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HOSPITAL COSTS AND INFORMATION THEORY CASE MIX INDEXES: RESULTS FOR QUEENSLAND
Abstract
The use of information theory as a basis for the construction of scalar case mix indexes for hospitals is well established but to date no results arising from an application of these indexes to Australian hospitals have been published. This paper provides a simplified explanation of the information theory approach and constructs the indexes for Queensland public hospitals. The usefulness of the indexes is then demonstrated with two applications. First, they are used to explain the variation in average cost per case between the hospitals in the study and are found to account for a small but statistically significant amount of such variation. Second, they are employed to provide estimates of state mean average and marginal costs by case type in Queensland. The resulting estimates are all both positive and plausible, characteristics not commonly found in estimates obtained using other techniques.
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NOTES AND REFERENCES
On the general problems associated with defining markets and industries See D. Needham, The Economics of Industrial Structure Conduct and Performance, Holt, Rinehart and Winston, London, 1978, Ch. 5 and references cited therein. For a more specific discussion of the problems of defining market structure in the hospital industry, See A. McGuire, ‘The theory of the hospital: a review of the models’, Social Science and Medicine, 20, 11, 1985, pp. 1177–84.
The current transfer of nurse education from hospitals to colleges of advanced education in Australia is an example of this. This is not to imply, of course, that the production of two or more of these broad output categories within a hospital is more costly than producing them in separate institutions. The point is simply that this is technologically feasible. The cost consequences of splitting off product lines in this way depend on whether there are economies or diseconomies of scope. See W.J. Baumol, J.C. Panzar and R.D. Willig, Contestable Markets and the Theory of Industry Structure, Harcourt Brace Jovanovich, New York, 1982 for a discussion of the concept of economies of scope.
For a detailed discussion of the meaning and measurement of hospital case mix, See M. C. Hornbrook, ‘Hospital case mix: its definition, measurement and use: Part I. The conceptual framework’, Medical Care Review, 39, 1, 1982, pp. 1–43 and M. C. Hornbrook, ‘Hospital case mix: its definition, measurement and use: Part II. Review of alternative measures’, Medical Care Review, 39, 2, 1982, pp. 73–123.
R.B. Fetter, Y. Shin, J.L. Freeman, R.F. Averill and J.D. Thompson, ‘Case mix definition by diagnosis-related groups’, Medical Care, 18, 2, 1980 (Supplement) is the definitive document on how DRGs are constructed.
A description of the DRG hospital payment scheme in the US can be found in B. C. Vladeck, ‘Medicare hospital payment by diagnosis related groups’, Annals of Internal Medicine, 100, 4, 1984, pp. 576–91.
G. Palmer, ‘Hospital output and the use of diagnosis-related groups for purposes of economic and financial analysis’, in J.R.G. Butler and D.P. Doessel (eds), Economics and Health 1985: Proceedings of the Seventh Australian Conference of Health Economists, School of Health Administration, University of New South Wales, Sydney, 1986, pp. 159–81; Health Department Victoria, DRGs 1982-83 and 1983-84: Measurement of the output of Victorian public hospitals in 1982-83 and 1983-84 using diagnosis related groups, Health Statistics Unit, Health Department Victoria, 1986; Health Department Victoria, DRGs 1984-85: Measurement of the output of Victorian public hospitals in 1984-85 using diagnosis related groups, Health Statistics Unit, Health Department Victoria, 1986; P. Broadhead and S. Duckett, ‘Death to the oxymoron: the introduction of ‘rational hospital budgeting’ in Victoria, or perhaps more accurately, an account of progress towards that goal’, in J.R.G. Butler and D.P. Doessel (eds), Economics and Health: 1987 Proceedings of the Ninth Australian Conference of Health Economists, School of Health Administration, University of New South Wales, Sydney, 1988, pp. 22–33.
R.G. Evans and H.D. Walker, ‘Information theory and the analysis of hospital cost structure’, Canadian Journal of Economics, 5, 3, 1972, pp. 398–418.
Hornbrook, op. cit., Part 11, p. 104.
T.D. Klastorin and C.A. Watts, ‘On the measurement of hospital case mix’, Medical Care, 18, 6, 1980, p. 678.
