Article Text

Mathematical modelling of health impacts
1. Jennifer Mindell1,
2. Mike Joffe2
1. 1London Health Observatory, UK
2. 2Department of Epidemiology and Public Health, Imperial College London, UK
1. Correspondence to:  Dr J Mindell  Department of Epidemiology and Public Health, University College London, 1–19 Torrington Place, London WC1E 6BT, UK

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Mathematical modelling is seldom applied to research of global measures of health or health inequalities mainly because of the lack of studies of interventions necessary to underpin modelling research.

In this issue, Cole and his colleagues elegantly demonstrate the use of modelling to estimate health impacts of a policy.1 The Los Angeles City living wage ordinance sets a minimum wage for certain city employees. It also requires employers to contribute towards health insurance premiums for the affected workers or to add that payment to their wages. Using results from other studies in a novel way, they found that provision of health insurance is a more cost effective measure to improve health than a modest rise in income in their Los Angeles population.

This is unsurprising in the American context. For the relation of health to the provision of any type of resource, there is likely to be a diminishing return so that the gradient of the relation becomes flatter as the level of the resource increases.2 The steepest part of the curve is the increase above zero. The many uninsured in the USA will therefore gain appreciably even from low levels of access to health care. However, even for low paid workers, the steepest part of the curve between income and health passed as soon as they were in employment/compared with the unemployed. In any other economically developed country, the relative impacts would probably be different.

The minimum level for a living wage to live up to its name will vary according to the costs of meeting needs in different locations. Morris et al calculated that minimum living costs in 1999 for young, single men exceeded earnings based on the then national minimum wage by up to 55% of earnings (income depending on age, and costs on region). However, the minimum costs were two to three times the basic social security (unemployment benefit) rate.3 Any attempt to reduce inequalities in health (or “differences” as they are officially termed in the USA, in a use of language reminiscent of Thatcherite “variations”) must ensure universal access to health care and to income sufficient to meet all basic needs.4

The problem with applying the method of Cole and colleagues more widely is the paucity of evidence on which their modelling depends for quantification of heath impacts. Health impact assessment prompts scientific questions for which there is little evidence to provide adequate answers. For example, there is a vast literature on inequalities and health but it is difficult to quantify the effect of added income on health. Even where there is excellent evidence for a causal relation, quantifying the difference an intervention is likely to make is fraught with difficulties. These are reduced but not abolished when a change model is used.5 Such questions cannot be answered using cross sectional surveys. In this instance, one needs to know the effects on health of a change in income, studying the same individuals. This may differ from the postulated effects extrapolated from differences in health between individuals, or groups, with different incomes.

Mathematical modelling is well established in infectious disease epidemiology6 but is seldom applied to non-communicable diseases or global measures of health or health inequalities, despite its great potential. Problems are threefold. Two—lack of research funding to examine health impacts of non-healthcare policies and the lack of interest of most major journals in publishing public health research—are compounded in the UK by the Research Assessment Exercise that has led to a dearth (or death?) of academic public health posts and research. The third is the lack of studies of interventions to underpin modelling research. This is both the most important and would be the easiest to address, given political will and the accompanying funding.

What is needed to take forward this type of research? Firstly, good quality primary studies on the effects of change.5 Even where there is good evidence of a causal relation, reversibility cannot be assumed7: as a quantified illustration, the magnitude of the effect of a rise or a fall in cigarette price on cigarette consumption (the elasticities) differ.8 In relation to socioeconomic inequalities, while cross sectional studies of unemployment and health are subject to direct and indirect selection effects,9 factory closure studies overcome this problem,10 but do not directly answer the question, “how much health gain would be expected from the creation of a certain number of jobs?”—which arises frequently in the context of health impact assessment.

In the UK, the 2004 Wanless Report lamented the lack of evidence of cost effectiveness of interventions to improve population health.11 Where such evidence does exist, almost all focuses on individual level interventions, yet health impact assessments consider projects, programmes, or policies that affect whole populations or significant groups. Explaining the health effects of interventions requires a robust study design that is able to answer the question asked12 but it does not require that the researchers initiate or implement the intervention whose effects are being examined. Wanless suggested that a useful design is to exploit opportunities of “natural experiments”11; for example, there is good evidence of some income redistribution in the UK in the past seven years, but so far there seems to be no interest in assessing the health impact, even though it is likely to reflect well on the government. It remains to be seen whether the UK or other governments and funders of research will become interested in the type of research that Cole and others are pioneering.

Mathematical modelling is seldom applied to research of global measures of health or health inequalities mainly because of the lack of studies of interventions necessary to underpin modelling research.

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## Footnotes

• Funding: none.

• Conflicts of interest: none declared.

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