, (13)
here I(A) is an indicator function equal to 1 when A is true and 0therwise, and P(�ij ; �s) is a step function of (calendar) time. Eq.12) specifies the hazard rate as the product of three components:
regression function, exp(zsij), that captures the effect of observed
xplanatory variables, a baseline hazard, �s0(t), that captures vari-
tion in the hazard over the spell, and a random term, �sij, that
ccounts for the patient’s and his treating doctor(s)’ unobservedharacteristics.23
The regression function (in log) is given by Eq. (13). It corre-ponds to a standard DD approach translated into a regressionquation, when there are many treatment and control groups.he first expression in the right-hand side of (13) introducesepartment-specific fixed effects. They take into account depart-ents’ time-invariant unobservable characteristics. The second
xpression is a step function of calendar time which allows forear-quarterly changes in hazard that are common to all depart-ents (time dummies). The third expression allows for a trend in
he hazard rate from each state s for each of the 25 MDCs (seeable 4). These trends may differ from one diagnosis category tonother given that the technological progress (or other trend fac-ors) is not the same for each type of health problem. These trendsllow to take into account the possibility that some of the adopt-
ng departments are those who have been experiencing a growingOS relative to non-adopting department due to the nature of theiredical treatments. The fourth expression accounts for changes21 No MC department moved back to the FFS scheme over the period.22 The total number of departments is 26 (see Table 1). However, given the very lowumber of patients in neuropediatrics, radio-oncology, and pneumopediatrics inur sample period, these departments have been removed from all our estimations.oreover, given the small number of returns in neonatology, this department has
lso been removed from our re-hospitalisation estimations.23 For reasons of confidentiality, no information has been provided on the patient’soctor.
cmoaaMt
r
Economics 36 (2014) 112–124
over common year-quarterly changes) in the hazard that occuror each treated department k (with k = 1, . . ., Rs), after the time ck itwitches to MC. The ˇs
k’s coefficients are interpreted as the impact
f the reform on treated departments (the average effect of treat-ent on the treated). Finally, the covariates xij account for patient’s
haracteristics such as his gender, his age and his diagnosis (365RG dummies).
As mentioned earlier, using DRG dummies can control for theelection bias due to the choice of a department to change the dis-ribution of patients after a move to MC. Indeed, different DRGave different relative lengths of stay. Thus, given the flexibilityf certain departments, they may choose to allocate resources dif-erently after a change to MC by changing the distribution of thereated patients across their DRGs. This will alter the average dura-ion of hospitalisation due to a change in patients characteristics.n increase in the proportion of patients with longer length of stayight consequently increase the gain of a switch to MC. On the
ther hand, some other departments might not be able, because ofarious constraints, to change the distribution of patients by DRGnd so the potential gain of the reform is less obvious for them.sing DRG dummies will thus correct for the differences in average
ength of stay between departments that are due to the realizationf potential gains of the reform.
The MPH model is nonparametrically identified under standardssumptions including minimal variations in covariates and inde-endence between the covariates and the individual random termsee Van den Berg (2001) for a recent survey]. The latter assump-ion raises a number of important issues in our setting. Firstly, ourconometric approach must address the selectivity bias associatedith departments’ decision to opt for MC. Recall that it is not thehysician but the department, by a vote at unanimity, that decideso make such a choice. This endogeneity problem may render dif-cult the identification of the impact of the reform. For instance,he incentive to move to MC is likely to be stronger in departmentshere physicians’ treatment approach is to favour longer hospital
engths of stay. This may create a positive bias on the effect of theeform on the duration of spells in hospital. In this setting, it is plau-ible to assume that the department-specific fixed effects take thisroblem into account. More precisely, a condition for identification
s that these effects capture the unobserved common character-stics of physicians’ preferences regarding the change of paymentystem within a department.24 Secondly, related to the latter point,e suppose that, conditional on department-specific fixed effects
nd other covariates, ck is strictly exogenous. This means thathe department’s decision to choose MC at time ck within theample period is independent from the treating physician’s unob-ervable characteristics other than those taken into account by hisepartment’s fixed effect. In this regard, the introduction of trendariables that may differ across the 25 MDCs helps the identifica-ion of the model by accounting for the fact that technical progressand other trend factors) in treating specific health problems maynfluence the decision of some departments to adopt MC over timend the date at which this choice is made (i.e., the choice of ck).
