Three Essays on the Impact of Financial Incentives,
Waiting Times and Home Care on Patients' Health and
Utilization of Health Care Services in Quebec
Thèse
Kossi Thomas Golo
Doctorat en économique
Philosophiæ doctor (Ph. D.)
Three Essays on the Impact of Financial Incentives,
Waiting Times and Home Care on Patients’ Health and
Utilization of Health Care Services in Quebec
Thèse
Kossi Thomas Golo
Sous la direction de:
Guy Lacroix, Directeur de recherche Bernard Fortin, Codirecteur de recherche
RÉSUMÉ
Cette thèse de doctorat est composée de trois chapitres distincts et indépendants qui ont pour objectif d’analyser certaines politiques de santé au Québec notamment les incitatifs financiers, les délais d’attente et les soins à domicile sur la santé des patients et l’utilisation de services hospitaliers.
Le premier chapitre porte sur l’impact des incitatifs financiers sur la santé des patients, spé-cialement le cas des soins spécialisés. Il faut noter de prime abord que la demande de soins de santé a beaucoup augmenté au Québec ces dernières années pour certains types de chirur-gies. Cette augmentation, dont les causes sont multiples notamment les changements démo-graphiques, a entraîné des temps d’attente plus élevés que les temps médicalement requis pour ces chirurgies.
Pour résorber ce problème, le gouvernement québécois a mis en place en 2004 le Programme d’Accès à la Chirurgie (PAC), afin d’inciter financièrement les hôpitaux à pratiquer plus de chirurgies pour lesquelles les délais d’attente étaient plus importants. Ce programme a per-mis de diminuer la durée moyenne d’attente pour ces chirurgies, mais a aussi entraîné une augmentation des dépenses liées à ces chirurgies. Ces dépenses accrues étaient également dûes à certaines lacunes du programme. Une réforme majeure, qui consistait essentiellement à la modification des incitatifs financiers, a eu lieu en avril 2011, afin que le financement vienne appuyer la bonne pratique et le choix du plateau technique le plus adéquat. Notre étude, constituant une première évaluation de cette réforme, a pour but d’analyser l’impact de cette réforme sur la santé des patients, notamment les durées de séjour à l’hôpital après l’opération chirurgicale et les réadmissions après la sortie de l’hôpital. Notre application porte sur les chirurgies thoraciques et cardiovasculaires. Les résultats montrent une
diminu-tion significative des durées de séjour après l’introducdiminu-tion de la réforme et un impact non significatif sur les réadmissions urgentes.
Dans le premier chapitre, les différentes politiques mises en places ont été initialement mo-tivées par des délais d’attente excessifs. Pourtant, peu d’études ont analysé les impacts des délais d’attente sur la santé des patients au Québec. Tel est l’objectif du deuxième chapitre de la thèse, analyser si un délai d’attente élevé est associé à un risque de détérioration de la santé des patients. Nous utilisons des modèles empiriques pour analyser cette problé-matique. Nous introduisons le différentiel de distance du domicile du patient à l’hôpital le plus proche relativement à l’hôpital le plus proche parmi les hôpitaux avec de faibles dé-lais d’attente comme variable instrumentale pour tenir compte de l’endogénéité potentielle des temps d’attente. Dans ce chapitre, nous analysons les variables de santé en termes de probabilité de réadmission urgente et de durée de séjour excédentaire (durée de séjour sup-plémentaire après la durée de séjour maximal recommandée). Les résultats montrent que les longs temps d’attente augmentent la probabilité d’être réadmis en urgence pour les patients qui ont eu une chirurgie de l’arthrose du genou, une chirurgie thoracique ou cardiovascu-laire, une neurochirurgie, ou une chirurgie pour une tumeur de l’utérus. Il n’y a pas d’effet significatif des temps d’attente sur la probabilité de readmission pour les chirurgies de l’ar-throse de la hanche et des tumeurs de la prostate. Les longs temps d’attente augmentent également la durée de séjour à l’hôpital et les coûts d’hospitalisation après une chirurgie de l’arthrose du genou ou de la hanche.
Le vieillissement de la population québécoise entraîne plusieurs enjeux cruciaux pour les services de soins de santé notamment les soins à domicile pour les personnes âgées (OIIQ,
2017). Les soins à domicile sont composés de tous les soins de santé que les établissements publics ou privés offrent aux individus à leur domicile. Ces services sont souhaitables pour toute personne qui a besoin de soins pour maladies chroniques, de soins palliatifs, de soins de réadaptation, de soins de fin de vie, ou des soins pour perte d’autonomie liée au vieillis-sement. Les soins à domicile pourraient constituer une alternative sécuritaire, à moindres coûts, aux soins de santé dans les hôpitaux. Les soins à domicile contribuent donc au main-tien à domicile des personnes en offrant des services paramédicaux des infirmières, des aide-soignantes, coordonnés avec ceux des autres intervenants à domicile comme les kiné-sithérapeutes, les aides-ménagères, les auxiliaires de vie. Nous analysons dans le troisième
chapitre, dans quelles mesures les services hospitaliers et les soins à domicile pour les per-sonnes âgées sont substituables. Nous analysons également l’impact des soins à domicile sur l’admission dans les centres d’hébergement de soins de longue durée (CHSLD). Notre analyse montre que l’augmentation des soins à domicile pour les personnes âgées réduit la probabilité d’admission et la durée de séjour en urgence. L’effet des soins à domicile est plus prononcé chez les personnes âgées avec des pertes d’autonomie plus légères. Les résultats montrent également qu’une augmentation des soins à domicile réduit la probabilité d’être admis en CHSLD.
ABSTRACT
This doctoral thesis is composed of three separate and independent chapters that aim to analyze certain health policies in Quebec, including financial incentives, waiting times and home care on patients’ health and the use of hospital services.
The first chapter focuses on the impact of financial incentives on the health of patients in Quebec, especially the case of specialized care. It should be noted, first of all, that the de-mand for health care has increased significantly in Quebec in recent years for certain types of surgery. This increase, which has many causes, including demographic changes, resulted in higher waiting times than the medically required times for these surgeries.
To solve this problem, the Quebec government implemented in 2004 the Access to Surgery Program (ASP) to financially encourage hospitals to perform more surgeries for which wait-ing times were longer. This program allowed to reduce the average waitwait-ing time for these surgeries, but has also led to an increase in expenses related to these surgeries. These in-creased expenditures were also due to some weaknesses in the program. A major reform, which consisted mainly of modifying the financial incentives, took place in April 2011, so that the funding would support good practice and the choice of the most appropriate techni-cal platform. Our study, which is a first evaluation of this reform, aims to analyze the impact of this reform on the health of patients, including the length of stay in hospital after surgery and readmissions post-discharge. The results show a significant decrease in length of stay after the introduction of the reform and a non-significant impact on urgent readmissions post-discharge within 30 days.
In the first chapter, the various policies were initially motivated by excessive waiting times. Yet, few studies have analyzed the impact of wait times on patient health in Quebec. This
is the purpose of the second chapter, to analyze whether a high waiting time is associated with a risk of deterioration of the patients’ health. We use empirical models to analyze this problem. We introduce the differential distance from the patients’ home to the nearest hos-pital relative to the nearest hoshos-pital among hoshos-pitals with low wait times as an instrumental variable to account for the potential endogeneity of the waiting time. In this chapter, we analyze health variables in terms of the probability of urgent readmission post-discharge within 30 days and excess length of stay (additional length of stay after the maximum rec-ommended length of stay). The results show that long waiting times increase the likelihood of emergency readmissions for patients who had a knee surgery, a thoracic or cardiovascular surgery, a neurosurgery or a surgery for a tumor of the uterus. There is no significant effect of waiting times on the probability of readmission for hip and prostate surgeries. Long wait-ing times also increase the hospital length of stay and costs of hospitalization for knee and hip surgeries.
