Review of Income and Wealth
Volume 71, Issue 2 e70014
ORIGINAL ARTICLE
Open Access

New Medical Treatments, Quality Improvements and Public Health Measures in the National Accounts: The Effects of the Diabetes Prevention Programme

Martin Weale, 

Corresponding Author

Martin Weale

ESCoE, King's College, London, UK

Correspondence:

Martin Weale ([email protected])

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First published: 30 April 2025
https://doi.org/10.1111/roiw.70014
Funding: This work was supported by the Economic Statistics Centre of Excellence.

ABSTRACT

This article discusses the problem of reflecting the impact of new and improved medical treatments including preventative public health measures in measures of health services gross output and in the prices of medical and public health services. Both the treatment in main-stream national accounts and in a satellite health account are considered. An algebraic framework is set out. In the main-stream national accounts, the new service is initially priced at its reservation price defined with reference to gains in quality-adjusted life years (QALYs) and reductions in costs. Withdrawn services are similarly treated. In the satellite account, the increase in QALYs plus cost savings less costs incurred are measured relative to the QALYs generated by medical services net of costs of production. The framework is applied to the UK's Diabetes Prevention Programme. The impacts on both prices and volumes of this are shown to be small.

1 Introduction

This article explores how the national accounts should reflect the provision of new medical services including preventative public health measures. The treatment of nonmarketed services in the national accounts remains a source of considerable controversy and the treatment of health services might be thought to be a major issue, at least in those countries where the health service is largely in the public sector. A number of authors, such as Brynjolfsson et al. (2019), argue that the conventional valuation of services free at their point of use, at their cost of production, leads to a sharp underestimate of the “value” of services such as social media. But this point may be even more relevant for health services.

This article sets out an approach to the introduction of four different health interventions into an overall volume measure of health services gross output or consumption. The key to all of them is to assume that, in the period before introduction of new treatments or after withdrawal of old treatments, they are available but only at their demand reservation prices, i.e., the minimum prices at which there would be no demand for the new or withdrawn goods or services. This makes it possible to infer the implications for a price index, and the volume index can be deduced from the price index and value data.

For health interventions, it is assumed the gross benefit can be measured in discounted quality-adjusted life years (QALYs). If a value is put on a QALY, a reservation price can be computed as the cost at which the intervention delivers only just enough health benefits to be worthwhile. With preventative treatment, the savings in future treatment costs are also material for the reservation price.

The first case we examine is a treatment for an existing but hitherto untreatable disease. The treatment is assumed to lead to a higher level of QALYs than that experienced by untreated patients but not necessarily the same level of QALYs as is enjoyed by those who do not contract the disease. In this example, it is assumed that the treatment and the benefits it delivers are contemporaneous. This provides a simple framework with which to illustrate the approach.

In our second example, we consider an improved treatment which displaces an existing treatment, either as a treatment which delivers more QALYs for the same price or as one which delivers the same benefit as before but at a lower price. We again assume that the treatment and the benefits are contemporaneous. We show that the reservation price approach is, when quality increases, directly equivalent to the quality-adjustment approach proposed by System of National Accounts (2008) and Schreyer (2012). We explore the implications of gradual roll-out of the new treatment. We also show that, when costs fall, the replacement treatment approach is directly equivalent to a fall in price.

Our third example considers a situation where continuing treatment may be needed and where the benefits do not coincide with the treatment. Such a situation may arise, for example, with an organ transplant. The main cost is at the start, although continuing treatment may be needed, and the benefits are likely to be spread over time.

The fourth example looks at a public health measure which reduces the probability of developing a chronic disease. The assumed fall in the price of the public health measure from its reservation price to its actual cost of production allows us to calculate the reduction in the overall price of medical treatment and thus the associated increase in volume.

In all four cases, we assume that aggregate price changes are computed using a Törnqvist index. The Fisher index would also deliver coherent, if slightly different, results. But the approach would not work if Laspeyres or Paasche indices were used, even if those indices were chain-linked. Laspeyres indices would markedly overstate the contribution of withdrawn goods or services. Paasche indices would overstate the contribution of new goods or services. And, since they would give a zero weight to withdrawn goods or services, they would be likely to understate the impact of product withdrawal.

We also consider all four cases through the lens provided by Cutler et al. (2022). This focuses on the health gain measured relative to the total health gain generated by health services. We show that the treatment proposed by Cutler et al. (2022) yields different answers from those linked directly to the main-stream national accounts.

In all these cases, it is important to bear in mind that we are discussing measurement of output rather than well-being. A reduction in the incidence of disease, as a result of public health measures, may have the impact of reducing the output of the health sector. Factors of production will be diverted to other economic activities and there may be an increase in well-being, even if GDP is broadly unchanged.

We illustrate the final case by looking at the effects of the Diabetes Prevention Programme in England (NHS England 2016), a public health measure. The evidence available to date (Ravindrarajah et al. 2023) suggests participation in the program reduces the risk of developing type-2 diabetes (T2D) or at least delays its onset. The approach we set out here shows how the effects of preventative public health measures can be incorporated into measures of the gross output of medical services. We find in fact that the contribution of the particular program considered to health service gross output and consumption is small.

We begin with a literature review. We then set out in Section 3 theoretical examples to illustrate our four cases. This is followed in Section 4 by a brief description of T2D and an account of the Diabetes Prevention Programme. In Section 5, we assess the implications of this for volume measures of health service gross output in the national accounts. Section 6 concludes.

2 Literature Review

While national accountants have been aware of the problems of measuring the output of public services since modern national accounts have existed, Atkinson (2005) produced a substantial report on the matter. A key concern of his was that the widely-used approach of measuring volume changes in outputs by volume changes in inputs left no room for productivity growth or changes in quality. The report made the distinction between outputs, the direct products of public services such as, in the case of medical services, consultations and procedures, and the outcomes such as improved life quality and extended life-span. At much the same time, Cutler et al. (2006) looked at the output of the United States' health sector in terms of life-years gained without any adjustment for the quality of life. Shortly afterward, Castelli et al. (2007) raised the possibility of measuring outcomes in QALYs and using this as a quality-adjusted metric for the output of the health sector.

Support for the principle of quality-adjustment is not universal. The System of National Accounts (2008) advises statistical offices that quality adjustments to public sector output volume measures should be made. The European System of Accounts (2010), however, prohibits such adjustments to public sector output while endorsing them for private sector output.

There are in fact two distinct approaches to producing quality-adjusted measures of health sector output and they lead to different answers. The first can be used to incorporate new and preventative treatments into the existing national accounts, whereas the second uses a satellite account, measuring directly the QALY impact of these treatments.

The first approach draws on the work by Brynjolfsson et al. (2019). They focus on developing an extended measure of GDP which pays proper attention to the introduction of new goods and services. They were concerned with social media, but their approach can equally be applied to medical services. Following Fisher and Shell (1972), and implicitly Hicks (1942), they suggest valuing new goods at their reservation prices in the period before their introduction and at their actual price (if traded in the market sector) or cost of production afterward. This makes it possible to incorporate new goods or services into a price index. This price index can then be used to deflate the relevant value figure to show the volume effect of the introduction of that new good or service. We use that approach in looking at the treatment of new medical services or public health measures in the main-stream national accounts; we adopt a symmetric approach to the removal of old superseded treatments, calculating a reservation price for them once they have been withdrawn. Use of QALYs as a measure of outcomes means that, provided the medical effects of the treatment are known, reservation prices can be computed directly. For other goods and services, experiments may need to be used to establish prices (Diewert et al. 2022), but that is not a concern here.

Cutler et al. (2022) go down an alternative route. They focus on QALYs as outcomes. They measure the increase in productivity in the medical sector as the value of the increase in expected QALYs that it delivers, less the increase in costs (measured in constant prices). Obviously reliance on QALYs as an outcome measure fits directly into this approach.