H. Theil, Economics and Information Theory, North-Holland, Amsterdam, 1967.
The following simple numerical example illustrates these points. Suppose there are 10 hospitals in the system, i.e. N = 10. For the first index, the prior probability for each hospital is taken as (1/N) or 0.1 — there is a one-in-ten chance of any particular case being treated by any given hospital in the system. For the second index, the prior probability is taken as the proportion of all cases in the system treated by a given hospital, so that if one hospital of the ten treats 50 per cent of the cases then the prior probability for this hospital is 0.5. For each index the revised probability for any given hospital is the proportion of all cases in the system of a particular type, e.g. malignant neoplasms, treated by that hospital. Suppose a hospital treats 40 per cent of these cases. The revised probability is then 0.4. In the first index, the information gain for this hospital for this case type is In (0.4/0.1) = In 4, while in the second it would be In (0.4/0.5) = In 0.8 if this hospital treated 50 per cent of all cases in the system.
This is necessary because the unstandardised weights are sensitive to the size distribution of hospitals. A large hospital may tend to treat a large proportion of all cases in the system of a particular type simply because of its size but the unstandardised weight would read this as high concentration.
Evans and Walker, op. cit., p. 401.
See Klastorin and Watts, op. cit., p. 679 for an example of this.
M. Tatchell, ‘Measuring hospital output: a review of the service mix and case mix approaches’, Social Science and Medicine, 17, 13, 1983, pp. 871–83.
P. M. Tatchell, An Economic Analysis of Hospital Costs in New Zealand, unpublished PhD thesis, University of Waikato, New Zealand, 1977.
Tatchell, op. cit., 1983, p. 876.
Klastorin and Watts, op. cit., p. 679. See also Hornbrook, op. cit., Part 11, pp. 111–16.
Only one hospital was excluded because of data problems.
The relative stay index compares a hospital's actual with its expected average length of stay. The latter is calculated using the hospital's actual case mix and the state mean length of stay in each case mix category. For an explanation of this index See Ontario Hospital Services Commission, Ontario Length of Stay Tables 1969–1971, Ontario Hospital Services Commission, Toronto, Canada, January 1972; Ontario Hospital Services Commission, The Relative Stay Index Report, 1971 Edition, Ontario Hospital Services Commission, Toronto, Canada, February 1972; J. Leigh and A.J. McBride, ‘Computing an index of relative hospital performance from an inpatient reporting system’, in Proceedings of the 6th Australian Computer Conference, 1974, pp. 119–30; and Queensland Department of Health, The Relative Stay Index: Queensland, Planning and Development Unit, Division of Research and Planning, Queensland Department of Health, Brisbane, April 1980.
Standard deviation divided by the mean. The means are unweighted, i.e. they are calculated as the sum of the case mix proportions divided by the number of hospitals.
Normally, average cost per case equals the product of average cost per day and average length of stay but this is not so for the means in Table 3 because they are unweighted means.
These results are contained in the Appendix.
Evans and Walker, op. cit., p. 402.
S.D. Horn and D.N. Schumacher, ‘An analysis of case mix complexity using information theory and diagnostic related grouping’, Medical Care, 17, 4, 1979, pp. 382–9.
P. R. Schapper, An Economic Analysis of Hospital and Medical Services, unpublished PhD thesis, University of Western Australia, Perth, 1984, Table 6.1, p. 132.
Evans and Walker, op. cit., p. 408. Evans and Walker do not actually present results equivalent to those presented here, reporting only equations which include various scale and activity variables along with the information theory index. This quotation then pertains to equations which include the effects of these other factors.
Tatchell, op. cit., 1977, pp. 295–6.
Horn and Schumacher, op. cit., p. 386.
C.A. Watts and T.D. Klastorin, ‘The impact of case-mix on hospital costs: a comparative analysis’, Inquiry, 17, 4, 1980, pp. 357–67.
J. Hardwick, ‘Hospital case mix standardisation: a comparison of the resource need index and information theory measures’, in Butler and Doessel, op. cit., 1986, pp. 36–63.
The relevant parameter estimates for the two Type 1 indexes are 618.87 and 644.61 using 18 and 47 diagnostic categories respectively.
Any differences in the results in these Tables, and the products of the weights in the Appendix and the relevant parameter estimate in the previous footnote, are due to rounding.
See, for example, A.W Jenkins, ‘Multi-product cost analysis: service and case-type cost equations for Ontario hospitals’, Applied Economics, 12, 1, 1980, pp. 103–13 and J.R.G. Butler, Hospital Cost Analysis, unpublished PhD thesis, University of Queensland, Brisbane, 1988, Ch. 5.