Improving geographic equity: A location-allocation model to redistribute hospital supply. The question

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1 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

2 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

3 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

4 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 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 B.II Methodology: obective function of MP model ( logu logu ) i N 2 12

5 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 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 C. Application to Potugal: GLM esults (second pat; log link; Poisson distibution) Indicato Vaiable Coefficient Othe Constant * Distance Distance() Distance()*distance() * * 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) * -2.97e-12* Geogaphic vaiations Dummy population in noth egion(i) Dummy population in cente egion(i) ** * Pimay cae Pimay cae utilization(i)/population(i) * Supply availability Dischages() * Altenative supply Hospital competition index () * 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) * * * * * * Model summay: 2217 obsevations; LogLikelihood= * Statistically significant at 1% level; ** Statistically significant at 5% level. 15

6 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 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? D. Concluding emaks " An intedisciplinay appoach is possible and useful (HE vs. OR) " Implementation is a big issue!!! 18