1 Impoving geogaphic equity: A location-allocation model to edistibute hospital supply Monica Oliveia Opeational Reseach Depatment & LSE Health and Social Cae, London School of Economics (Financial suppot fom the Ministy of Science and Technology, Potugal) 1 2 The question How do we change the distibution of hospital supply to impove equity by populations? Pevious methods fo analysing hospital changes have: elied on cude assumptions on patients behaviou, neglected the pocess of demand fo hospital cae, and neglected the inteaction between hospital size and the levels of utilisation of altenative hospitals 2 3 Stuctue of the pesentation A. The poblem B. A location-allocation model fo edistibuting hospital supply B.I. The flow demand (econometic) model B.II. The mathematical pogamming model C. Application to the Potuguese system D. Discussion and concluding emaks 3
4 A. Poblem: health system context Obective: How to change the distibution of hospital supply in ode to achieve geate equity in utilisation? Context: I. Equity obectives II. Redistibution III. Cental planning and (mainly) public povision IV. Hospital utilisation explained by patients o doctos pefeences V. Health system nealy fee at the point of use 4 5 A. Poblem: some evidence (hospital doctos) 5 6 A. Poblem: pevious liteatue I. Location-allocation models II. Pevious liteatue: II.1. Spatial inteaction models II.2. Entopy models III.3. Mathematical pogamming models Pitfalls:! Behavioual assumptions ae simplistic and unsatisfactoy modelling of hospital inteaction! No clea undestanding of the pocess of health cae demand 6
7 B. Methodology: building a location-allocation allocation model 7 8 B. Methodology: key steps I. Build econometic model of flows and do the egession: [ U = f ( D,...)] II. Use econometic model as a constaint fo MP model, which edistibutes hospital supply; un MP model: [ D, U i, ] III. Analyse outputs: [ newd, newu i, ] 8 9 B.I Methodology: the pocess of health cae demand 9
10 B.I Methodology: the econometic model Ε[ U / x] = P( U > 0 / x)* Ε[ U = PatA* PatB " Two pats: intuition " Data chaacteistics " Estimation: Logit (Pat A) and GLM (Pat B) / > 0, x] " Modelling inteaction: a covaiate fo altenative hospital supply 10 11 B.II Methodology: mathematical pogam stuctue I. Maximises an equity function II. Multi-hospital system with a set of pe-detemined, discete and finite locations III. Utilisation flows as geneated by the econometic model IV. Total supply constained to the cuent level V. Lowe and uppe bounds fo edistibution 11 12 B.II Methodology: obective function of MP model ( logu logu ) i N 2 12
13 B.II Methodology: linking the obective function with the two-pat model logu logu pˆ * U = log U ' U = log U = log pˆ FIXED = + logu BEHAVIOURAL MODEL ' logu THE EQUITY REFERENCE 13 14 C. Application to Potugal: econometic issues " Expected empiical findings " One cannot analyse hospital policies without accounting fo othe vaiables of the health system " Modelling difficulties: a. Multicollineaity b. Captuing the specifics of cental hospital sites 14 15 C. Application to Potugal: GLM esults (second pat; log link; Poisson distibution) Indicato Vaiable Coefficient Othe Constant 6.468201* Distance Distance() Distance()*distance() -0.0423718*.0000776* Peceptions Population(i)*gavity accessibility index(i) 2.95e-07* Need and socio-economic Population(i)*demogaphic need index(i)*illiteacy ate(i) Population(i)*population(i).0000354* -2.97e-12* Geogaphic vaiations Dummy population in noth egion(i) Dummy population in cente egion(i) -.2022617** -.3838279* Pimay cae Pimay cae utilization(i)/population(i) -.1160661* Supply availability Dischages().0000352* Altenative supply Hospital competition index () -.1873067* Institutional factos Dummy fo fist hospital()*dischages() Dummy fo second hospital()*dischages() Dummy fo cental hospital() Dummy fo population in the noth using the Poto hospital site()*dischages() Dummy fo population in the cente using the Coimba hospital site()*dischages() Dummy fo population in the south using the Lisbon hospital site()*dischages(i) 0000231*.0000141* -4.304794*.0000158*.0000255* -.0000136* Model summay: 2217 obsevations; LogLikelihood=-297950 * Statistically significant at 1% level; ** Statistically significant at 5% level. 15
16 C. Application to the Potuguese system: outputs ( newd ' s)! Geogaphic edistibution : south and inteio hospitals; peipheal hospitals of uban aeas; model concentates edistibution to a small numbe of hospitals! Reduction in utilisation ( newu, ' s) i i 16 17 D. Discussion " Utilisation is educed: a pice fo equity? " Supply is concentated in a small numbe of hospital sites: manipulating hospital supply as an insufficient tool fo influencing the pattens of utilisation? 17 18 D. Concluding emaks " An intedisciplinay appoach is possible and useful (HE vs. OR) " Implementation is a big issue!!! 18