To deliver a growth rate for gross output since 1999, they divide by their estimate of QALYs attributable to medical care in the base year. They focus on undiscounted QALYs but also look at the effects of discounting future years by 3% p.a. The fact that they are producing a satellite account for medical services means they do not need to worry about the effects of their results on the rest of the national accounts or the price index for medical services. But the value used for QALYs (US$100,000 per healthy life year in their work) will yield an estimate of the output of medical services which is likely to be quite different from that shown in the US National Accounts. Atkinson (2005) was well aware of this issue. This awkwardness also seems to be one of the elements lying behind the critique in Triplett (2009) although he was also concerned about accuracy of health-sector outputs measured in QALYs. Cutler et al. (2022) resolve the matter by constructing a satellite account, outside the main-stream of the national accounts. Cutler's approach does not have any difficulty with the introduction of new goods and services since the increase in gross output is simply measured as the resulting increase in QALYs.

A third strand of the literature should be mentioned. Schreyer (2012), building on the work of Atkinson (2005) and Castelli et al. (2007), advocates using indicators of quality to make quality adjustments to output. Applied to medical services this would naturally mean treating QALYs generated as the dominant indicator of quality, although a case can be made (Castelli et al. 2007) for using factors such as patient satisfaction as secondary indicators of quality.

While this offers a clear approach to measuring quality changes, it does not deal with the question of new treatments, whether direct or preventative. It does, in contrast to Cutler et al., however, produce data which fit into the main-stream national accounts. Even when QALYs are used as the only indicator of quality, a difference between this and Cutler's approach arises from the way in which different components of the affected industry (e.g., medical services) are aggregated. Cutler et al. (2022) imply that shares in total medically-generated QALYs should be used while Schreyer (2012) uses shares of production costs in current or lagged health service consumption as cost weights for combining the different activities. The use of cost weights rather than QALY weights has the consequence that the magnitude of the overall quality adjustment will depend on the way in which the individual components are aggregated. If adjustment takes place at the aggregate level and QALYs are the only indicator of quality, then the reported absolute increase in output will be the same as that proposed by Cutler et al. (2022).

3 Theory

We begin this section by looking at the introduction of a treatment for a hitherto untreatable disease. We then look at the introduction of a new and better, or cheaper, treatment which supersedes an existing treatment. In our third case, we look at the implications of treatment spread over time. Finally, we examine the effect of the introduction of a public health measure which reduces the prevalence of an existing, partially treatable, disease.

In all cases, the issue that arises is the management of the introduction of a new good or service. As is common in this area, we focus on the implications for the price deflator, with volume changes derived from that so as to be consistent with the value data. In the second case, we also need to consider how to account for the withdrawal of the superseded treatment.

If a Laspeyres output deflator is used, and a new good or service has appeared between the base year and the current period, then it will have zero weight in the price index because expenditure on it in the base period is zero. This carries the implication that a Laspeyres output deflator is always going to be behind the game. The problem is not resolved by the use of a chain-linked Laspeyres index. If we think of new goods or services as goods or services which appear because their price has fallen below a reservation price, then the usual upward bias in the Laspeyres deflator will be augmented. The benefits of the new good or service do not appear.

If a Paasche or Fisher output deflator is constructed, a price has to be inferred for the base period, notwithstanding that expenditure was zero in that period. The same problem over a base-period price arises if, as in this study, a Törnqvist price index is adopted. The general Törnqvist price index is given by the expression
  Δ l o g ( P t , t + 1 ) = 1 2 ∑ i p i , t y i , t ∑ i p i , t y i , t + p i , t + 1 y i , t + 1 ∑ i p i , t + 1 y i , t + 1 Δ l o g ( p i , t + 1 ) $$ \kern0.5em \Delta \mathit{\log}\left({P}_{t,t+1}\right)=\frac{1}{2}\sum \limits_i\left(\left\{\frac{p_{i,t}{y}_{i,t}}{\sum_i{p}_{i,t}{y}_{i,t}}+\frac{p_{i,t+1}{y}_{i,t+1}}{\sum_i{p}_{i,t+1}{y}_{i,t+1}}\right\}\Delta \mathit{\log}\left({p}_{i,t+1}\right)\right) $$ (1)
where p i , t $$ {p}_{i,t} $$ is the price of good i $$ i $$ in period t $$ t $$ and y i , t $$ {y}_{i,t} $$ is the corresponding volume. Δ l o g ( P t , t + 1 ) $$ \Delta \mathit{\log}\left({P}_{t,t+1}\right) $$ is defined as l o g ( P t + 1 / P t ) . $$ \mathit{\log}\left({P}_{t+1}/{P}_t\right). $$ The origins of the index and its properties are discussed in online Appendix A.

Fisher and Shell (1972) suggest the problem can be resolved by the use of a reservation price. They, however, make the distinction between a supply reservation price and a demand reservation price, suggesting that, when an output price index like the GDP deflator is under consideration, the supply reservation price is the relevant one. In practice, we cannot observe a supply reservation price; on the other hand a demand reservation price can be calculated as the maximum a consumer (the health service in this case) is prepared to pay for the treatment in question based on a standard valuation of the health benefits it delivers. If the demand reservation price were to exceed the supply reservation price, then there would be production at or above the supply reservation price. So we can infer that the demand reservation is always at or below the supply reservation price in the period before the treatment is introduced. By measuring the actual price relative to the demand reservation price we are probably understating the fall in price due to the introduction of the new treatment, and thus understating its impact on the output price index. On the other hand, this makes our treatment consistent with the reservation price recommended for use in the production of cost of living indices. We show here how the relevant demand reservation prices can be derived in our particular circumstances.

Similar issues arise with treatments that are withdrawn, perhaps because better treatments have become available. Expenditure on them drops to zero. With a Fisher or Törnqvist index the move of the actual price to its new demand reservation price can be accommodated appropriately.

Recognizing that, in countries where health services are largely provided by the government and that market prices are not observed, we assume throughout the rest of this article that the price of treatment is measured by the cost of treatment. We refer to actual and reservation costs in lieu of actual and reservation prices. However, to stay close to conventional nomenclature, we refer to price indices rather than cost indices.

3.1 A New Treatment: Contemporaneous Treatment and Benefit

We first set out the Törnqvist price index that we use. For simplicity, we assume that the only change which happens between period 0 and period 1 is that a new treatment for a disease is introduced in period 1, with reservation cost C R e s , 0 $$ {C}_{Res,0} $$ in period 0 and actual cost C 1 $$ {C}_1 $$ in period 1. It is assumed that a fraction ρ $$ \rho $$ of a population N $$ N $$ develop the disease. Expenditure on the new treatment is 0 in period 0 and ρ N C 1 $$ \rho N{C}_1 $$ in period 1, with all other expenditure on medical services, M $$ M $$ , unchanged. So the share of expenditure on the new treatment is 0 in period 0 and ρ N C 1 / ( ρ N C 1 + M ) $$ \rho N{C}_1/\left(\rho N{C}_1+M\right) $$ in period 1. The index weights the cost change by the mean of these. The change in the log of the cost of the new service is l o g ( C 1 / C R e s , 0 ) $$ \mathit{\log}\left({C}_1/{C}_{Res,0}\right) $$ and by assumption none of the other costs change. P 0 $$ {P}_0 $$ is the price index in year 0, and Y 0 $$ {Y}_0 $$ the corresponding volume index while P 1 $$ {P}_1 $$ and Y 1 $$ {Y}_1 $$ are the indices in year 1.