A related identification issue is whether the ˇsk’s coefficients
an be interpreted as the impact of the reform on treated depart-ents. As in the standard DD approach, a basic condition is that,
nce controlling for common shocks and common time effectscross departments, there is no shock other than the reform that
ffects the treated departments’ outcomes after their adhesion toC. Again, the presence of trend variables that may vary acrosshe MDCs helps the identification of the model. This allows to take
24 Note that other factors could influence the decision to move to MC – such as theecommendations by specialist associations at the provincial level.
Health
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trlsanalyse the robustness of this result, we re-estimated the modelusing the Inverse Gaussian distribution. In that case also, we couldnot reject the null hypothesis that the variance of the distribution
D. Échevin, B. Fortin / Journal of
nto account the fact that trend factors in medical treatments mayifferently affect patients’ average LOS and their risk of rehospital-
sation in adopting and non-adopting departments. Also, patientsn departments that remained under FFS (control groups) must note affected by the reform (no general equilibrium effects). Dumontt al. (2008) provides a test which rejects the presence of a gen-ral equilibrium effect in the case of this reform. Finally, one mustssume that patients did not move from one department to anotherithin a same spell because their department opted for the MC
ystem.25
In line with the Meyer model, the baseline hazard for each states approximated by a finite number of parameters, each represent-ng the average exit rate per time interval considered. This allowsor flexibility in the relationship between the spell duration and theazard rate from a state.
The heterogeneity terms �sij
are assumed to be distributed as parametric Gamma function with mean normalized to one andariance equal to (�2)
s. We use this parametric function rather
han a non-parametric approach for a number of reasons. Firstly,t has been recently proved by Abbring and Van den Berg (2007)hat the distribution of unobserved heterogeneity in MPH modelsonverges to a Gamma distribution under realistic assumptions.26
herefore, using a Gamma function is likely to provide asymptot-cally more efficient estimators. Second, contrary to the Heckmannd Singer (1984) (HS) alternative approach which assumes a non-arametric specification of the heterogeneity by introducing anxogenous discrete number of support points, the Meyer modelields an asymptotically normal estimator so that standard largeample inference can be used. Indeed, one basic problem withhe HS estimator is that its asymptotic distribution is not known.
onte Carlo simulations by Baker and Melino (2000) have shownhat the HS approach provides inconsistent estimates of the MPH
odel, when the baseline hazard is left fairly free. Thirdly, Han andausman (1990) reports empirical results indicating that a flexible
pecification of the hazard function sharply reduces the sensitivityf the estimates to a parametric heterogeneity assumption.
Here a number of remarks are in order. Firstly, since �sij
includesoth a patient’s and his treating physician(s)’ unobservable charac-eristics, we cannot assume that it is invariant across various spellsithin a same state as in a standard multi-spell model. Indeed, aatient may change physicians from one spell at the hospital tonother. Note however that within a given spell j, patient i’s het-rogeneity term is time-invariant. This accounts for the problemf inconsistent estimated standard errors in the presence of seri-lly correlation of outcomes (see Bertrand et al., 2004). However,e ignore the presence of dependency between unobserved het-
rogeneity across spells of a same individual.27 Nevertheless, weo introduce some dependency across spells by allowing the re-ospitalisation hazard of a patient outside of hospital to be relatedo his diagnosis in his preceding spell of hospitalisation. Also, wegnore occurrence and lagged duration dependence (i.e., depen-
ence of the termination probability of the spell in progress onither the number or the duration of previous spells) as well as seri-lly correlated unobserved heterogeneity. Incomplete information25 One must also suppose that physicians do not move from one department tonother or migrate because of the reform. Indeed, there is strong evidence thatrench-speaking physicians (mostly from Quebec) are less likely than English-peaking physicians to migrate to all provinces (see Dostie and Léger, 2009).oreover, these authors conclude that, in Canada, physicians’ migration decision
s insignificantly correlated with exogenous changes in fee-for-services rates.26 Given the very large number of observations in our data set, the asymptoticroperties of our estimators are likely to hold.27 We provide some evidence later on that this is unlikely to affect the parametersf interest estimators very much.
i
72
damtipp
Economics 36 (2014) 112–124 119
egarding previous hospital spells leaded us to adopt this strategy.lso, introducing diagnosis dummies is likely to partly control for
hese problems. Finally, as discussed earlier, left-censoring of therst spell is not a problem in our panel data, while right-censoringre taken into account in the estimations.