The aging of the Quebec population is leading to many crucial issues for health care services, particularly home care for the elderly (OIIQ,2017). Home care is composed of all health care that public or private institutions provide to individuals in their homes. These services are desirable for anyone who needs care for chronic illnesses, palliative care, rehabilitation care, end-of-life care, or care for loss of autonomy linked to aging. Home care could be a safe, low-cost alternative to health care in hospital. Home care, thus contributes to people to stay at home and receive paramedical services from nurses and care assistants, coordinated with those received from other home care providers such as physiotherapists, housekeepers and carers. In the third chapter, we analyze the extent to which hospital services and home care for the elderly are substitutes. We also analyze the impact of home care on admission to long-term care facilities (LTCFs). Our analysis shows that increased home care for the elderly reduces the probability of admission and the length of stay in emergency. The effect of home care is greater for seniors with less disabilities. The results also show that an increase in home care reduces the probability of being admitted to LTCFs.
Table des matières
Résumé iii
Abstract vi
Table des matières viii
Liste des tableaux x
Liste des figures xii
Remerciements xv
Introduction 1
1 Impact of Hospital Financial Incentives on Health Outcomes : Evidence from
Thoracic and Cardiovascular Surgeries in Quebec 3
1.1 Introduction . . . 4
1.2 Context . . . 6
1.3 Health outcome variables . . . 9
1.4 Data and Variables . . . 11
1.5 Empirical Model. . . 15
1.6 Results . . . 20
1.7 Robustness Tests . . . 23
1.8 Conclusion and discussion . . . 28
2 Do Waiting Times Affect Health Outcomes ? Evidence from Elective Surgeries in Quebec 31 2.1 Introduction . . . 32
2.2 Previous literature . . . 33
2.3 Measuring waiting times . . . 35
2.4 Health outcomes variables . . . 37
2.5 Data . . . 39
2.6 Empirical Model. . . 42
2.7 Results . . . 48
2.8 Robustness Checks . . . 52
2.9 Impact of waiting on hospital costs . . . 56
3 Substitution between Home Care and Health Care Utilisation : The Case of
the Elderly in Quebec 60
3.1 Introduction . . . 61
3.2 Previous literature . . . 62
3.3 Context and Conceptual framework . . . 63
3.4 Data and descriptive statistics . . . 65
3.5 Empirical Method . . . 71
3.6 Results . . . 75
3.7 Impact of home care on admission to long-term care facilities (LTCFs). . . 86
3.8 Concluding remarks . . . 89 Conclusion 91 Bibliographie 93 A 109 A.1 Annex 1. . . 109 A.2 Annex 2. . . 117 A.3 Annex 3. . . 123
Liste des tableaux
1.1 ASP tariff categories from 2004-2005 to 2010-2011. . . 6
1.2 Cost categories and tariffs from 2011-2012 to 2013-2014 for thoracic and car-diovascular surgeries in ASP . . . 13
1.3 Patients characteristics . . . 14
1.4 Number of patients by destination and group. . . 14
1.5 Number of treated patients by destination and period . . . 15
1.6 Proportion (%) of patients in the treatment group over years . . . 15
1.7 Average length of stay in hospital and Readmissions rates by post-discharge destination . . . 21
1.8 Test equality of survivor functions (Null Hypothesis : Equality of functions) . 21 1.9 Estimates of ln(duration) of two-state model . . . 22
1.10 Ordinary Least Square Difference-in-difference . . . 23
1.11 Placebo treatment - Estimates of ln(duration) of two-state model . . . 25
1.12 Parallel Paths (H0: Treatment and Control groups have the same trend) . . . 26
1.13 Readmission rates . . . 27
1.14 Estimates of ln(duration) of two-state model . . . 27
2.1 Description of patients . . . 40
2.2 Summary of average waiting over hospitals . . . 41
2.3 First stage regression (Log of waiting times). . . 48
2.4 Marginal effects on 30-day emergency readmission+ . . . 50
2.5 Impact of waiting times . . . 52
2.6 marginal effects of Impact of waiting times . . . 53
2.7 First step regression. . . 54
2.8 Variables Z, estimates of µ2on X . . . 55
2.9 Impact of waiting time and Exogeneity test . . . 55
2.10 Description of NIRRU . . . 57
2.11 Marginal effects on costs of Hospitalization . . . 58
3.1 Descriptive statistics on health care and home care utilization . . . 68
3.2 Descriptive statistics of exogenous variables . . . 69
3.3 First stage regression (linear regression of Log of home care) . . . 76
3.4 Exogenous test. . . 77
3.5 Biprobit model - impact of home care utilization on admission to hospital or an emergency department . . . 79
3.6 Impact of Log(social care) on health care utilization - Social care treated as exogenous - No instrumental variables. . . 81
3.7 Impact of Log(home care) on health care utilisation . . . 82
3.8 Average home care by ISO-SMAF category . . . 84
3.9 Impact of Log(home care) on health care utilization by ISO-SMAF category . 85 3.10 Description. . . 87
3.11 Marginal effect of impact of home care on admission to long-term care facilities 88 A.1 List of targeted surgeries since 2011-2012 . . . 109
A.2 Price list for the year 2013-2014 . . . 110
A.3 Statistics for test equality of survivor functions . . . 113
Liste des figures
1.1 Average Length of Stay and Readmission rates . . . 20
1.2 Difference-in-difference estimation . . . 25
2.1 Conceptual framework of waiting times - The phenomenon . . . 35
2.2 Conceptual framework of waiting times - Determinants of waiting times . . . 36
3.1 Adjusted predictions with 95% Confidence interval . . . 89
A.1 Evolution of Length of Stay - Home destination. . . 111
A.2 Evolution of Length of Stay - CLSC destination . . . 112
A.3 Evolution of Length of Stay - Other destinations . . . 112
A.4 Survival functions in hospital - Home destination . . . 114
A.5 Survival functions in hospital - CLSC destination. . . 114
A.6 Survival functions in hospital - Other destinations . . . 115
A.7 Hazard functions in hospital - Home destination . . . 115
A.8 Hazard functions in hospital - CLSC destination . . . 116
A.9 Hazard functions in hospital - Other destinations. . . 116
A.10 Evolution of Quebec’s population. . . 124
À ma très chère tendre et battante mère Adjowa NOUWOATSI. À la mémoire de mon père Koami
La santé est universellement considérée comme le moindre des biens et il est dans la vie peu d’affaires importantes où la santé, lorsqu’il en est question, ne se trouve reléguée à la dernière place. Cela tient peut-être en partie, mais en partie seulement, au fait que la vie est le lot des gens sains, qui comme toujours en ce cas méprisent ce qu’ils possèdent ou n’imaginent pas qu’ils puissent le perdre.
Giacomo Leopardi ; Zibaldone di pensieri (1827)
REMERCIEMENTS
La réalisation de cette thèse n’aurait pas été possible sans la contribution de plusieurs per-sonnes. Je tiens tout d’abord à remercier mon directeur de thèse, M. Guy Lacroix pour son encadrement, sa disponibilité, son soutien financier, ses promptes réactions. Je remercie éga-lement mon codirecteur, M. Bernard Fortin, pour sa disponibilité, ses commentaires et sug-gestions utiles et constructifs qui m’ont aidé à améliorer ma thèse. Je remercie les membres du Jury qui ont accepté d’évaluer ma thèse.
J’aimerais aussi remercier tout le personnel enseignant et administratif du département d’éco-nomique de l’université Laval ainsi que la Chaire de recherche Industrielle Alliance sur les enjeux économiques des changements démographiques pour le soutien financier, aca-démique et les bonnes conditions de travail mises à ma disposition.