Plugging in these values, the change in the log Törnqvist index of the price of medical services between period 0 and period 1 is Δ l o g P 0 , 1 $$ \Delta \mathit{\log}{P}_{0,1} $$ , with
Δ l o g P 0 , 1 = l o g P 1 P 0 = 1 2 ρ N C 1 ρ N C 1 + M l o g C 1 C R e s , 0 $$ \Delta \mathit{\log}{P}_{0,1}=\mathit{\log}\frac{P_1}{P_0}=\frac{1}{2}\frac{\rho N{C}_1}{\rho N{C}_1+M}\mathit{\log}\frac{C_1}{C_{Res,0}} $$ (2)
We can use the fact that the changes in the log price and log volume indices add to the change in the log of the values (see Appendix A) to derive the corresponding change in volume, Δ l o g Y 0 , 1 $$ \Delta \mathit{\log}{Y}_{0,1} $$ as
Δ l o g Y 0 , 1 = l o g Y 1 Y 0 = l o g M + ρ N C 1 M − Δ l o g P 0 , 1 $$ \Delta \mathit{\log}{Y}_{0,1}=\mathit{\log}\frac{Y_1}{Y_0}=\mathit{\log}\frac{M+\rho N{C}_1}{M}-\Delta \mathit{\log}{P}_{0,1} $$ (3)
if the new treatment is used. Since C 1 $$ {C}_1 $$ is, by assumption, less than C R e s , 0 $$ {C}_{Res,0} $$ , we can see that both terms on the right-hand side augment output. The value of output rises and at the same time the price of output falls.

3.1.1 Measurement Using the Reservation Cost

We now proceed to estimate the reservation cost. We assume that the quality of life is represented by health status indicated by the variable h $$ h $$ . We consider a population split between healthy people, each of whom has a health status h h $$ {h}^h $$ and people with the disease in question with a health state h u $$ {h}^u $$ . The disease does not last beyond the period in which it becomes apparent so h $$ h $$ represents both the fraction of a QALY and the total number of QALYs enjoyed by each patient in the different health states. The new treatment delivers a health status of h t r e a t e d $$ {h}^{treated} $$ to the diseased patient after treatment. V $$ V $$ is the value put on a QALY. Then the value of the QALY gain from treatment, and thus the demand reservation cost of gross output, is V ( h t r e a t e d − h u ) $$ V\left({h}^{treated}-{h}^u\right) $$ . If the actual cost is above this, then treatment will not be cost-effective and thus demand will be zero. If on the other hand the actual cost is below this, then treatment will be worthwhile because the money value of the benefit will exceed the cost of the treatment. When the cost equals the money value of the benefit, we assume no treatment takes place. Treatment is worthwhile if
V ( h t r e a t e d − h u ) > C 1 $$ V\left({h}^{treated}-{h}^u\right)>{C}_1 $$ (4)
and, if so, total nominal consumption of medical services increases by ρ N C 1 $$ \rho N{C}_1 $$ .
To measure the change in price and volume indices, using the reservation cost approach, all we need to do now is to substitute for the reservation cost in Equations (2) and (3), giving
Δ l o g P 0 , 1 = ρ N C 1 2 ( M + ρ N C 1 ) l o g C 1 V ( h t r e a t e d − h u ) $$ \Delta \mathit{\log}{P}_{0,1}=\frac{\rho N{C}_1}{2\left(M+\rho N{C}_1\right)}\mathit{\log}\frac{C_1}{V\left({h}^{treated}-{h}^u\right)} $$ (5)
and
Δ l o g Y 0 , 1 = l o g M + ρ N C 1 M − Δ l o g P 0 , 1 $$ \Delta \mathit{\log}{Y}_{0,1}=\mathit{\log}\frac{M+\rho N{C}_1}{M}-\Delta \mathit{\log}{P}_{0,1} $$ (6)
With Δ l o g P 0 , 1 < 0 $$ \Delta \mathit{\log}{P}_{0,1}<0 $$ if the reservation cost exceeds the actual cost. it follows immediately that the increase in output is larger than would be inferred if the fall in price were ignored.

We defer the important question of how to handle a staggered roll-out of a new treatment to Section 3.2.2. There we study a replacement treatment. The results of course can be applied to a new treatment as a special case.

3.1.2 Direct Measurement Using QALYs

An alternative means of computing the increase in gross output, recommended implicitly by Castelli et al. (2007), Schreyer (2012) and Cutler et al. (2022) is with reference to the outcome of the treatment, in terms of the increase in QALYs to which it gives rise. Castelli et al. (2007) and Schreyer (2012) focus implicitly only on a situation where the treatment leads to an immediate increase in QALYs, whereas Cutler et al. (2022) discuss the issue of discounting. But in our particular case, the issue of discounting does not arise because the treatment and the benefit are contemporaneous.

The increase in QALYs is given straightforwardly as
ρ N ( h t r e a t e d − h u ) $$ \rho N\left({h}^{treated}-{h}^u\right) $$ (7)
but to measure the percentage increase in output resulting from the new treatment, it is necessary also to know the number of QALYs generated by existing medical services. Cutler et al. (2022) assume that half of those expected by the population aged 65 and over in 1999 could be attributed to medical services. Some similar assumption is needed to put the increase in QALYs generated by new treatment into its context.

3.2 An Improvement in Treatment and a Reduction in Costs

Here we consider the situation where the treatment is improved while the cost remains the same or where the treatment is unchanged but is provided more cheaply. The first case can be seen in two ways. First, it can be seen as the withdrawal of an existing good and its replacement by a new good. Secondly, it can be seen as an increase in quality. We show that, as might be hoped, the two treatments yield the same results, confirming that the treatment of quality proposed by Schreyer (2012) is consistent with the treatment of new goods and services suggested here. We demonstrate that this remains to be the case when the new treatment is rolled out gradually. The second case, similarly, can be seen as a straight reduction in cost, or as the replacement of an expensive good by a cheaper one. We show, also in this case, that both approaches give the same answer.

3.2.1 An Improvement in Treatment

The connection between quality changes and new and disappearing goods can be seen by the following simple example. We develop the previous treatment in Section 3.1, but now consider an initial treatment which delivers a utility gain of ( h t r e a t e d − h u ) $$ \left({h}^{treated}-{h}^u\right) $$ QALYs and an improved treatment, available in period 1 which delivers ( h t r e a t e d , ∗ − h u ) $$ \left({h}^{treated,\ast }-{h}^u\right) $$ QALYs at cost, C 1 ∗ $$ {C}_1^{\ast } $$ .