. Results
In what follows, we provide maximum likelihood estimationesults from our two-state MPH model.28 We also present a robust-ess analysis of our results with respect to various specifications.
n all of them, we included six time intervals (in days) to accountor our flexible baseline hazard in each state. The intervals consid-red are 0, 1, 5, 10, 15, 20 + in the case of spells in hospital and 0,0, 50, 100, 500, 1000+ in the case of spells out of hospital.29 These
ntervals were chosen based on histograms of spells in each stage. number of experiments suggest that the impact of other covari-tes is little affected by changes in the number and the size of thesentervals.
As regards the covariates, after a number of experiments, weave introduced in each model year-quarterly time dummies. Also,
quadratic polynomial in age, a gender dummy and six dummiesor the day at which the patient was admitted in the hospital haveeen included as covariates. In the latter case, one expects that aatient admitted on Saturday or Sunday will stay longer in hospi-al since medical exams and treatments are usually less numerousuring the weekend.
Table 3 provides the parameter estimates of the hazard raterom hospital. We test several specifications of the same model.n the first specification (model 1), we use Gamma heterogeneityf the error term but we add neither DRG dummies nor specificrends for the 25 MDCs. The coefficients (which measure theverage treatment effect on each treated department) are nega-ive for 12 departments/specialities and, among these, significantt the 5% level for 8 departments out of 15 which have moved toC in our sample. Patients in these 8 departments represent 68.26%
f all MC patients in our sample. The coefficients are positive andignificant for only two departments (vascular surgery and hema-ology). Patients in these two departments represent 12.4% of all
C patients in our sample. This indicates that the rate of exit fromospital is reduced in most departments that moved to MC. Theegative effect varies from 9.3% in general pediatrics to 36.2% inheumatology.
Interestingly, we find that the variance of the Gamma distribu-ion (�) is not statistically significant according to the LR test.30 Theejection of unobserved heterogeneity is a standard result in theiterature especially in the presence of a flexible parametric repre-entation of the baseline hazard (see Baker and Melino, 2000). To
s zero. The absence of unobserved heterogeneity problems partly
28 See Meyer (1990) for a derivation of the maximum likelihood function.29 The percentiles of the days used as cutoffs for intervals are respectively the 16th,0th, 85th, 91th and 94th percentiles for hospital length of stay and the 5th, 14th,0th 43th and 62th for the length of stay out of hospital.30 Note that the test is a boundary one that takes into account the fact that the nullistribution is not the usual chi-squared (with one degree of freedom) but is rather
50:50 mixture of a chi-squared (degree of freedom = 0) variate (which is a pointass at zero) and chi-squared (degree of freedom = 1). The standard chi-squared
est is incorrect since the model with no unobservable heterogeneity is not nestedn the model with Gamma heterogeneity. Furthermore, in a previous version of theaper, we estimate a Cox specification analog to model 2 and found very similararameters’ estimates.
120 D. Échevin, B. Fortin / Journal of Health Economics 36 (2014) 112–124
Table 3Estimates of hazard rates from hospital.