Je voudrais exprimer ma profonde gratitude à toutes les personnes du ministère de la Santé du Québec et des Services sociaux du Québec qui m’ont aidé et qui m’on permis d’accéder aux données que j’ai utilisées dans ma thèse. Un merci spécial à M. Normand Lantagne pour son soutien et ses commentaires constructifs sur mes différents travaux.
J’adresse aussi mes remerciements à Mme Kelly Fotso qui m’a soutenu durant les derniers mois de ma thèse. Merci à tous mes amis du Québec représenté par M. Franck Mpodé pour tout ce qu’ils m’ont apporté durant ces sept années de formation.
Mes remerciements vont en outre à ma famille particulièrement à ma mère pour son soutien, prière et confiance. Enfin, je remercie mon Dieu pour la vie, la santé, la force, les capacités et toutes les autres choses que je ne peux énumérer.
I
NTRODUCTIONThe improvement of health system productivity has been an important policy objective for successive governments in Quebec. In fact, the Quebec health care context makes more pres-sure on government spending. Quebec Health system is facing the concurrent challenges of managing rising demand, due principally to the aging of the population. Health system decision-makers are facing challenging issues to provide timely and effective care within a limit of a fixed budget. The health system is the sector that takes the largest share in the Quebec government’s budget. Improving health system performance and getting better va-lue for the money spent on health care becomes then crucial. To optimize resources, Que-bec government should improve the efficiency of the health system by putting resources on more efficient areas. In many cases, improving health system productivity requires the use of financial incentives, or increase activities which could reduce significantly health care uti-lization. In this thesis, we analyze some factors which can affect health care utiuti-lization. There are financial incentives, waiting times and home care.
Using incentives to improve hospital performance is widely increasing (Custers et al.,2008). There are good theoretical reasons to believe that the way health care is financed can have an impact on health care supply, and then on health care utilization and on patients’ health (Prendergast, 1999;Campbell,2003). The financial incentives may be a part of physicians’ remuneration (Échevin & Fortin,2014;Lippi Bruni et al.,2009;Alshammari & Hux,2009) or hospitals’ funding. The financial incentives act on the behaviours of workers and managers in hospitals, which can change supply of services or organization of services. The first chap-ter contributes to empirical evidence of the lichap-terature of the impact of financial incentives for hospital on health care utilization and patients’ health.
Other factors can affect patients’ health and health care utilization. Waiting for care is often seen as an inevitable part of health services supply and may be associated with physical and psychological adverse effects. Waiting lists can also divert resources devoted to patients’ treatments to processes related to the management of people waiting (Harding et al.,2013). Waiting for elective surgery can be defined as the time from when a patient and their surgeon decide that surgery is the best treatment option to when the surgery actually occurs (SMH,
2010). Patients waiting for elective surgeries are placed on a waiting list, which are the results of high demand and constrained capacity. The second chapter analyses whether long waiting is associated with bad post-treatment health outcomes.
To have a significant impact on efficiency in the health care system, we should act on the people who use the most health services, which means the elderly. The populations aging illustrates the success of a society, due to medical, scientific, technological, political and social achievements. This evolution implies a growing need for care for these elderly. Age partici-pates to increasing use of health services (Schulz et al.,2004). The seniors can receive health services at their own home or in health care institutions. Many elderly prefer to stay at home as long as they can and especially as long as their health’s state allows them. Recent decades have seen an increase in the use of home care (Thumé et al. ,2011). Receive home care can have an impact of health care utilization. The aim of our third chapter, analyze the substitu-tion rate between home care and health care utilizasubstitu-tion. We also analyze the impact of home care on admission to long-term care facilities (LTCFs).
This thesis consists of these three separate and independent chapters. Some definitions and concepts in one chapter are repeated identical or almost identically in other chapters.
- CHAPITRE
1
-I
MPACT OFHOSPITAL
FINANCIAL
I
NCENTIVES ONHEALTH
OUTCOMES
: EVIDENCE FROM
THORACIC AND
CARDIOVASCULAR
S
URGERIES INQUEBEC
Abstract
We provide an analysis of the effect of hospital financial incentives on health outcomes. To do so, we exploit Access to Surgery Program (ASP) implemented in Quebec (Canada) and a major reform on this program. The reform consisted mainly of modifying the financial incentives of hospitals, which can modify the hospitals’ supply of services, and then affect health outcomes measured by hospital length of stay and risk of unplanned readmission. The analysis is focusing on thoracic and cardiovas-cular surgery. We estimate a two-state model with a difference-in-difference estimator. We also take account of the different post-discharge destinations with a mixture competing risk model. We find that after the reform the hospital length of stay decreased respectively of around 8.2% (0.84 days), 6.4% (0.80 days) and 9.6% (2.52 days) for patients who left for home, local community service centres and other care institutions. However, the risk of 30-day unplanned readmission post-discharge does not appear affected by the reform.
Keyword :Financial incentives, Hospital length of stay, Readmission, Difference-in-difference JEL-codes : I11, I18
1.1. Introduction
The question of how financial incentives affect hospital decision-making has been a frequent subject of research in both economics and medicine. Do hospital decision makers base their medical-care decisions only on what is in the best interest for their patients, or what is in the best interest for them ? In that case, does health care funding affect a hospital’s decision and the quality of services ? In other words, how do hospitals respond to financial incentives ? Empirical analysis showed that hospitals respond to financial incentives (Batty & Ippolito,
2017;Croxson et al.,2001) . The financial incentive is related to the way in which the activi-ties of the hospital are remunerated. There are many methods of hospital funding and each of them has a different impact on hospital supply of services and then on patient health. Historical funding or global budget is the predominant funding method used in Canada (Sutherland,2011). This method consists in a fixed annual amount of funding for hospitals and, in return, the hospital should provide all basic services (Sutherland,2011). Global bud-gets are a good method to control hospital costs, but the consequence is that hospitals can reduce the number of admissions to stay within their budget, which can increase waiting lists (Street & Duckett,1996).
Another channel of hospital financing is activity-based funding (ABF), which is based on the type and the quantity of care provided, as well as patient characteristics (Sutherland et al.,
2012). The hospital’s income depends on the number, and the type of patients it treats. Each hospital receives the same financing for the same type of patient. ABF can also take account for more complicated cases. This method is often used to encourage hospital to increase admissions and then reduced wait times (Sutherland et al. , 2012). Comparative to global budget, ABF is associated with shorter lengths of stay (Moreno-Serra & Wagstaff,2001) and more admissions (Palmer et al.,2014).
Finally, there is the fee-for-service method whereby a hospital is paid for each service provi-ded. Differences between payment schemes create differences in the incentives for hospitals, which can be translated into differences in performance, in terms of quantity and quality of health care services. Some studies found that relatively to ABF, fee-for-services increa-sed the average length of stay and health expenditures (Yip & Eggleston,2001;Dismuke &
Guimaraes,2002).
The contribution of our study is in many levels. Firstly, we analyze the impact of change in the same channel of funding. Before the reform, a hospital received the same amount for each patient who received a thoracic surgery funded by the Access to Surgery Program (ASP). After the reform, a hospital received different amounts depending on the remunera-tion of physicians and the presence of anesthesia. These two types of funding are variants of activity-based funding (ABF). The impact of changing from one funding channel to another has been widely studied (Poel et al.,2016;Yip & Eggleston,2001;Moreno-Serra & Wagstaff,
2001;Kwon,2003;Kroneman & Nagy,2001;Dismuke & Guimaraes,2002). We analyze how the change in the same channel of funding can affect the quality of services through the im-pact on health outcomes. Secondly, many studies on the imim-pact of hospital payment scheme focus only on the quantity of services (Januleviciute et al., 2016;Byrne et al., 2007;Biorn et al.,2003). The study of length of stay and readmission is important in that case, it allows taking into account the quality of services. The third contribution is methodological, we use duration models instead of using length of stay at levels or logarithmic (Perelman & Closon,
2007;Theurl & Winner,2007;Yin et al.,2013). The use of duration models offers more flexi-bility. The correlation between different health states can be integrated with the multi-state model. Duration models also can integrate censored observations and allow taking into ac-count all possible destinations after leaving a state. Finally, a significant number of studies have described the effect of hospital payment scheme on health outcomes by using a des-criptive analysis with a pre-reform/post-reform comparison (Kwon,2003;Lang et al.,2004;
Kroneman & Nagy, 2001). The use of difference-in-difference method offers robust results by integrating a control group.