With QALYs as the outcome variable, the new treatment has, before introduction, a reservation cost of
C R e s , 0 ∗ = C 0 ( h t r e a t e d , * − h u ) / ( h t r e a t e d − h u ) $$ {C}_{Res,0}^{\ast }={C}_0\left({h}^{treated,\ast }-{h}^u\right)/\left({h}^{treated}-{h}^u\right) $$ (8)
If the actual cost, C 1 ∗ $$ {C}_1^{\ast } $$ is equal to or higher than this, then the new treatment is not worth the increase in cost. When that is not the case, C R e s , 0 ∗ $$ {C}_{Res,0}^{\ast } $$ is used to compute the change in cost from the introduction of the new treatment. Similarly, after the introduction of the new treatment, the reservation cost of the old treatment in period 1 is
C R e s , 1 = C 0 ( h t r e a t e d − h u ) / ( h t r e a t e d , ∗ − h u ) $$ {C}_{Res,1}={C}_0\left({h}^{treated}-{h}^u\right)/\left({h}^{treated,\ast }-{h}^u\right) $$ (9)
Thus, making the assumption that the number of patients benefitting from the improved treatment is the same as that benefitting from the old treatment, the contribution to the Törnqvist price index of the fall in the cost of the withdrawn treatment from its actual cost to its reservation cost is
Δ l o g P 0 , 1 W = 1 2 ρ N C 0 M + ρ N C 0 l o g { ( h t r e a t e d − h u ) / ( h t r e a t e d , ∗ − h u ) } $$ \Delta \mathit{\log}{P}_{0,1}^W=\frac{1}{2}\frac{\rho N{C}_0}{M+\rho N{C}_0}\mathit{\log}\left\{\left({h}^{treated}-{h}^u\right)/\left({h}^{treated,\ast }-{h}^u\right)\right\} $$ (10)
and the contribution of the new treatment is
Δ l o g P 0 , 1 N = 1 2 ρ N C 1 ∗ M + ρ N C 1 ∗ l o g { ( h t r e a t e d − h u ) / ( h t r e a t e d , ∗ − h u ) } $$ \Delta \mathit{\log}{P}_{0,1}^N=\frac{1}{2}\frac{\rho N{C}_1^{\ast }}{M+\rho N{C}_1^{\ast }}\mathit{\log}\left\{\left({h}^{treated}-{h}^u\right)/\left({h}^{treated,\ast }-{h}^u\right)\right\} $$ (11)
Adding these together, with C 1 ∗ = C 0 $$ {C}_1^{\ast }={C}_0 $$ , since the cost is taken to be unchanged, the overall contribution of the replacement treatment is
Δ l o g P 0 , 1 = ρ N C 0 M + ρ N C 0 l o g { ( h t r e a t e d − h u ) / ( h t r e a t e d , ∗ − h u ) } $$ \Delta \mathit{\log}{P}_{0,1}=\frac{\rho N{C}_0}{M+\rho N{C}_0}\mathit{\log}\left\{\left({h}^{treated}-{h}^u\right)/\left({h}^{treated,\ast }-{h}^u\right)\right\} $$ (12)
and with total spending unchanged the resulting increase in the volume measure is
Δ l o g Y 0 , 1 = ρ N C 0 M + ρ N C 0 l o g { ( h t r e a t e d , ∗ − h u ) / ( h t r e a t e d − h u ) } $$ \Delta \mathit{\log}{Y}_{0,1}=\frac{\rho N{C}_0}{M+\rho N{C}_0}\mathit{\log}\left\{\left({h}^{treated,\ast }-{h}^u\right)/\left({h}^{treated}-{h}^u\right)\right\} $$ (13)
This is entirely consistent with the quality adjustment proposed by Schreyer (2012) which suggests that an index of quality be established (here given by QALYs generated) and that this index, relative to its base year, be used to scale the output measure, in this case the number of patients treated. The treatment differs from that advocated by Cutler et al. (2022) because the change in the number of QALYs is weighted by the expenditure share rather than by the QALY count measured as a share of the total number of QALYs generated.

3.2.2 Gradual Roll-Out

Suppose now that the new treatment is rolled out gradually. A fraction ϕ $$ \phi $$ of patients benefit in year 1 and the remainder, 1 − ϕ $$ 1-\phi $$ , benefit in year 2. The situation is summarized in Table 1. Here, as in Section 3.2.1, the reservation cost of the improved treatment is given by Equation (8), and thus the ratio of the reservation cost of the new treatment to the cost of the old treatment is given as ( h t r e a t e d , * − h u ) / ( h t r e a t e d − h u ) $$ \left({h}^{treated,\ast }-{h}^u\right)/\left({h}^{treated}-{h}^u\right) $$ . Similarly the reservation cost of the old treatment, once the new treatment becomes available, is given by Equation (9).

TABLE 1. The gradual roll-out of a cheaper treatment.
Year Old treatment New treatment Total spending
0 ρ N C 0 $$ \rho N{C}_0 $$ 0 M + ρ N C 0 $$ M+\rho N{C}_0 $$
1 ( 1 − ϕ ) ρ N C 0 $$ \left(1-\phi \right)\rho N{C}_0 $$ ϕ ρ N C 1 ∗ $$ \phi \rho N{C}_1^{\ast } $$ M + ρ ( 1 − ϕ ) N C 0 + ϕ ρ N C 1 ∗ $$ M+\rho \left(1-\phi \right)N{C}_0+\phi \rho N{C}_1^{\ast } $$
2 0 ρ N C 1 ∗ $$ \rho N{C}_1^{\ast } $$ M + ρ N C 1 ∗ $$ M+\rho N{C}_1^{\ast } $$
QALY gain h t r e a t e d − h u $$ {h}^{treated}-{h}^u $$ h t r e a t e d , ∗ − h u $$ {h}^{treated,\ast }-{h}^u $$
We now calculate the change in the overall index between year 0 and year 1, Δ l o g P 0 , 1 $$ \Delta \mathit{\log}{P}_{0,1} $$ , and between year 1 and year 2, Δ l o g P 1 , 2 $$ \Delta \mathit{\log}{P}_{1,2} $$
Δ l o g P 0 , 1 = 1 2 ϕ ρ N C 0 M + ρ N C 0 + ϕ ρ N C 1 ∗ M + ρ N C 1 ∗ l o g h t r e a t e d − h u h t r e a t e d , ∗ − h u $$ \Delta \mathit{\log}{P}_{0,1}=\frac{1}{2}\left(\frac{\phi \rho N{C}_0}{M+\rho N{C}_0}+\frac{\phi \rho N{C}_1^{\ast }}{M+\rho N{C}_1^{\ast }}\right)\mathit{\log}\left(\frac{h^{treated}-{h}^u}{h^{treated,\ast }-{h}^u}\right) $$ (14)
The first term shows the effect of the fraction ϕ $$ \phi $$ from whom the old treatment is withdrawn and the second shows expenditure on the new treatment as a share of total period 1 expenditure.
We similarly evaluate
Δ l o g P 1 , 2 = 1 2 ( 1 − ϕ ) ρ N C 0 M + ρ N C 0 + ( 1 − ϕ ) ρ N C 1 ∗ M + ρ N C 1 ∗ l o g h t r e a t e d − h u h t r e a t e d , ∗ − h u $$ \Delta \mathit{\log}{P}_{1,2}\kern0.5em =\frac{1}{2}\left(\frac{\left(1-\phi \right)\rho N{C}_0}{M+\rho N{C}_0}+\frac{\left(1-\phi \right)\rho N{C}_1^{\ast }}{M+\rho N{C}_1^{\ast }}\right)\mathit{\log}\left(\frac{h^{treated}-{h}^u}{h^{treated,\ast }-{h}^u}\right) $$ (15)
and it can be seen that, with C 1 ∗ = C 0 $$ {C}_1^{\ast }={C}_0 $$ ,
Δ l o g P 0 , 1 + Δ l o g P 1 , 2 = ρ N C 0 M + ρ N C 0 l o g h t r e a t e d − h u h t r e a t e d , ∗ − h u $$ \Delta \mathit{\log}{P}_{0,1}+\Delta \mathit{\log}{P}_{1,2}=\frac{\rho N{C}_0}{M+\rho N{C}_0}\mathit{\log}\left(\frac{h^{treated}-{h}^u}{h^{treated,\ast }-{h}^u}\right) $$ (16)
the answer to be expected from Equation (12).

There are two further points to note. First, Equation (14) also provides an expression for the impact of a better treatment, when only a subgroup, ϕ ρ N $$ \phi \rho N $$ of the patients can benefit. This is the reality of many health measures. Secondly, we note that considerable care is needed in the application of the approach of Fisher and Shell (1972). In year 1, the old treatment has to be treated as a withdrawn good for the patients who migrate to the new treatment, although in aggregate the treatment remains available. In year 2, the new treatment has to be treated as a new good although it was available to some people in year 1. These points are particularly relevant when we come to look at public health measures which render old treatments unnecessary but only for some of the patients.