Model 1 Model 2 Model 3 Model 4
Coef. P > |z| Coef. P > |z| Coef. P > |z| Coef. P > |z|˛1 Cardiology 1.210 0.000 1.097 0.000 1.138 0.000 0.997 0.000
Cardiac surgery 0.415 0.003 1.375 0.000 1.332 0.000 1.183 0.000General surgery 1.087 0.000 1.444 0.000 1.456 0.000 1.294 0.000Orthopedic surgery 0.864 0.000 1.238 0.000 1.172 0.000 1.166 0.000Thoracic surgery 0.715 0.000 1.448 0.000 1.494 0.000 1.354 0.000Vascular surgery 0.835 0.000 1.483 0.000 1.566 0.000 1.417 0.000Endocrinology 1.370 0.000 1.573 0.000 1.619 0.000 1.398 0.000Gastroenterology 2.258 0.000 2.411 0.000 2.424 0.000 2.229 0.000Hematology 0.679 0.000 0.847 0.000 0.903 0.000 0.813 0.000Internal medicine 0.862 0.000 0.901 0.000 0.949 0.000 0.795 0.000Microbiology–infectiology 1.619 0.000 1.634 0.000 1.658 0.000 1.517 0.000Neonatology 0.805 0.000 0.820 0.000 0.759 0.000 0.678 0.000Nephrology 0.767 0.000 0.848 0.000 0.889 0.000 0.713 0.000Neurosurgery 0.831 0.000 1.332 0.000 1.293 0.000 1.228 0.000Neurology 0.855 0.000 0.972 0.000 1.019 0.000 0.877 0.000Obstetrics–gynecology 1.305 0.000 1.477 0.000 1.529 0.000 1.386 0.000ENT 1.416 0.000 1.830 0.000 1.789 0.000 1.568 0.000General pediatrics 0.925 0.000 1.074 0.000 1.083 0.000 0.975 0.000Pedopsychiatry – – – – – – – –Pneumology 0.807 0.000 0.894 0.000 0.941 0.000 0.799 0.000Diagnostic radiology 2.648 0.000 3.092 0.000 3.108 0.000 2.970 0.000Rheumatology 1.249 0.000 1.467 0.000 1.436 0.000 1.015 0.000Urology 1.401 0.000 1.577 0.000 1.626 0.000 1.485 0.000
ˇ Cardiac surgery −0.007 0.914 −0.025 0.706 −0.086 0.191 −0.075 0.000General surgery −0.180 0.000 −0.150 0.000 −0.103 0.001 −0.075 0.000Orthopedic surgery −0.033 0.458 −0.052 0.247 0.078 0.130 −0.075 0.000Vascular surgery 0.274 0.000 0.014 0.721 −0.134 0.001 −0.075 0.000Neurosurgery −0.061 0.189 −0.077 0.102 0.011 0.826 −0.075 0.000ENT −0.169 0.001 −0.286 0.000 −0.181 0.002 −0.075 0.000Endocrinology −0.165 0.191 −0.167 0.185 −0.167 0.198 −0.075 0.000Gastroenterology −0.200 0.005 −0.225 0.002 −0.173 0.020 −0.075 0.000Internal medicine −0.111 0.000 −0.096 0.001 −0.094 0.002 −0.075 0.000Nephrology −0.111 0.002 −0.137 0.000 −0.129 0.000 −0.075 0.000Rheumatology −0.362 0.001 −0.482 0.000 −0.385 0.001 −0.075 0.000General pediatrics −0.093 0.002 −0.088 0.004 −0.037 0.246 −0.075 0.000Neonatology −0.166 0.000 −0.135 0.000 −0.003 0.927 −0.075 0.000Pedopsychiatry 0.057 0.699 0.032 0.841 0.104 0.560 −0.075 0.000Hematology 0.099 0.006 0.071 0.050 0.059 0.133 −0.075 0.000
� const1 −4.161 0.000 −5.430 0.000 −5.485 0.000 −5.354 0.000const2 −3.644 0.000 −4.783 0.000 −4.835 0.000 −4.705 0.000const3 −4.025 0.000 −4.915 0.000 −4.962 0.000 −4.832 0.000const4 −4.239 0.000 −5.012 0.000 −5.055 0.000 −4.926 0.000const5 −4.442 0.000 −5.127 0.000 −5.170 0.000 −5.040 0.000const6 −4.892 0.000 −5.338 0.000 −5.382 0.000 −5.252 0.000
Age −0.014 0.000 −0.006 0.000 −0.006 0.000 −0.006 0.000Age2 0.000 0.996 0.000 0.000 0.000 0.000 0.000 0.000Male 0.019 0.002 0.031 0.000 0.030 0.000 0.030 0.000Tuesday 0.049 0.000 0.043 0.000 0.041 0.000 0.041 0.000Wednesday 0.036 0.000 0.038 0.000 0.037 0.000 0.037 0.000Thursday 0.051 0.000 0.031 0.003 0.030 0.004 0.030 0.004Friday 0.013 0.212 0.013 0.228 0.012 0.236 0.012 0.243Saturday −0.030 0.005 −0.055 0.000 −0.055 0.000 −0.055 0.000Sunday −0.038 0.001 −0.057 0.000 −0.059 0.000 −0.060 0.000
ln(�) −20.991 0.962LR-test � 0.000 1.000Log L −193,736 −178,505 −178,210 −178,231Number of observations 144,510 144,510 144,510 144,510Gamma heterogeneity Yes No No NoDRG dummies No Yes Yes Yes
Source: Authors’ computations using hospital health record database. Note: Proportional hazard model with piecewise constant baseline hazard is used for all specifications.All models include year-quarterly time dummies. Models 3 and 4 include linear and quadratic trends for each of the 25 MDCs.
