Prioritizing health care interventions: A multicriteria resource allocation model to inform the choice of community care programmes

Abstract

Many countries, including Portugal, are currently dealing with budget cuts and a shortage of resources in the health sector, while the demand for health care services is increasing. The Group of Health Centres (GHC) of Northern Lisbon faces the challenge of prioritizing community care programmes in order to decide which programmes to fund. We describe the development with the GHC of a Multi-criteria model to allocate human resources in community care programmes (MARCCO). Building MARCCO was a socio-technical process using multi-criteria decision analysis (MCDA) in a decision conferencing environment. The GHC used the results obtained by MARCCO to select programmes and to redesign its information system. MARCCO contributes to the literature by showing how a constructive approach using MCDA methods and decision conferencing is an alternative to conventional approaches used in the prioritization of interventions in the health care sector.

Appendix: The MACBETH linear programming formulation

The basic MACBETH scale (Fig. 9.3b) suggested by M-MACBETH for a matrix of judgements (Fig. 9.3a) is obtained by linear programming [8]. Let:

• C _k , k = 0…., 6, be the seven MACBETH categories of difference in attractiveness: “null” (C ₀), “very weak” (C ₁), “weak” (C ₂), “moderate” (C ₃), ‘strong’ (C ₄), “very strong” (C₅) and “extreme” (C ₆);

• X be a finite set of performance levels (as in Table 9.1);

• x ⁺ and x ^– be the most and least preferred levels of X, respectively;

• x and y be two elements of X such that x is at least as attractive as y;

• (x, y) ∈ C _k (k = 0,…, 6) be a MACBETH judgment of the difference in attractiveness between x and y expressed by the single category C _k;

• (x, y) ∈ C _l U…UC _s (l, s = 1,…,6 with l < s) be a MACBETH judgment of the difference in attractiveness between x and y expressed by a subset of categories from C _l to C _s (in cases of judgmental hesitation or disagreement).

The “basic MACBETH scale” is obtained by solving the following linear program, whereu(x) is the score assigned to performance level x:

minimize u(x ⁺)

subject to:

• $$ u\left({x}^{-}\right)=0; $$
• $$ \forall \left(x,y\right)\in {C}_0:u(x)-u(y)=0; $$
• $$ \forall \left(x,y\right)\in {C}_1\mathrm{U}\dots \mathrm{U}{C}_S\;\mathrm{with}\;l,s\in \left\{1,2,3,4,5,6\right\}\;\mathrm{and}\;l\le s:u(x)-u(y)\ge l; $$
• $$ \begin{array}{l}\forall \left(x,y\right)\in {C}_1\mathrm{U}\dots \mathrm{U}{C}_S\;and\forall \left(w,z\right)\in {C}_{l^{\prime }}\mathrm{U}\dots \mathrm{U}{C}_{S^{\prime }}\\ \mathrm{with}\;l,s,{l}^{\prime },{s}^{\prime}\in \left\{1,2,3,4,5,6\right\},l\le s,{l}^{\prime}\le {s}^{\prime}\;\mathrm{and}\;l>{s}^{\prime }:\\ \mathrm{u}(x)-u(y)\le \mathrm{u}\left(\mathrm{w}\right)-\mathrm{u}\left(\mathrm{z}\right)+1-{s}^{\prime }.\end{array} $$

When this linear program is infeasible, the set of judgments is inconsistent. When it is feasible, the optimal solution may not be unique. If multiple solutions exist, there is more than one possible score for at least one performance level x ∈ X\{x ^–, x ⁺}, in which case their average is taken to ensure the uniqueness of the basic MACBETH scale (see details in [7]).