3.2.3 A Reduction in Cost

That the two treatments, replacement of an expensive good by a cheaper one and a simple reduction in cost, give the same answer can be seen directly from the previous case. There the implied reduction in cost reflected an increase in quality. In this case, the cost is simply lower. The log of total expenditure will fall by the decline in log of cost weighted by the two expenditure shares and, provided there is no change in the number of procedures, the Törnqvist volume index will remain unchanged. Similarly, there is no change in the number of QALYs generated, so a QALY-based index of gross output will remain unchanged. This does not, of course, mean that welfare is unchanged. If medical treatment becomes cheaper, more can be spent on other things.

While these results come as no surprise, it is worth pointing out that statistical offices may need to revise their processes to ensure that this path is followed. Shapiro et al. (2001) draw attention to the fact that an old treatment of cataracts was replaced by a new one in specialist centers. The new treatment was much cheaper than the old one. But the Bureau of Economic Analysis handled it in a way that did not identify the reduction in cost in the US national accounts.

3.3 Treatment and Benefits Spread Over Time

We now develop the approach of Section 3.1 to consider a situation where the patient needs sustained treatment to manage the condition, but, while the treatment may continue throughout life, very different costs are incurred at different stages, and the costs of the treatment in any particular year are not aligned to the benefits in that year. An example of this would be an organ transplant. Large costs are incurred at the start of the treatment but the patients have to take drugs throughout life to avoid fatal rejection of the transplant. The discounted sum of the expected benefits may exceed the discounted sum of the expected costs, but in the year in which the treatment starts, costs may well exceed the benefit in that year. This approach encompasses forms of “one-off” treatment such as cataract surgery with no continuing maintenance costs. Expected benefit exceeds expected costs over the life-time but not necessarily in the year of treatment. But it is in fact the need for continuing treatment rather than the receipt of continuing benefits that distinguishes this case from that of Section 3.1.

To measure the cost and quantity changes, we assume that treatment must commence in the year in which the disease is contracted, notwithstanding that continuing treatment is needed. This allows us to compare the cohort exposed to the disease in year t $$ t $$ = 0, for whom no treatment is available, with the cohort exposed to the disease in year t $$ t $$ = 1, for whom treatment is available. The individuals in the cohort exposed in t $$ t $$ are not at further risk if they do not contract the disease in t $$ t $$ . There are, however, subsequent cohorts exposed to the disease; all cohorts are assumed to be of the same size and to face the same risk of contracting the disease. It should be noted that these assumptions are needed so as to identify clearly what is going on; the cost change associated with the introduction of the treatment does not rely on them, while the implications of this for the overall price index, the value change and the quantity index do.

We again consider three possible situations. In the first case, the individual is healthy. In the second case, s/he contracts the disease and is treated. In the third case, s/he contracts the disease and is not treated. π τ h $$ {\pi}_{\tau}^h $$ is the probability of living for τ $$ \tau $$ years after exposure for the healthy individual. π τ t r e a t e d $$ {\pi}_{\tau}^{treated} $$ is the probability for a treated individual and π τ u $$ {\pi}_{\tau}^u $$ is the probability for an untreated individual. π 1 h = π 1 t r e a t e d = π 1 u = 1 $$ {\pi}_1^h={\pi}_1^{treated}={\pi}_1^u=1 $$ . The healthy individual enjoys a health status of h τ h $$ {h}_{\tau}^h $$ in year τ $$ \tau $$ after exposure with comparable terms for the treated and untreated individuals, h τ t r e a t e d $$ {h}_{\tau}^{treated} $$ and h τ u $$ {h}_{\tau}^u $$ respectively. The h $$ h $$ terms are measured as fractions of a fully healthy life year. Even for the average individual without the disease, h $$ h $$ is likely to be below 1 as ageing progresses. δ $$ \delta $$ is the discount factor.

We can then write the discounted value of remaining life-time QALYs for the three types of individual, with the year of exposure equal to 1, as
Q h = ∑ τ = 1 ∞ π τ h δ τ − 1 h τ h $$ {Q}^h\kern0.5em =\sum \limits_{\tau =1}^{\infty }{\pi}_{\tau}^h{\delta}^{\tau -1}{h}_{\tau}^h $$ (17)
Q t r e a t e d = ∑ τ = 1 ∞ π τ t r e a t e d δ τ − 1 h τ t r e a t e d $$ {Q}^{treated}\kern0.5em =\sum \limits_{\tau =1}^{\infty }{\pi}_{\tau}^{treated}{\delta}^{\tau -1}{h}_{\tau}^{treated} $$ (18)
and
Q u = ∑ τ ∞ π τ u δ τ − 1 h τ u $$ {Q}^u=\sum \limits_{\tau}^{\infty }{\pi}_{\tau}^u{\delta}^{\tau -1}{h}_{\tau}^u $$ (19)
c τ $$ {c}^{\tau } $$ is the cost of treatment in the τth year of the disease and c R e s τ $$ {c}_{Res}^{\tau } $$ is its reservation cost. Treatment costs are assumed to change only with the time that has passed since contracting the disease, so for any τ $$ \tau $$ , c τ $$ {c}^{\tau } $$ does not change over time. We therefore do not use time subscripts. The total discounted cost of treatment is
C = ∑ τ = 1 ∞ π τ t r e a t e d δ τ − 1 c τ $$ C=\sum \limits_{\tau =1}^{\infty }{\pi}_{\tau}^{treated}{\delta}^{\tau -1}{c}^{\tau } $$ (20)
With V the money value put on a QALY, the benefit exceeds the costs if
V ( Q t r e a t e d − Q u ) > C $$ V\left({Q}^{treated}-{Q}^u\right)>C $$ (21)
This condition is more likely to be met by those who have a high survival rate than those who have low survival prospects. We look at the cohorts exposed to the disease in year t $$ t $$ = 0, before the treatment was available and in year t $$ t $$ = 1 with treatment available. With N the cohort size and ρ $$ \rho $$ the risk of contracting the disease in the relevant year, we can write ρ N $$ \rho N $$ as the number of people beginning the new treatment. Then the discounted sum of consumption of health services increases by ρ N C $$ \rho NC $$ in the year in which the treatment is introduced. For national accounting purposes, however, we need to consider what happens in each year of treatment, since the national accounts measures of output relate to activity in each year, rather than to outcomes which may arise long after the activity in question.

3.3.1 Measurement Using the Reservation Cost

Defining the reservation cost was straightforward when all the treatment and thus all the costs were incurred in the first year. Here, the reservation cost has to be derived from a comparison of discounted costs and discounted benefits, and not from a comparison of costs and benefits in any particular year. The treatment, while consisting of different activities in each year of the disease, has to be seen as a package. This contrasts with the example discussed in Section 3.1, where each year could be treated separately. We still face the problem that, while in the national accounts each year is distinct, here the introduction of the new service in one year makes sense only if the continuing treatment is available in the next year.