Health Economics 36 (2014) 112–124 121
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Table 4List of major diagnostic categories (MDC).
# MDC
1 Nervous system2 Eye3 Ear, nose, mouth, throat4 Respiratory system5 Circulatory system6 Digestive system7 Liver, bile duct and pancreas8 Bones, aritculations, muscles9 Skin, breasts10 Endocrinal, metabolic or nutritional troubles11 Urinal system12 Male reproductory system13 Female reproductory system14 Pregnancy, childbirth and puerperium15 Newborns16 Blood, immunatory system17 Immunoproliferative troubles and undefined tumors18 Infections diseases and parasites19 Mental and behavioural problems20 Drug-related mental and behavioural problems21 Wounds, poisoning and other external troubles22 Burns23 Other elements affecting health and use of substances24 IHV-related problem25 Multiple traumatic lesions
Table 5Impact of the reform on the simulated expected duration in hospital.
Department Difference (days) Relative effect
Cardiac surgery 1.56 0.101(1.16)
General surgery 0.79 0.119(0.07)
Orthopedic surgery −0.82 −0.084(0.34)
Vascular surgery 0.93 0.153(0.15)
Neurosurgery −0.11 −0.012(0.35)
ENT 1.00 0.215(0.62)
Endocrinology 0.57 0.185(0.23)
Gastroenterology 0.32 0.190(0.04)
Internal medicine 1.21 0.108(0.21)
Nephrology 1.69 0.155(0.25)
Rheumatology 3.20 0.529(0.62)
General pediatrics 0.13 0.039(0.10)
Neonatology 0.01 0.003
D. Échevin, B. Fortin / Journal of
ustify our assumption that spells in and out of the hospital arendependent.
In model 2, we add the 365 DRG dummies while excludingamma heterogeneity.31 The DRG dummies are jointly significantt the 1% level according to a LR test. Model 2 slightly alters ouresults. The reform still has a significantly negative impact on thexit rate from hospital of 8 departments out of 15. In this specifica-ion, it is no more significant for the vascular surgery departmentut still positive and significant for the hematology department.he negative effect varies from 8.8% in general pediatrics to 48.2%n rheumatology. This specification suggests that the reform hasncreased LOS in hospital for 68.26% of all MC patients in our sam-le.
Model 3 (preferred specification) provides results when addinginear and quadratic trends for each of the 25 MDC. Based on aR test, these trends are significantly different from zero at the% level. Estimates in models 2 and 3 are slightly different. Theeform now has a significantly negative impact on the exit rate fromospital of the vascular surgery department, while it is no longerignificant for the general pediatrics, neonatology and hematol-gy departments. In this specification, the impact of the reform onhe exit rate from hospital is negative whenever it is significant7 departments). Finally, model 4 yields estimates when imposinghe equality of the coefficients.32 According to our results, the exitate from hospital decreased by about 7.5% on average in depart-ents that moved to MC, with this effect being significant at the
% level.Looking at other covariates in model 3, we find, as expected, that
ge has a negative impact on the exit rate from hospital and thattarting hospitalisation during the weekend has a negative impacts well. Being a male has a positive impact on the exit rate (pre-umably due to a higher average opportunity cost in terms of wagearnings and easier substitutability between home and hospitalare). The effect of the MDC trends variables (not reported in theable) appears to be positive.