Our results suggest that hospitals did react to the incentives resulting from the reform, re-ducing the hospital length of stay. There was no change in volume of admission in hospital between cost categories or between hospital post-discharge destination. The reduction of length of stay means reduction of costs of hospitalization. The reform did not affect the 30-day unplanned readmission.
1.2. Context
Quebec has reported significant waiting times for some elective surgeries for many years. The government addressed these waiting times by implementing financial incentives for hospitals to increase the number of surgical services they provide. The Access to Surgery Program (ASP) was implemented in Quebec in April 2004 (MSSS,2014b). Its funding covers the volume of additional surgeries compared with the volume of the fiscal year12002-2003. It initially targeted hip, knee and cataract surgeries, mainly due to problems of access for these surgeries. This program has helped to reduce significantly waiting times for several types of surgeries in these past years. The initiative is a first experience of activity-based funding in the Quebec health network administered by the Ministry of Health and Social Services (MSSS2)
1.2.1 Access to Surgery Program (ASP) and the reform
The Access to Surgery Program (ASP) initially comprised five categories, three targeted sur-geries and two general sursur-geries, for which a specific financial allocation was attributed.
TABLE1.1 – ASP tariff categories from 2004-2005 to 2010-2011
Type of Surgery Category Allocation Description
Hip prosthesis targeted $ 11,000 Total hip prosthesis Knee prosthesis targeted $ 10,600 Total knee prosthesis Cataract surgery targeted $ 1,100 Cataract surgery
Surgery with admission general $ 4,200 Any surgery where the patient is admitted in a hospital Day Surgery general $ 700 All one day surgery performed
in the operating room
Source : MSSS(2015)
Over the years, surgical practices evolved and several deficiencies were identified in the pro-gram (MSSS,2014b). In fact, only the surgical procedures performed in operating rooms were taken into account for the allocation of funding. Thus, there was an incentive to perform sur-geries in operating rooms to benefit from this funding when, in some cases, another technical platform could have been more efficient. Some types of day surgeries have been transferred
1. 1st April to 31st March
to inpatient surgery for additional funding. In addition, there were not enough cost cate-gories to reflect with precision the real cost of surgeries. These problems led to unexpected additional production (more patients in the operating rooms and more hospital patients), thus generating an increase in expenses.
Adjustments were then needed so that the funding may support good practice and the choice of the most suitable technical platform. In 2011, some changes happened in how tariffs are set. Since 2011, volumes have been tracked using Quebec health insurance board (RAMQ3) remuneration data, ensuring a more efficient use of resources, in particular the operating unit. This database covers a wider range of surgeries.
In addition, new cost categories were created, without distinctions between inpatients and day surgeries patients, and without distinctions between technical platforms used. The list of eligible surgeries to the ASP and associated tariffs were revised : targeted interventions have been amended (Annex A.1.1) and the two general categories were replaced by categories based on the complexity of the intervention and on whether they recommended anesthesia units (AnnexA.1.2). Each year after 2011, the tariff of all categories are reviewed. The change encouraged the hospital to use the right technical platform in the execution of the surgical intervention and makes it possible to take into account the evolution of the medical practices. All major surgical procedures that are included in the pricing table for surgery RAMQ are included (MSSS,2012), except from
— Pacemaker
— Operative assistance
— Supervision, care, assessment and consultation — Coronary bypass and heart valve
Transitional measures were applied for hospital that faced a significant reduction of funding after the reform.
1.2.2 Expected effects of the reform The main points of the reform are :
1. Elimination of cost differences according to the technical platforms used (operating room, endoscopy, imaging, nuclear medicine, radiotherapy, functional explorations, outpatient clinics, ...)
2. Elimination of cost differences between day surgery (outpatients) and hospitalization (inpatients) for the same type of surgery
3. Increased number of cost categories to reflect the true cost of surgeries
Each of the different points of the change can affect hospital supply of services, then affect health outcomes.
The elimination of cost differences according to the technical platforms used will remove the incentives to use a special technical platform, since the hospital will receive the same amount for all technical platforms. This part of change will encourage the hospital to be more efficient and use the less costly platform between all available platform.
The elimination of cost differences between outpatient and inpatient for the same type of surgery will remove the incentive to keep patients more than one day if it is not for clinical reasons. The beds of hospital will be used efficiently. Moreover, based on some criteria, some inpatient surgeries can be transferred to outpatients to reduce hospital costs (Gilliard et al.,
2006). In fact, outpatient surgeries are less costly than inpatient surgeries (Crawford et al. ,
2015). The systematic review ofCrawford et al. (2015) also showed that outpatient surgeries are safe alternatives to inpatient care for patients with lower risk of complications or do not need close supervision after same day surgery.
The impact of the third point, increase costs categories to reflect the real costs of surgeries, will depend on the type of hospital. After the change, the hospital with more complica-ted cases will receive more funding. If hospitals have the possibility to change the patient between cost categories, there is an incentive to do that. The incentive of increase of cost ca-tegories will then depend on how the caca-tegories are set. If the cost of surgeries is positively correlated the hospital length of stay, hospitals will be encouraged to keep longer patients at hospital. Categorization of interventions in the Access to Surgeries Program is based pri-marily on activities reported to the RAMQ by physicians. A tariff is determined for each category based on the intensity of resource utilization (NIRRU4) and the average unit cost.
The unit cost is determined based on direct and indirect costs, after excluding costs rela-ted to teaching, research, remoteness and pediatrics. The NIRRU is assigned according to diagnosis-related group (DRG). DRGs are a patient classification system that provides a way to relate the type of patients treated by a hospital (Vertrees,2001). Two typical admissions with same DRG and same gravity will have the same NIRRU whatever the length of stay. A thoracic and cardiovascular surgery usually takes place in the operating room and patients are generally inpatients. In ASP thoracic and cardiovascular are more affected by the last point of the reform, the increase of the number of cost categories. The reform can be analyzed like the change from patients-based funding to case-mix funding. If there are no incentives to change cost categories and no possibility to increase the number of admissions because of no long waiting list or no capacity of the thoracic and cardiovascular department, the other incentive is to short length of stay for use beds for admission of other types of surgery.
1.3. Health outcome variables
We are interested to two health outcomes : hospital length of stay and readmission post-discharge within 30 days. We do not have access to death after hospital post-discharge.
1.3.1 Hospital Length of Stay
The efficiency of the hospital is often dependent on how efficiently beds were being used in the hospital. The use of beds is highly correlated to length of stay of inpatients (Baek et al.,2018). Length of stay (LoS) is a term used to describe the duration of a hospitalization in hospital. A large part of the treatment costs is generated by the duration of the hospi-talization. A reduction of the duration in hospital can then result in a significant reduction of hospital costs (Kossovsky et al. , 2002). However, the process of investigation, unders-tanding a patient’s situation to select appropriate treatment requires times. The increase of LoS can indicate that the hospital spend more time identifying the patient’s situation to do better treatment. In that case, LoS associated positively to quality of health services ( Chalk-ley & Malcomson,2000). The reduction of the hospital LoS may therefore increase the risk to not complete the evaluation and treatments needed and discharge patients who are
in-sufficiently stabilized. On another side, when investigations and treatments are completed, extending LoS will not provide any additional benefit for the patients. Extending LoS than necessary generated unnecessary costs and exposes patients to undesired outcomes such as nosocomial infections.