The most obvious way to derive the reservation costs is to assume that these are proportional to the actual cost of treatment in the year of introduction of the new treatment and in the subsequent years when separate treatments are introduced. We denote c R e s 1 $$ {c}_{Res}^1 $$ as the reservation cost of the first activity in year 0 with c R e s τ $$ {c}_{Res}^{\tau } $$ similarly defined for year τ − 1 $$ \tau -1 $$ . Then the reservation costs in the year preceding the τth year of treatment are
c R e s τ = V ( Q t r e a t e d − Q u ) C c τ $$ {c}_{Res}^{\tau }=\frac{V\left({Q}^{treated}-{Q}^u\right)}{C}{c}^{\tau } $$ (22)
If M $$ M $$ , expenditure on other medical services, is assumed constant, a Törnqvist price index for year 1 can be calculated with the change in the log cost of the treatment of
l o g c 1 c R e s 1 $$ \mathit{\log}\frac{c^1}{c_{Res}^1} $$ (23)
and an average expenditure share of the treatment of
1 2 ρ N c 1 M + ρ N c 1 $$ \frac{1}{2}\frac{\rho N{c}^1}{M+\rho N{c}^1} $$ (24)
If no other changes take place elsewhere in the health industry, then the change in the price of output is
Δ l o g P 0 , 1 = 1 2 ρ N c 1 M + ρ N c 1 l o g c 1 c R e s 1 $$ \Delta \mathit{\log}{P}_{0,1}=\frac{1}{2}\frac{\rho N{c}^1}{M+\rho N{c}^1}\mathit{\log}\frac{c^1}{c_{Res}^1} $$ (25)
and the change in the volume of output, Y, is, consistent with maintaining coherence in the current price accounts,
Δ l o g Y 0 , 1 = l o g M + ρ N c 1 M − Δ l o g P 0 , 1 $$ \Delta \mathit{\log}{Y}_{0,1}=\mathit{\log}\frac{M+\rho N{c}^1}{M}-\Delta \mathit{\log}{P}_{0,1} $$ (26)
In the second year of treatment, the change in the log cost of treatment is
l o g c 2 c R e s 2 $$ \mathit{\log}\frac{c^2}{c_{Res}^2} $$ (27)
and the average share of expenditure is, with the assumption that a new group of patients receives the year 1 treatment
1 2 π 2 t r e a t e d ρ N c 2 M + ρ N c 1 + π 2 t r e a t e d ρ N c 2 $$ \frac{1}{2}\frac{\pi_2^{treated}\rho N{c}^2}{M+\rho N{c}^1+{\pi}_2^{treated}\rho N{c}^2} $$ (28)
The change in the price index of output is
Δ l o g P 1 , 2 = 1 2 π 2 t r e a t e d ρ N c 2 M + ρ N ( c 1 + π 2 t r e a t e d c 2 ) l o g c 2 c R e s 2 $$ \Delta \mathit{\log}{P}_{1,2}=\frac{1}{2}\frac{\pi_2^{treated}\rho N{c}^2}{M+\rho N\left({c}^1+{\pi}_2^{treated}{c}^2\right)}\mathit{\log}\frac{c^2}{c_{Res}^2} $$ (29)
and the change in the volume of output, Y, is, consistent with maintaining coherence in the current price accounts,
Δ l o g Y 1 , 2 = l o g M + ρ N ( c 1 + π 2 t r e a t e d c 2 ) M + ρ N c 1 − Δ l o g P 1 , 2 $$ \Delta \mathit{\log}{Y}_{1,2}=\mathit{\log}\frac{M+\rho N\left({c}^1+{\pi}_2^{treated}{c}^2\right)}{M+\rho N{c}^1}-\Delta \mathit{\log}{P}_{1,2} $$ (30)
The share of the new treatment in period 2 reflects the assumption that the period 1 treatment is offered to a new cohort of patients.
In subsequent years, as the treatment continues to be rolled out to the first cohort, the changes in price and quantity can be evaluated similarly. We made the assumption that there are no changes to the costs of the initial and continuing treatment. This means also that the reservation cost of the continuing treatment remains unchanged. Then Equation (29) becomes, when we compare year 2 and year 3,
Δ l o g P 2 , 3 = 1 2 π 3 t r e a t e d ρ N c 3 M + ρ N ( c 1 + π 2 t r e a t e d c 2 + π 3 t r e a t e d c 3 ) l o g c 3 c R e s 3 $$ \Delta \mathit{\log}{P}_{2,3}=\frac{1}{2}\frac{\pi_3^{treated}\rho N{c}^3}{M+\rho N\left({c}^1+{\pi}_2^{treated}{c}^2+{\pi}_3^{treated}{c}^3\right)}\mathit{\log}\frac{c^3}{c_{Res}^3} $$ (31)
The expression for the volume of output can similarly be updated and both price and volume indices can be rolled forward.

3.3.2 Direct Measurement Using QALYs

The increase in QALYs is, τ − 1 $$ \tau -1 $$ years after the start of treatment, given as
ρ π τ t r e a t e d N h τ t r e a t e d − ρ π τ u N h τ u $$ \rho {\pi}_{\tau}^{treated}N{h}_{\tau}^{treated}-\rho {\pi}_{\tau}^uN{h}_{\tau}^u $$ (32)
and this, measured as a proportion of all other discounted QALYs generated by medical treatment shows the increase in the volume of gross output. Once again the issue of relating this to the number of QALYs generated by existing medical services arises.

3.4 Public Health Measures

These observations lead us on to a discussion of public health measures. In contrast to the previous examples, a public health measure is an intervention designed to reduce the risk of one or more diseases. It follows immediately that the resulting increase in QALYs should be treated as an increase in gross output, when measured in the manner Cutler et al. (2022) suggest. But the more substantial question, which we consider first, is how it should be treated in the existing framework of main-stream national accounts.

The public health measure is assumed to be a preventative treatment intended for people with a particular condition, and designed to prevent it mutating into a serious disease. Thus, the Diabetes Prevention Programme, which we consider in sections 4 and 5, is made available to people thought to be at elevated risk of developing diabetes.

The generic program considered here has a cost per participant of H $$ H $$ . Participation in the program has the consequence of reducing the risk of contracting the disease from ρ $$ \rho $$ to ρ p $$ {\rho}_p $$ , but leaving the cost of treatment unchanged. While it might be thought that the risk of developing the disease depends on how long patients have been at risk, we make the simplifying assumption that it depends only on whether the patient is treated in the preventative program or not. We also assume that the QALY impact of contracting the disease is independent of age. This means that the expected benefit of the program is assumed to be the same for all participants. In practice, population averages can be used.

The annual cost of the health program is assumed proportional to the number undertaking it. C $$ C $$ is the discounted sum of the costs of treatment, with c $$ c $$ the annual cost of treatment. π τ h $$ {\pi}_{\tau}^h $$ , π τ u $$ {\pi}_{\tau}^u $$ and π τ t r e a t e d $$ {\pi}_{\tau}^{treated} $$ are defined as in Section 3.3. Q h $$ {Q}^h $$ is the discounted number of QALYs enjoyed by someone not affected by the disease. Q t r e a t e d $$ {Q}^{treated} $$ is the measure for someone affected and treated. The cost of the public health measure is allocated on a per capita basis.

Table 2 shows the relevant costs and the benefits with and without the public health measure in place. Once again, there are two ways of looking at the problem. The first focuses on the cost changes while the second focuses on the QALY gain.

TABLE 2. Costs and benefits per person with and without the public health intervention.
No public health measure Public health measure
Welfare Cost Welfare Cost
Not affected ( 1 − ρ ) Q h $$ \left(1-\rho \right){Q}^h $$ 0 ( 1 − ρ p ) Q h $$ \left(1-{\rho}_p\right){Q}^h $$ ( 1 − ρ p ) H $$ \left(1-{\rho}_p\right)H $$
Treated ρ Q t r e a t e d $$ \rho {Q}^{treated} $$ ρ C $$ \rho C $$ ρ p Q t r e a t e d $$ {\rho}_p{Q}^{treated} $$ ρ p ( H + C ) $$ {\rho}_p\left(H+C\right) $$

3.4.1 Measurement Using Reservation Costs

First we look at the reservation cost approach. A key issue we need to discuss is when a treatment like participation in a public health program counts as new, requiring the reservation price to be used, and when does it not. In Section 3.3, we assumed that clearly-identifiable cohorts could be observed. There the treatment was new when applied to the first cohort for which it was available. But Section 3.2.2 showed that, when roll-out was gradual, it was erroneous to regard it as new only in its year of introduction. A definition consistent with Section 3.2.2 is that a treatment is new when it is provided to someone who already has the condition in question when it is introduced.