We simulate the impact of the reform on the duration of hos-italisation in Table 5 using Katz and Meyer’s (1990) approach.elative effects of the change in the payment system on expecteduration are also provided. They are estimated for each treatedepartment over the sample period 1999–2006. The simulationsse parameter estimates to predict the expected duration of hos-italisation over the sample period, with or without the effect ofhe change. The simulation procedure states as follows. Firstly,he predicted survivor function is simulated for each patient andach day of hospitalisation and then aggregated for the samplever individuals. Second, the predicted mean duration is calculatedy accumulating the aggregate survivor function by day.33 Finally,e estimate the difference between expected durations estimatedith and without the change. Relative effect is obtained by divid-
ng the difference by the expected duration estimated without thehange.
We find that LOS in hospital has increased by 0.28 days overalln treated departments. This corresponds to a percentage increase
f 4.2%. The department of rheumatology experienced the largestmpact with an increase in LOS by 3.20 days (or 52.9%) while theepartment of neonatology experienced the lowest positive impact31 When adding both DRG and Gamma heterogeneity, the variance of the Gammaistribution still appears to be not statistically significant and parameters estimatesre almost the same as in model 2.32 A LR test rejects this restriction which conducts us to prefer Model 3 specifica-ion.33 Note that the number of days used for this computation should be large enoughn order for the procedure to converge.
(0.12)Pedopsychiatry −1.46 −0.112
(6.24)Hematology −0.64 −0.063
(0.24)All departments 0.28 0.042
(0.07)
Source: Authors’ computations using hospital health record database. Notes: Stan-dard errors in parentheses. Katz and Meyer’s (1990) approach has been used toconvert estimated exit rates into expected durations. Model 3 specification isused for the simulation of expected durations of each department over the period1999–2006.
122 D. Échevin, B. Fortin / Journal of Health Economics 36 (2014) 112–124
Table 6Estimates of re-hospitalisation hazard rates.
Model 1 Model 2 Model 3 Model 4
Coef. P > |z| Coef. P > |z| Coef. P > |z| Coef. P > |z|˛1 Cardiology 1.172 0.000 −0.218 0.687 −0.390 0.482 −0.256 0.605
Cardiac surgery −1.065 0.040 0.578 0.411 0.363 0.613 0.357 0.580General surgery 0.073 0.828 −0.407 0.454 −0.515 0.359 −0.325 0.507Orthopedic surgery −0.098 0.791 −0.741 0.218 −0.870 0.162 −0.447 0.383Thoracic surgery 0.229 0.558 0.190 0.759 0.031 0.961 0.158 0.785Vascular surgery 1.073 0.001 0.057 0.916 −0.093 0.868 0.070 0.887Endocrinology 2.168 0.000 0.045 0.942 −0.199 0.756 −0.608 0.232Gastroenterology 0.600 0.108 −0.795 0.164 −0.980 0.096 −0.897 0.086Hematology 1.982 0.000 −0.399 0.459 −0.525 0.345 −0.443 0.367Internal medicine 0.694 0.039 −0.793 0.143 −0.890 0.111 −0.603 0.216Microbiology–infectiology 0.361 0.488 −0.728 0.294 −0.899 0.203 −0.777 0.238Nephrology 1.492 0.000 0.392 0.469 0.310 0.578 0.294 0.548Neurosurgery 0.845 0.017 0.600 0.291 0.528 0.367 0.726 0.138Neurology 0.737 0.025 −0.440 0.413 −0.601 0.277 −0.467 0.342Obstetrics–gynecology 1.611 0.000 −0.577 0.291 −0.745 0.185 −0.613 0.222ENT −0.529 0.168 −1.140 0.057 −1.238 0.045 −1.142 0.032General pediatrics 0.297 0.370 −0.687 0.203 −0.724 0.193 −0.731 0.129Pedopsychiatry – – – – – – – –Pneumology 2.088 0.000 0.081 0.879 -0.081 0.884 0.052 0.916Diagnostic radiology 0.860 0.083 −0.644 0.334 −0.856 0.208 −0.743 0.240Rheumatology 0.754 0.053 −0.122 0.838 −0.315 0.609 0.243 0.639Urology 0.770 0.019 −0.185 0.736 −0.354 0.529 −0.225 0.654