1.3.2 Defining and measuring readmission
Another important factor in the analysis of the quality of hospital services is the readmission rate. Readmission is often used as a proxy for hospital quality of service. The control of read-missions to hospitals is particularly relevant as they have significant implications for costs and quality (Epstein et al., 1991). A high number of readmissions will increase health care costs, since it will increase the duration of hospitalization and the resources used. Readmis-sion is also an indicator of quality because it reflects the fact that the goal of improvement of patients’ health is not reached. Patients’ satisfaction will decrease if they have to be readmit-ted, as their expectations of recuperation are not realized. In that case, Readmissions can be a source of patient and family stress, and may contribute substantially to the loss of functional ability, particularly for elderly patients. Readmission also put patients at additional risk of hospital-acquired infections and complications.Ludke et al. (1993) showed empirically the existence of an inverse relationship between readmission and quality.Ashton et al. (1995) found that readmission was statistically more likely to occur when quality criteria have not been complied.Ashton et al. (1997) proposed that readmission is associated with the quality of the process of inpatient treatment. Even if some readmission result for the normal pro-gression of care, readmission may result of poor quality of care or inadequate transitional care.
There are many definitions of readmission in the literature. For our analysis, we focus on all-cause unplanned readmission (emergent readmission) within 30 days after hospital di-scharge. We use this indicator for many reasons. First, this measure is the one most com-monly used and it is more associated with quality of services (Lucas & Pawlik,2014; Sau-cedo et al.,2014;Avram et al.,2014). Second, from the patient’s perspective, readmission is undesirable outcome of care whatever the reason and can expose the patient to hospitaliza-tion problems like iatrogenic errors. It’s not obvious to determine if a readmission is related to a previous hospitalization, but within a 30-day time frame, readmissions are more likely
attributable to care received during the index hospitalisation5 and during the transition to the outpatient setting. Finally, all-cause readmission may encourage hospital to work on any potential cause that can increase the probability of patients to be readmitted, instead to focus on a specific domain.
1.4. Data and Variables
1.4.1 Data
The empirical analysis is based on repeated cross-sectional data from the public hospital in Quebec contained in APR-DRG (J57) which derives from another database called Med-Echo6. MED-ECHO contains demographic, administrative and clinical data on all admis-sions to acute care hospitals and all registrations in day surgery units in Quebec. The Med-Echo database is analogous to the Discharge Abstract Database (DAD) of Canadian Institute for Health Information (CIHI), which collects hospital discharge summary information in the other Canada’s provinces (Sutherland et al.,2013).
The data concern patients’ hospitalizations and only patients who stayed in hospital one completed day or more are considered in our database, there was a marginal number of patients who left the hospital the same day after the thoracic and cardiovascular surgery. Each patient discharged from hospital was registered in the database over a period of six years (1st April 2008 to 31st March 2014 : three years before the reform and three years after) with their precise date of admission to hospital, age, gender and the department of admission, as well as the time when the patient left the hospital, and other patients’ and hospitals’ characteristics. This data set also contains the complete length of stay (LoS) in hospital. It allows us to calculate LoS out of hospital for each patient over this period, in order to determine if the patient was readmitted within 30 days after hospital discharge.
5. The "index hospitalization" refers to the first time, in a series of hospitalizations, that a patient is admitted to a hospital for a specific condition or diagnosis. If the patient returns to the hospital and needs to be admitted again for the same diagnosis (the specific time frame for return varies by the diagnosis), then that second stay may be called a "readmission".
1.4.2 Main Variables
The database already contains the length of stay in hospital. The data contain patients who are discharged from the hospital each year. The LoS is the duration between the discharge and the admission in hospital. There is no left-censoring in the first state (admission in hos-pital) since the time of admission is available for all patients. Right-censoring does not exist either in the first state, since all patients left hospital before 1st April 2014 (every patient completed the stay in hospital).
For the out of hospital analysis, we focus on 30-day unplanned post discharge readmission. We use all emergency readmissions as unplanned readmission. There is no left-censoring for spells outside of hospital after a first period of hospitalization within the sample period. After hospital discharge, the patients are followed during their first 30 days outside the hos-pital. We censored to 31 days all patients who stay out of hospital after 30 days since we focus on 30 days readmission.
1.4.3 Definition of sample, treatment and control groups
Our analysis focuses on thoracic and cardiovascular surgeries, because mainly of the availa-bility of the control group, type of surgeries which did not affect by the reform. Thoracic and cardiovascular is surgery on great vessels and the chest organs, including the heart, lungs, esophagus, and trachea. We grouped thoracic and cardiovascular surgeries into two broad categories, coronary bypass and heart vale surgeries, and other thoracic and cardiovascular surgeries according to the broad categories of Canadian Classification of Health Interven-tions (CCI), developed by Canadian Institute for Health Information (CIHI), to accompany International Statistical Classification of Diseases and Related Health Problems, 10th Revi-sion, Canada (ICD-10-CA).
Coronary bypass and heart vale surgeries include
— Bypass, coronary arteries (1.IJ.76) which include graft, coronary artery bypass ; — Excision total with reconstruction, aortic valve (1.HV.90) which includes Replacement
with or without excision of the aortic valve, and Replacement of the aortic valve ; — Repair, mitral valve (1.HU.80).
The category of other thoracic and cardiovascular surgeries mainly includes — Bypass, abdominal aorta (1.KA.76) ;
— Extraction, carotid artery (1.JE.57) ;
— Excision partial, lobe of the lung (1.GR.87) ; — Excision total, lobe of the lung (1.GR.89) ; — Repair, abdominal aorta (1.KA.80).
Coronary bypass and heart vale surgeries were not financed through the ASP. These surge-ries were financed through global budget of hospitals before and after the reform. For other thoracic and cardiovascular surgeries, before the 2011 reform the hospital received $4,200 for each additional hospitalization (general category - surgery with admission, Table1.1). Since the reform, the tariff for thoracic and cardiovascular have been divided into categories according to the remuneration of physicians and the presence of anesthesia.
TABLE1.2 – Cost categories and tariffs from 2011-2012 to 2013-2014 for thoracic and cardiovascular
surgeries in ASP
Cost category Description (physician remuneration) 2011-2012 2012-2013 2013-2014 Category 2.1 Less than $100 with anesthesia $519 $388 $388 Category 2.2 Between $100 and $199 with anesthesia $717 $536 $ 536 Category 5.2 Between $200 and $299 with anesthesia $1,269 $949 $949 Category 6 Between $300 and $399 $1,825 $1,364 $1,364 Category 7 Between $400 and $599 $2,514 $1,879 $1,879 Category 8 Between $ 600 and $999 $5,314 $3,973 $3,973 Category 9 $1,000 and over $9,652 $7,215 $7,215
The table1.2shows that after the reform for the first year, on the seven cost categories, only two categories have tariffs higher than $4,200, the pre-reform tariff. For the other two years, there is only one cost category with a tariff higher than $4,200.
1.4.4 Descriptive statistics
Our data contains 41 hospitals, we grouped hospitals with less than 1% percent of patients over the six years. We then have 25 groups of hospitals for our analysis, 12 of them did not have coronary bypass and heart valve surgeries.
The average length of stay in hospital is around 12.0 days and it’s comprised between 1 and 366 days. Its median is 7 days, the 25th percentile is 4 days while the 75th percentile is 13
days. Only 1% percent of patients stayed at a hospital more than 74 days.
TABLE1.3 – Patients characteristics
Mean Std. Err. Min P10 P25 P50 P75 P90 Max LoS in hospital (days) 12.0 18.5 1 2 4 7 13 26 366 Age in hospital (years) 63.9 15.8 0 48 58 66 74 80 103 Week-End admissions 13.8%
LoS out of hospital (days)
•All patients 892.6 681.8 0 46 240.5 798 1,501 1,888 2,190
•Returning Patients 277.9 381.6 0 8 26 106 380 820 2,176
•Emergency Return 228.8 358.2 0 6 15 63 271 728 2,122 Age out of hospital (years) 63.9 15.8 0.04 48.0 58.0 66.0 74.0 88.0 103.2 Percent of male 67.8%
The patients leave the hospital for several destinations. We consider three mutually exclusive destinations :(a)home,(b)CLSCs7and(c)other out of the hospital destinations.