We refer to patients with the condition at the introduction of the program as new patients. Those who develop the condition justifying participation after the introduction of the program are described as follow-on patients. In the first year of introduction, all patients are new. In subsequent years, only some may be. And if the whole cohort is treated in the first year, there will be no new patients in future years.

To evaluate the reservation cost, we first need to look at the cost saving. This, making the assumption that treatment is provided to everyone who would benefit from it, is
Δ W C o s t s = ( ρ − ρ p ) N C $$ \Delta {W}_{Costs}=\left(\rho -{\rho}_p\right) NC $$ (33)
Additionally, with V $$ V $$ the value put on a QALY, the sum of total of welfare without the public health measure in place is
W = N V { ( 1 − ρ ) Q h + ρ Q t r e a t e d } $$ W= NV\left\{\left(1-\rho \right){Q}^h+\rho {Q}^{treated}\right\} $$ (34)
while with the public health measure in place it is
W P H = N V { ( 1 − ρ p ) Q h + ρ p Q t r e a t e d } $$ {W}_{PH}= NV\left\{\left(1-{\rho}_p\right){Q}^h+{\rho}_p{Q}^{treated}\right\} $$ (35)
Comparing the two welfare values, the money value of the gain in wellbeing is
Δ W W e l b = N V ( Q h ( 1 − ρ p ) + ρ p Q t r e a t e d − Q h ( 1 − ρ ) − ρ Q t r e a t e d ) = N V ( Q h − Q t r e a t e d ) ( ρ − ρ p ) $$ {\displaystyle \begin{array}{ll}\hfill \Delta {W}_{Welb}& = NV\left({Q}^h\left(1-{\rho}_p\right)+{\rho}_p{Q}^{treated}-{Q}^h\left(1-\rho \right)-\rho {Q}^{treated}\right)\\ {}\hfill & = NV\left({Q}^h-{Q}^{treated}\right)\left(\rho -{\rho}_p\right)\end{array}} $$ (36)
The total reservation cost, Δ W T o t $$ \Delta {W}_{Tot} $$ of the public health measure, needs to reflect both the welfare gain and the benefit of the saving in treatment costs. This means it is given as
Δ W T o t = Δ W C o s t + Δ W W e l b = N ( C + V ( Q h − Q t r e a t e d ) ) ( ρ − ρ p ) $$ \Delta {W}_{Tot}=\Delta {W}_{Cost}+\Delta {W}_{Welb}=N\left(C+V\left({Q}^h-{Q}^{treated}\right)\right)\left(\rho -{\rho}_p\right) $$ (37)
The actual cost is of course H $$ H $$ making the ratio of actual to reservation cost
H / H r e s = H / { ( C + V ( Q h − Q t r e a t e d ) ) ( ρ − ρ p ) } $$ H/{H}_{res}=H/\left\{\left(C+V\left({Q}^h-{Q}^{treated}\right)\right)\left(\rho -{\rho}_p\right)\right\} $$ (38)
With the assumptions we have made about disease risk and mortality, this is the same for all new patients.

We need now to work out the change in the Törnqvist index of the price of medical services. The cost of first-year treatment is shown as the first term in the discounted sum in Equation (20). With a probability of contracting the disease of ρ $$ \rho $$ and n 1 $$ {n}_1 $$ people, the total first year expenditure in the absence of the program is ρ n 1 c $$ \rho {n}_1c $$ .

With the program in place there are two changes. First, a smaller proportion of the population, ρ p < ρ $$ {\rho}_p<\rho $$ , requires treatment, reducing expenditure. Secondly, the costs of the public health measure have to be met. So, with c $$ c $$ the annual cost of treatment assumed constant, first year expenditure changes to n 1 ( ρ p c + H ) $$ {n}_1\left({\rho}_pc+H\right) $$ , and the share of expenditure on the program becomes, in the period of its introduction,
n 1 H M 1 + n 1 ( ρ p c + H ) $$ \frac{n_1H}{M_1+{n}_1\left({\rho}_pc+H\right)} $$ (39)
while in the period before introduction it had been zero. Here M 1 $$ {M}_1 $$ reflects all medical expenditures in year 1, except those provided to new participants in the public health program and the cost of the health program for new participants. M t $$ {M}_t $$ , its analogue in year t $$ t $$ , includes the cost of the provision of the health program and the treatment of follow-on participants but not the costs of the program and treatment for new participants.
We also need to take account of the withdrawn treatment, as Section 3.2.2 indicated. We face, once again, the situation of Section 3.3.1—that the calculations have to be performed on the basis of discounted costs and benefits rather than those in any particular year. But with c ( ρ − ρ p ) $$ c\left(\rho -{\rho}_p\right) $$ the cost of the withdrawn service, we can say that this service will not be withdrawn unless H / H r e s < 1 $$ H/{H}_{res}<1 $$ , and the demand reservation cost, at which it would not be withdrawn is given by c ( ρ − ρ p ) H / H r e s . $$ c\left(\rho -{\rho}_p\right)H/{H}_{res}. $$ The share of the withdrawn services in spending before the introduction of the public health measure is therefore
n 1 c ( ρ − ρ p ) M 0 $$ \frac{n_1c\left(\rho -{\rho}_p\right)}{M_0} $$ (40)
The overall change in the Törnqvist price index for medical services as a result of the program is, making the assumption that there are no price changes apart from those arising from the introduction of the program, then given as:
Δ l o g P 0 , 1 = 1 2 n 1 c ( ρ − ρ p ) M 0 + n 1 H M 1 + n 1 ( ρ p c + H ) l o g H H r e s $$ \Delta \mathit{\log}{P}_{0,1}\kern0.5em =\frac{1}{2}\left(\frac{n_1c\left(\rho -{\rho}_p\right)}{M_0}+\frac{n_1H}{M_1+{n}_1\left({\rho}_pc+H\right)}\right)\mathit{\log}\left(\frac{H}{H_{res}}\right) $$ (41)
and, with Y 0 , 1 $$ {Y}_{0,1} $$ representing the output measure,
Δ l o g Y 0 , 1 = l o g n 1 ( ρ p c + H ) + M 1 M 0 − Δ l o g P 0 , 1 $$ \Delta \mathit{\log}{Y}_{0,1}=\mathit{\log}\frac{n_1\left({\rho}_pc+H\right)+{M}_1}{M_0}-\Delta \mathit{\log}{P}_{0,1} $$ (42)
It should be noted that the denominator in the first term of Equation (42) is the total money value of expenditure in period 0. Before the introduction of the new program, M 0 $$ {M}_0 $$ covers all expenditure including the treatment of patients who develop the disease ahead of the public health program. M 1 $$ {M}_1 $$ covers all expenditure in period 1 except that on the public health program and the treatment costs of those patients who develop the disease despite participating in the program.
We also face the issue of what should be done in subsequent years, as the new patients live out their life-spans. Less treatment is needed and consumption of medical services falls. This has to be seen as a withdrawal of treatment from the patients who have benefitted from the public health intervention. The logic of Section 3.3.1 and in particular Equation (22) applies. The change in the price index is
Δ l o g P t − 1 , t = 1 2 c ( ρ − ρ p ) ∑ τ = 1 t n τ π t + 1 − τ t r e a t e d M t − 1 + n t − 1 H + ρ p c ∑ τ = 1 t − 1 n τ π t + 1 − τ t r e a t e d + n t H M t + n t H + ρ p c ∑ τ = 1 t n τ π t + 1 − τ t r e a t e d l o g H H r e s $$ {\displaystyle \begin{array}{ll}\hfill \Delta \mathit{\log}{P}_{t-1,t}& =\frac{1}{2}\left\{\frac{c\left(\rho -{\rho}_p\right){\sum}_{\tau =1}^t{n}_{\tau }{\pi}_{t+1-\tau}^{treated}}{M_{t-1}+{n}_{t-1}H+{\rho}_pc{\sum}_{\tau =1}^{t-1}{n}_{\tau }{\pi}_{t+1-\tau}^{treated}}\right.\\ {}\hfill & \kern1em +\left.\frac{n_tH}{M_t+{n}_tH+{\rho}_pc{\sum}_{\tau =1}^t{n}_{\tau }{\pi}_{t+1-\tau}^{treated}}\right\}\mathit{\log}\left(\frac{H}{H_{res}}\right)\end{array}} $$ (43)
The left-hand term in Equation (43) shows, in its numerator, the saving in treatment costs and thus the value of the withdrawn treatment as a result of the public health measure being in place from year 1 to year t $$ t $$ . In the denominator, it shows total spending in year t − 1 $$ t-1 $$ . The second term has in its numerator the cost of the provision of the public health scheme in year t $$ t $$ to new participants only. The costs of the provision of the scheme to follow-on participants and any other costs associated with the treatment of follow-on participants are included in M t $$ {M}_t $$ .