ˇ Cardiac surgery −0.153 0.541 −0.185 0.492 −0.224 0.409 −0.021 0.624General surgery −0.028 0.798 0.139 0.254 0.061 0.653 −0.021 0.624Orthopedic surgery −0.150 0.445 0.342 0.171 0.300 0.264 −0.021 0.624Vascular surgery 0.697 0.000 0.392 0.003 0.272 0.048 −0.021 0.624Neurosurgery 0.913 0.000 0.150 0.438 0.044 0.829 −0.021 0.624ENT −0.083 0.663 −0.006 0.977 −0.079 0.741 −0.021 0.624Endocrinology −0.739 0.000 −0.714 0.018 −0.617 0.059 −0.021 0.624Gastroenterology −0.076 0.680 −0.141 0.479 −0.131 0.522 −0.021 0.624Internal medicine 0.173 0.114 0.301 0.017 0.194 0.140 −0.021 0.624Nephrology −0.063 0.591 −0.131 0.313 −0.254 0.065 −0.021 0.624Rheumatology 0.403 0.023 0.444 0.045 0.453 0.050 −0.021 0.624General pediatrics −0.080 0.375 −0.049 0.666 −0.177 0.143 −0.021 0.624Pedopsychiatry 0.067 0.758 −0.104 0.697 −0.169 0.552 −0.021 0.624Hematology 0.128 0.186 −0.066 0.581 −0.125 0.338 −0.021 0.624
� const1 −22.649 0.996 −13.033 0.277 −12.880 0.257 −12.798 0.202const2 −20.196 0.996 −10.437 0.384 −10.266 0.366 −10.185 0.310const3 −20.570 0.996 −10.475 0.382 −10.284 0.365 −10.204 0.309const4 −21.533 0.996 −11.332 0.345 −11.136 0.327 −11.057 0.271const5 −21.441 0.996 −11.076 0.356 −10.864 0.339 −10.786 0.283const6 −22.695 0.996 −12.250 0.307 −12.030 0.289 −11.953 0.234
Age −0.026 0.000 −0.013 0.000 −0.012 0.000 −0.012 0.000Age2 0.000 0.000 0.000 0.477 0.000 0.678 0.000 0.694Male −0.063 0.015 −0.008 0.785 −0.007 0.829 −0.007 0.811
ln(�) −11.674 0.773 −0.236 0.004 −0.098 0.204 −0.100 0.194Log L −42971 −38014 −37972 −37983Number of observations 125,291 125,291 125,291 125,291Gamma heterogeneity Yes Yes Yes YesDRG dummies No Yes Yes Yes
Source: Authors’ computations using hospital health record database.Note: Mixed proportional hazard model with piecewise constant baseline hazard and Gamma distribution is used for all specifications. All models include year-quarterlytime dummies. Models 3 and 4 include linear trends for each of the 25 MDCs.
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ith a LOS being stable. Internal medicine has also experienced aow positive and significant impact on days in hospital. These smallncreases may partly be explained by the fact that fewer servicesre provided by these specialists. Moreover, regarding neonatol-gy, the discharge of newborns does not generally depend on theolume of services provided and thus may not be influenced by
he reform. For instance, in the case of acute medical problems,n order to be discharged, premature infants must know how toeed by themselves and grow; cardiorespiratory stability is also arerequisite that may only depend on time. On the other hand, theahtn
ischarges in rheumatology may be more dependent on the volumef services provided.
Table 6 presents the parameter estimates for the risk of re-ospitalisation to the same department with the same DRG. Model
includes neither DRG dummies nor MDC trend variables andssumes Gamma heterogeneity with the covariates given by age,
2
ge , gender and year-quarterly time dummies as in the model ofazard rates from the hospital. Results indicate that the impact ofhe reform is non significant for 10 departments, positive and sig-ificant for three departments (vascular surgery, neurosurgery, and
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D. Échevin, B. Fortin / Journal of
heumatology), and negative for only one department (endocrinol-gy), out of 14 MC departments.34 This specification suggests thathe reform has increased the re-hospitalisation rates for 17.8% of
C patients and has reduced these rates for 0.76% of them. In thispecification, the variance of the Gamma distribution is high andignificantly different from zero, which suggests the presence ofnobserved heterogeneity.