The table 1.4 shows that the first destination of patients after hospital discharge is home, respectively 46.7% and 62.8% in control and treatment groups.
TABLE1.4 – Number of patients by destination and group
Destination Bypass and Heart valve surgeries Other TCV procedures All groups
Home 10,850 18,248 29,098 (46.7%) (62.8%) (55.7%) CLSC 6,589 7,290 13,879 (28.3%) (25.1%) (26.5%) Other destinations 5,810 3,505 9,315 (25.0%) (12.1%) (17.8%) All destinations 23,249 29,043 52,292 (100%) (100%) (100%)
The following table (1.5) shows that the composition in the treatment group is almost the same group before and after the reform. The reform does not seem to have affected the destination of patients after hospital post-discharge.
7. CLSCs (centres locaux de services communautaires, local community service centres) in Quebec are free clinics which are run and maintained by the provincial government. They are a form of Community Health Centre.
TABLE1.5 – Number of treated patients by destination and period
Destination Before the reform After the reform All period
Home 9,504 8,744 18,248 (64.2%) (61.4%) (62.8)% CLSC 3,578 3,712 7,290 (24.2%) (26.1%) (25.1)% Other 1,715 1,790 3,505 (11.6%) (12.6%) (12.1%) All destination 14,797 14,246 29,043 (100.0%) (100.0%) (100.0%)
In the same way, there is no change between cost categories after the reform (table1.6). The composition of the treatment group is the same before and after the reform.
TABLE1.6 – Proportion (%) of patients in the treatment group over years
Reform Before the reform After the reform
Year 2008-2009 2009-2010 2010-2011 2011-2012 2012-2013 2013-2014 Category 2.1 1.08 1.19 1.43 1.14 1.22 1.12 Category 2.2 34.61 33.70 34.37 36.33 34.60 33.17 Category 5.2 13.34 13.00 12.36 12.30 13.25 13.51 Category 6 4.39 3.65 3.42 3.44 3.72 4.03 Category 7 4.68 4.49 4.49 3.97 3.63 4.47 Category 8 38.67 40.48 40.93 39.75 40.14 40.40 Category 9 3.21 3.47 2.99 3.04 3.44 3.31 All categories 100.0 100.0 100.0 100.0 100.0 100.0
By combining the tables1.1and1.6, after the reform an average hospital receives in average 2,990.81 CAD, 2277,84 CAD and 2293.22 CAD respectively in 2011-2012, 2012-2013 and 2013-2014. However, a transition over these three post-treatment years is applied to hospitals that face to a significant reduction of funding. This transition corresponds to the consideration of a proportion of the difference between the funding before and after the reform.
1.5. Empirical Model
The empirical analysis is based on duration models. The use of duration models gives more flexibility to the model. The duration allows correlation between in-hospital and out-of-hospital states. In fact, length of stay in out-of-hospital can affect the risk of unplanned readmission (Li et al. ,2013; Rinne et al. ,2017). Duration models also allow multiple destinations and
censored observations.
The length of stay in hospitalization can be calculated as the probability of leaving hospital given the length of stay until the time of leaving (Fenn & Davies,1990). Let T the survival time, continuous and non-negative, with probability density function f(t)and cumulative distribution function F(t) =Pr{T≥t}. We focus on the survival function S(t) =Pr{T>t}, the probability of being in hospital or at home at t and the hazard function H(t) = f(t)/S(t).
1.5.1 Mixture Competing risk model
Competitive risks occur when subjects may experience more than one event that "compete" with the desired outcome (Noordzij et al.,2013). The outcome dataset in competing risk mo-dels can be represented by (T,D,X), where T is the time of leaving the state (supposed to be positive and continuous), D is the destination after leaving the state and takes one of the values in the finite set {1,2, . . .}, and X is a vector of covariates (Li et al., 2015). We consi-der a competing risk model with three post-hospital destinations : home, local community service centres (CLSCs8) and other out of the hospital destinations. We excluded patients
who died in the hospital in the analysis for these following reasons. Firstly, comparatively to main destinations (defined above), there are few people who died in hospital (less than 3%). Secondly, people who died in hospital did not complete their length of stay in hospital. Thirdly, we can not observe the readmission to hospital for these patients.
The likelihood function for patient i in one specific state is the extension of the likelihood function used inLi et al. (2015) by including the unobserved heterogeneity
Li = π1i·L1(ti|Xiβ1+θ1) δ1i ×π2i·L2(ti|Xiβ2+θ2) δ2i ×π3i·L3(ti|Xiβ3+θ3) δ3i (1.1) where πdiLd(ti|Xiβd+θd)is the contribution to the likelihood function of a patient i with
covariate X, unobserved heterogeneity θ, and post a hospitalization destination d (Lau et al.
,2008). For each patient i, the indicator function δdiis equal to 1 for one specific destination
and 0 for the others.
δdi= 0 if Di 6=d 1 if Di =d (1.2)
πdthe probability of leaving to the destination d, is given by
πd= Pr(D=d) =
exp(φd)
exp(φ1) +exp(φ2) +exp(φ3)
, d=1,2,3 (1.3)
For d=1,2, the probability can be written as
πd= Pr(D=d) = exp(ψd) 1+exp(ψ1) +exp(ψ2) (1.4) where ψd= φd−φ1, and π3=1− (π1+π2) (1.5) 1.5.2 Two-state model
In this section, we present the basic two-state model we used to identify the impact of the reform on two outcomes for other thoracic and cardiovascular procedures (the treatment group) : patients’ exit rates from hospital and the risk of readmission within 30 days. We assume that two states are possible for a patient : In hospital and Out of hospital. We analyze then the impact of the reform on leaving each state. Leaving the second state corresponds to the readmission to hospital. These two states are linked by a parameter θ.
We derive the likelihood for the general parametric two-state model. L=
N
∏
i=1
Li (1.6)
where N is the number of patients. Li is the likelihood contribution of individuals i, it is
given by the product of the likelihood of theses two states
Li = Li(In Hospital) ·Li(Out Hospital) (1.7)
Analytically for a specific destination d (d=1,2,3), we have
Ld(ti|Xiβd+θd) =Ld(tini |Xiinβind +θdin) ·Ld(touti |Xioutβdout+θdout) (1.8)
By combining equations (1.1) and (1.8), we have Li =
π1i·L1(tini |Xiinβ1in+θ1in) ·L1(touti |Xioutβout1 +θout1 )
δ1i
×
π2i·L2(tini |Xiinβin2 +θ2in) ·L2(tiout|Xioutβ2out+θ2out)
δ2i
×
π3i·L3(tini |Xiinβin3 +θ3in) ·L3(touti |Xioutβ3out+θ3out)
δ3i
Right-censored data are not present in hospital, but there is right-censored out of hospital, the for destination d=1,2,3
Ld(tini |Xiinβin1 +θdin) = Hd(tini |Xiinβdin+θdin) ·Sd(tiin|Xiinβind +θdin) (1.10) and
Ld(touti |Xioutβ1out+θoutd ) = [Hd(touti |Xioutβoutd +θdout)]cout·Sd(tiout|Xioutβdout+θdout) (1.11)
where cout =0 if the individual is censored and cout =1 otherwise.
1.5.3 Hazard function distribution and unobserved heterogeneity
The hazard function can be defined as an instantaneous rate of occurrence of an event ( Ro-dríguez,2007).
H(t|Xβ+θ) = lim
dt→0
Pr(t≤ T<t+dt|T≥t, Xβ+θ)
dt , (1.12)
where T is the length of stay in a state, X is a vector of explanatory variables, and θ unob-served heterogeneity. We assume a log-logistic hazard function since it is well adapted for an empirical non-monotonic hazard function (Bennett,1983) like in our analysis. From the hazard, we can derive the survival and probability density functions and then likelihood. The survival function S(·), the hazard function H(·) and the probability density f(·) are defined as follows (Rodríguez,2010) :
S(t|Xβ+θ) = 1 1+ (λt)γ, where λ=e −Xβ+θ (1.13) H(t|Xβ+θ) = λγ(λt) γ−1 1+ (λt)γ , where λ =e −Xβ+θ (1.14) f(t|Xβ+θ) = λγ(λt) γ−1 (1+ (λt)γ)2 , where λ= e −Xβ+θ (1.15)
Use patients’ characteristics as regressors sometimes arises problems of unobserved hete-rogeneity of patients (Hamilton et al. , 1996). The observed explanatory variables can not capture all differences in the outcomes. It is therefore necessary to consider factors which are not observed but can affect the outcomes. These factors are called unobserved heterogeneity
(θ) and their distribution also can influence the estimation. The gamma distribution is gene-rally used for the proportional hazard9, our hazard function is not proportional.Hamilton et al. (1996) used a discrete distribution to deal with unobserved heterogeneity of the patient. This method does not give any specific distribution form to unobserved heterogeneity and assumes that the population consists of two (or more) latent sub-populations (latent classes), which are homogeneous within.
The contribution of the likelihood function of an individual i in a specific hospital discharge destination d is
Ld(ti|Xiβ+θd) = K
∑
k=1
pk·Ld(tini |Xiinβind +θdkin) ·Ld(touti |Xioutβdout+θoutdk ) (1.16)
θdj is the unobserved heterogeneity in state j for the destination d
θdj = µjθd; j=in,out (we normalise µin =1) (1.17)
The heterogeneity θdis known to lie in the interval[θdL,θdH]. We suppose that the
heteroge-neity parameter is distributed as a discrete random variable with K points of support. We have Pr(θd=θdk) = pk ≥0, k=1,2, . . . ,K, and
∑
k pk =1 (1.18) If K=1, then θd= θdL =θdH =θ¯d 1.5.4 Difference-In-Difference estimatorTo analyze the impact of the reform on duration in all states, we use a difference-in-difference model. The standard difference-in-difference estimator (Athey & Imbens,2006) is
DD =E(Yi|Gi =1,Ri =1) −E(Yi|Gi =1,Ri =0) − E(Yi|Gi =0,Ri =1) −E(Yi|Gi =0,Ri =0) (1.19) 9. Abbring & den Berg(2007) proved that the distribution of unobserved heterogeneity in proportional ha-zard models converges to a Gamma distribution under realistic assumptions. These assumptions are held for a large number of observations.
R=0 before the reform (before April 2011) and R=1 after the reform (after April 2011). G is the treatment variable (G = 1 if the individual is in the treatment group and 0 in the control group).
In the likelihood function Xijβdj (equation1.1) can be decomposed in
Xijβjd= βjd0+βd1j Gij+βjd2Rij+βjd3(Gij·Rji) +Zijβj∗ (1.20)
where βd3j is the difference-in-difference estimator. Z include all other explanatory variables : gender, age, indicator of gravity, weekend admission, variables that describe where the pa-tient comes from, papa-tient health regions, the trend and the square of the trend, and for hos-pital fixed effects.
1.6. Results
In what follows, we provide firstly the impact of the reform by comparing length of stay in hospital before and after the reform. We also compare readmission rates.
FIGURE1.1 – Average Length of Stay and Readmission rates
The figure1.1 shows that in the control group there is no significant difference in average of length of stay in hospital before and after the reform. However, in other thoracic and cardiovascular procedures (treatment group) there is a decrease of length of stay of more than one day after the reform. The readmission rates are almost the same before and after the reform in control and treatment group.
When we analyze the length of stay in hospital for each destination post-discharge hospital there are some differences in length of stay for the control group but this difference is less comparatively to the treatment group (table1.7).
TABLE1.7 – Average length of stay in hospital and Readmissions rates by post-discharge destination
Home CLSC Other destinations
Group Before ref. After ref. Before ref. After ref. Before ref. After ref. Length of stay in hospital (days)
Control 10.64 10.71 11.49 10.89 13.94 14.06 Treatment 10.28 9.11 12.61 10.96 26.22 22.91 All 10.42 9.67 12.14 10.93 18.52 17.42 Readmission rates Control 5.04% 5.28% 4.86% 4.78% 3.36% 3.25% Treatment 5.69% 5.19% 6.20% 7.19% 6.06% 7.09% All 5.44% 5.22% 5.64% 5.95% 4.37% 4.71%
The curve of length of stay in hospital (Annex A.1.3) for each shows that after the reform there is no change or slight increase in the evolution of length of stay in the control group for all destination after hospital discharge. The average length of stay decreases in the treatment group after the reform comparatively to before the reform.
We can also note that the survival functions before and after the reform for the control group are overlapped while those of other types of thoracic and cardiovascular surgeries are dif-ferent for all post-discharge destinations. In the treatment group, the curve after the reform is below the curve before the reform, which means there is a reduction in the probability of staying in hospital after the reform. In other words, there is a reduction of length of stay in hospital after the reform (AnnexA.1.5).
TABLE1.8 – Test equality of survivor functions (Null Hypothesis : Equality of functions)
Destination Group Logrank Cox Wilcoxon Tarone-Ware Peto All Control 00.05 00.05 02.46 01.26 02.55 Treatment 74.47*** 67.10*** 95.43*** 93.26*** 94.75*** Home Control 00.82 00.69 02.72 02.12 02.04 Treatment 72.19*** 63.51*** 98.26*** 96.46*** 96.94*** CLSC Control 14.57*** 12.49*** 22.12*** 19.44*** 22.70*** Treatment 21.42*** 19.20*** 19.42*** 19.85*** 19.83*** Other destinations Control 1.19 01.07 09.53** 5.34* 10.44**
Treatment 12.90*** 12.33*** 14.26*** 15.56*** 14.32*** *** p<0.1% - ** p<1% - * p<5%
The tests of equality of survival functions show these differences10. All tests (Table 1.8) confirm the equality of survival functions in the control group and reject the equality in the treatment group for patients who left for home and when we consider all patients. For the patients who left to CLSC, there is no difference in the treatment and control group for all tests.
For the hazard function, we also see that there is no difference in the control group before and after the reform. There is an increase in the exit rate after the reform, especially before fifteenth first days, in the treatment group (AnnexA.1.6).
The analysis of the table 1.7 shows that after the reform the 30-day readmission increased in other thoracic and cardiovascular procedures while it decreased in the control group for patients who left to CLSCs and other destinations. It is the opposite of patients who left for home. The proportion of change is more in the treatment group. The readmission rates increase for all destination of 0.02 percentage points in control while it is around 0.10 per-centage points for a treatment group (figure1.1and Table1.13).