Model 2 adds DRG dummies while still allowing for Gammanobserved heterogeneity. In this specification, the impact of theeform is no longer significant for neurosurgery but is positive andignificant for internal medicine. As a consequence, the reform isredicted to increase the re-hospitalisation rate for 17.5% of MCatients.
Model 3 provides results when adding a linear trend for eachf the 25 MDC.35 Again, based on a LR test, these trends are sig-ificantly different from zero at the 1% level. The reform is nowot significant for 12 departments out of 14 MC departments. It iso longer significant at the 5% level for endocrinology and inter-al medicine but still positive and significant for vascular surgerynd rheumatology. However, in Model 4 (our preferred specifica-ion), which imposes all the coefficients to be equal (not rejectedt the 5% level), the average impact of the reform is not signifi-ant. This result thus suggests that the reform had no impact onhe re-hospitalisation rate at the global level. As regards the otherovariates in model 4, we find that age has a negative impact one-hospitalisation rates. However, being a male has no significantffect on the risk of re-hospitalisation.
All in all, our results are consistent with our theoretical frame-ork according to which patients treated by physicians who move
o MC spend more days in hospital over the period. It is also con-istent with the prediction that, given that the reform has no effectn a patient’s risk of re-hospitalization, it will increase his LOSn hospital. Empirically, this effect is reflected by an increase inhe duration of hospitalisation but no change in the risk of re-ospitalisation at the global level.
. Conclusion
This paper aims at analysing the impact of a reform in Que-ec that introduced an optional mixed compensation system forpecialists in hospital, combining a fixed per diem with a reducedee for services provided, as an alternative to the standard fee-or-service scheme. Using patient-level data from a major teachingospital, this paper assesses the effect of the reform upon patients’
ength of stay in hospital and their risk of re-hospitalisationo departments that opted for this new system. Based on thestimates of a two-state transition model analog to a difference-in-ifferences approach, our results are twofold. Firstly, we find thathe length of stay in hospital has increased on average by about 4.2%n these departments. This corresponds to an average increase of.28 days in hospital. Secondly, at the global level, the risk of re-ospitalisation does not seem to be affected by the reform. Theseesults are consistent with our theoretical model which suggestshat such a reform will induce physicians who opt for the mixedompensation scheme to adopt a practice pattern which increasesheir patients’ number of days of hospitalisation per period, as wells their patients’ length of stay in hospital, for a given risk level of
e-hospitalisation.These effects are relatively strong and were probably not antic-pated by policy makers. Moreover an increase in patients’ hospital
34 Recall that neonatology has been removed from our re-hospitalisation ratespecifications.35 The hazard model for re-hospitalisation did not converge with quadratic trends.
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Economics 36 (2014) 112–124 123
ength of stay is likely to be seen as a perverse impact of theeform. However, the full policy implications of our analysis areixed. On the one hand, an increase in patients’ number of days in
ospital is costly both in time and money, ceteris paribus. Indeed,his is why a large number of health care policies such as therospective payment system introduced in the U.S. mainly aimt reducing hospital length of stay. On the other hand, such anncrease may be partly justified for two reasons. Firstly, it may bessociated with more time spent by physicians on nonclinical activ-ties such as teaching and administrative tasks, which are likely toe neglected under a fee for service scheme. As mentioned ear-
ier, Dumont et al. (2008) provide evidence consistent with thisffect as related to the Quebec reform. Second, as long as physi-ians spend more time treating their patients in hospital, this maymprove patients’ health. However, our results do not suggest thiss the case since the risk of re-hospitalisation has not decreased athe global level in any treated departments. On the contrary, twoepartments (namely internal medicine, and rheumatology) have
ncreased their re-hospitalisation rate of patients with the sameiagnosis.
A natural extension of our research would be to compare thevolution of health status of two random groups of patients with
same diagnosis but one treated by physicians under a fee-for-ervice scheme and the other one by physicians under a mixedompensation scheme. We leave that for future research.
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