TABLE1.9 – Estimates of ln(duration) of two-state model
Home CLSC Other destinations
In hosp. Out hosp. In hosp. Out hosp. In hosp. Out hosp. DID estimates -0.086*** 0.038 -0.066** -0.100 -0.101*** -0.278 Male -0.072*** 0.049 -0.096*** 0.032 -0.036* 0.237 Age (years), Ref. :<65
- Age 65-74 0.051*** -0.005 0.062*** -0.028 0.084*** -0.156 - Age≥75 0.137*** -0.258** 0.163*** -0.133 0.144*** -0.202 Gravity, Ref. : Low
- Moderate 0.365*** -0.481*** 0.270*** -0.472*** 0.259*** -0.282 - High 0.769*** -1.021*** 0.632*** -0.867*** 0.620*** -0.784** - Extreme 1.551*** -1.543*** 1.364*** -1.449*** 1.239*** -0.694* Weekend admission 0.093*** -0.083 0.176*** -0.125 0.112*** 0.225 Shape parameter (γ) 2.641*** 0.868*** 3.120*** 0.878*** 2.580*** 0.881***
Unobserved heterogeneity Yes Yes Yes
Points of distribution K 1 1 1
theta (θ) -1.753*** -1.959*** -2.432***
mu (µ) 1.000 4.462*** 1.000 3.647*** 1.000 2.911***
Patient SSR dummy Yes Yes Yes Yes Yes Yes
Hospital dummy Yes Yes Yes Yes Yes Yes
Number of observation 29,098 29,098 13,879 13,879 9,315 9,315 *** p<0.1% - ** p<1% - * p<5%
The table1.9 provides the estimation of the logarithm of length of stay in hospital and out 10. See AnnexA.1.4for the description of the tests of equality of survival functions
of hospital. Every unit change in an explanatory variable Xr corresponds to a change of
sign(βr) ×100× [1−exp(βr)]percent in the expected survival time. That means after the
reform the patients’ time in hospital decreases by 100× [1−exp(−0.086)] = 8.2%, 100× [1−exp(−0.066)] = 6.4% and 100× [1−exp(−0.101)] = 9.6% respectively for patients who left for home, CLSCs and other hospital exit. There is no significant impact on length of stay out of hospital, so there is no impact on 30-day readmission for all post-discharge destinations.
We also note that the more the patient is aged, the more he stays in hospital. The severe cases and the patients admitted during the weekend (Friday to Sunday) stay longer in hospital. That is understandable, because severe cases need more cares and during the weekend there are fewer resources in hospitals.
Concerning length of stay out of hospital, patients aged more than 75 years old are more readmitted to hospital than patients aged less than 65 years old for patients who left for home. The severe cases are also more quickly readmitted.
1.7. Robustness Tests
1.7.1 Comparison to basic OLS-DD model
TABLE1.10 – Ordinary Least Square Difference-in-difference
Home CLSC Other destinations
In hosp. Out hosp. In hosp. Out hosp. In hosp. Out hosp. DID estimates -0.073*** -0.011 -0.063*** 0.030 -0.098*** -0.060 Male -0.071*** 0.005 -0.100*** 0.007 -0.023 0.032 Age (Reference : < 65)
Age 65-74 0.049*** 0.005 0.054*** -0.017 0.089*** -0.025 Age >= 75 0.134*** -0.040** 0.148*** -0.024 0.155*** -0.001 Gravity (Reference : Low)
Moderate 0.388*** -0.084*** 0.307*** -0.095*** 0.295*** -0.047 High 0.841*** -0.216*** 0.704*** -0.201*** 0.687*** -0.172*** Extreme 1.626*** -0.403*** 1.445*** -0.382*** 1.309*** -0.211*** Weekend admission 0.084*** -0.002 0.162*** -0.032 0.111*** 0.027
*** p<0.1% - ** p<1% - * p<5%
The table1.10presents the impact of the reform on the logarithm of length of stay in hos-pital and the duration out of hoshos-pital (readmission) with the basic ordinary least square
difference-in-difference.
The comparison of tables1.9and1.10shows that the results of duration model and basic OLS have almost the same result for the impact of the reform on length of stay in hospital, but the results are different for readmission. However, in both models, the reform has a significant impact on length of stay in hospital and no significant impact on 30-day readmission after hospital discharge. The difference of the impact of the reform on length of stay in hospital between both models is respectively 1.20, 0.28 and 0.27 percentage points for patients who left for home, CLSCs and other destinations.
The similarity results in hospital and the dissimilarity results out of hospital can be due to many factors. Firstly, in hospital there are no censored observations. Moreover, the corre-lation between length of stay in hospital and the duration out of hospital affects more the readmission. Finally, in both models the dependent variable follows log-normal distribu-tion. We already know that in OLS model Log(LoS) follows log-normal distribudistribu-tion. The log-logistics distribution is similar to log-normal distribution (Clark & El-Taha,2015), since logistic distribution is similar to the normal distribution and the function Log is a bijection of]0;+∞[inR.
1.7.2 Placebo treatment
The "placebo" test consists in re-estimating the difference-in-differences model over the pre-treatment periods, but with the assumption that the pre-treatment took effect at an earlier date. The placebo test permits analyzing if the effect we observe at the treatment date is already observed over pre-treatment periods. If the effect is already observed on pre-treatment per-iods, the effect observed on the treatment date can be inconsistent, since it can be the natural evolution of the effect observed on pre-treatment periods. To do the placebo test we arbitra-rily choose a treatment time ("fake treatment time") before the real treatment time, and test to see if we have significant effect. Since this treatment precedes the announcement of the policy change, the difference-in-difference estimator should be statistically insignificant or close to zero. If this placebo treatment is non-zero, the estimation is probably biased (Duflo,
2002).
use then the fiscal year 2010-2011 as the year of the post-treatment and the two other years as the period before the treatment. As we expect, the placebo test in table1.11shows that the placebo treatment is not significantly different from zero respective of the destination state. We can conclude that the difference in length of stay started just after the implementation of the change in the funding of the program.
TABLE1.11 – Placebo treatment - Estimates of ln(duration) of two-state model
Home CLSC Other destinations In hosp. Out hosp. In hosp. Out hosp. In hosp. Out hosp. DID estimator 0.041 0.073 0.032 -0.523 0.034 -0.089
*** p<0.1% - ** p<1% - * p<5%
In general, when there are many years, we can verify if the trends of average outcomes are parallels for treatment and control groups before the reform and if there is a change just after the reform for the treatment group (Duflo,2002).
1.7.3 The parallel Paths assumption
The assumption of parallel paths is the central element to identify the treatment effect in difference-in-differences estimators (Mora & Reggio,2012). It consists that the average change of outcome in the treatment group is the same in the control group if there were no treatment.
In the figure1.2, the parallel paths are represented by the orange and green lines. In absence of treatment, the trend for two groups are parallel. However, after the reform we do not observe the orange line, we rather observe the blue line.
Let∆ denote the first difference operator. Parallel-Path assumption is given by
E(∆RY|X,G=1) =E(∆RY|X,G=0) (1.21)
The focus to verify the parallel trend on the pre-treatment periods. We test the equality of trends of control and treatment groups during the pre-treatment periods. Empirically, let’s consider the following equation
E(Y(t)|X,T) =$+ T
∑
τ=t2 $τIτ,t+ψGG+ T∑
τ=t2 ψτG×Iτ,t×G (1.22) with t1 =2008−2009, t2=2009−2010, t3 =2010−2011, t4=2011−2012, t5=2012−2013 and t6=T =2013−2014. Iτ,t = 1 if t=τ 0 if t6=τ, t=t1,· · · ,TWe include all interactions of the time dummies (I) and the treatment group indicator (G). We remove the interaction of the first year and then express all the other interactions relative to the omitted period which serves as the baseline. The assumption of parallel paths is res-pected if ψt2 and ψt3 are non significant which means the difference-in-difference estimator
is not significantly different between the treatment and control groups in the pre-treatment period.
TABLE1.12 – Parallel Paths (H0: Treatment and Control groups have the same trend)
Home CLSC Other destinations In hosp. Out hosp. In hosp. Out hosp. In hosp. Out hosp. G×I2009−2010 0.022 0.039 0.072 -0.001 -0.166 -0.378
G×I2010−2011 0.018 0.040 0.053 0.173 -0.536 -0.253 *** p<0.1% - ** p<1% - * p<5%
For all destinations, we do not reject the null hypothesis of the same trend for the pre-treatment period. We conclude then there is a parallel path during the pre-pre-treatment periods.