While it may come as a surprise that a price reduction takes place at all, if the public health program were to lead to cheaper treatment rather than no treatment for some patients, we should expect to see a price reduction implied for the continuing treatment. Here for the reasons explained in Section 3.3.1, we are obliged to treat the public health program and its consequences as a single package, with the consequence that we use the ratio of the actual cost of the program to the demand reservation cost to define the implied fall in cost of the withdrawn treatment.

As with the other examples, we can calculate the change in the volume index from the change in the value of spending and the price change, as shown in Equation (44)
Δ l o g Y t − 1 , t = M t + n t H + ρ p c ∑ τ = 1 t n τ π t − τ t r e a t e d M t − 1 + n t − 1 H + ρ p c ∑ τ = 1 t − 1 n τ π t − 1 − τ t r e a t e d − Δ l o g P t − 1 , t $$ \Delta \mathit{\log}{Y}_{t-1,t}=\frac{M_t+{n}_tH+{\rho}_pc{\sum}_{\tau =1}^t{n}_{\tau }{\pi}_{t-\tau}^{treated}}{M_{t-1}+{n}_{t-1}H+{\rho}_pc{\sum}_{\tau =1}^{t-1}{n}_{\tau }{\pi}_{t-1-\tau}^{treated}}-\Delta \mathit{\log}{P}_{t-1,t} $$ (44)
It is worth noting that the volume change may be positive or negative, depending on how the reduction in value compares with the reduction in price given by Equation (43).

The form of the calculations would not change very much if there were additional costs, beyond those of treatment, for people who contract the disease. If, for example, it were unpleasant or required a period of quarantine, the estimated discounted costs to the patient could be reflected by an increment to C $$ C $$ . In other words, C $$ C $$ might measure the total social costs of contracting the disease, and not merely the medical costs. But following the general principle that the national accounts are based on observable transactions, this should probably not feature in the national accounts.

That does, however, raise a further issue. For some diseases, there may be patients who are not aware that they would benefit from treatment and who suffer as a result; the public health measure may serve to reduce the number of patients in this category.

3.4.2 Direct Measurement Using QALYs

An alternative means of reckoning is to consider QALYs as an outcome indicator, and to assess the proportionate change in output in terms of the proportionate change in QALYs. With the treatment in place but before the introduction of the public health measure, the increase in QALYs in year t + τ − 1 $$ t+\tau -1 $$ as a result of treatment is
ρ ( π τ t r e a t e d h τ t r e a t e d − π τ u h τ u ) $$ \rho \left({\pi}_{\tau}^{treated}{h}_{\tau}^{treated}-{\pi}_{\tau}^u{h}_{\tau}^u\right) $$ (45)
With the public health measure replacing treatment, the associated increase in QALYs is
( 1 − ρ p ) π τ h h τ h + ρ p π τ t r e a t e d h τ t r e a t e d $$ \left(1-{\rho}_p\right){\pi}_{\tau}^h{h}_{\tau}^h+{\rho}_p{\pi}_{\tau}^{treated}{h}_{\tau}^{treated} $$ (46)
while before the measure was introduced, utility in the period in question was
( 1 − ρ ) π τ h h τ h + ρ π τ t r e a t e d h τ t r e a t e d $$ \left(1-\rho \right){\pi}_{\tau}^h{h}_{\tau}^h+\rho {\pi}_{\tau}^{treated}{h}_{\tau}^{treated} $$ (47)
so the increase in QALYs is
( ρ − ρ p ) ( π τ h h τ h − π τ t r e a t e d h τ t r e a t e d ) $$ \left(\rho -{\rho}_p\right)\left({\pi}_{\tau}^h{h}_{\tau}^h-{\pi}_{\tau}^{treated}{h}_{\tau}^{treated}\right) $$ (48)
It is, however, more usual to attribute output to the time when the activity which gives rise to that output takes place. That points to the first-year increase in output being measured by the increase in the discounted sum of QALYs (see Equations (17) and (18)), i.e., as
( ρ − ρ p ) ( Q h − Q t r e a t e d ) $$ \left(\rho -{\rho}_p\right)\left({Q}^h-{Q}^{treated}\right) $$ (49)
and with this metric the proportionate change in gross output would be given by calculating this as a fraction of the total discounted sum of QALYs attributable to medical services. The net measures can be calculated by adding back any cost savings to the money value of the QALY gain, and deducting the cost of the program itself. This is then measured as a proportion of the money value of the QALYs generated by medical services net of the costs involved.

4 An Example: Diabetes and the Diabetes Prevention Programme

T2D is a disease whereby the sufferer is unable to control blood sugar levels adequately. T2D increases the risk of cardiovascular disease and is also associated with foot problems sometimes leading to amputation of toes or feet, visual impairment, and kidney disease. These complications become more likely the longer the patient is diabetic, pointing to health gain even if an intervention delays rather than prevents the onset.

The prevalence of doctor-diagnosed T2D has increased from 2% of the adult population in 1990 to 6% in 2021. Among people 75 and over prevalence has increased from 6% to 16% over the same period. Excess weight is a major risk factor. Thus in 2018, the prevalence of diabetes among people with a body mass index of at least 30 was 12% while for those with a body mass index of 18.5 to 25, described as the normal range, it was only 5%. The increasing prevalence over time is widely associated with the increasing average body mass index, from 25.8 in 1993 to 27.6 in 2019 but may also have happened because mortality rates of those with T2D have declined (Holden et al. 2017).

The Diabetes Prevention Programme (DPP) was set up on a test basis in 2017 (NHS England 2016). It offers classes to people who are regarded as being at risk of developing diabetes. Patients are referred to it if they have blood sugar levels regarded as higher than normal but not yet so high as to be regarded as diabetic. In a series of 15 classes, advice is offered on factors such as what constitutes a healthy diet, weight management and exercise. A recent study (Ravindrarajah et al. 2023) suggested that, three years after completion of the course, 127/1000 referrals had developed diabetes while, among those who did not undertake the course, the prevalence of diabetes was 154/1000. These figures, although suggesting that the course was successful, were derived from a matched cohort study rather than a random control trial. Evidence from other countries where random control trials have been carried out pointed to larger effects, suggesting the possibility that the impact of the program was understated in the UK study. But the question faced here is how should the effects of programs such as DPP be shown in the measures of national income rather than the precise magnitude of the effect of the DPP.

4.1 The Costs of Diabetes

For the United Kingdom, there are estimates of the total cost of T2D to the National Health Service. Hex et al. (2024) suggest that in 2021/22 the costs of diagnosis and management amounted to £3.2bn while the treatment of complications cost £5.6bn. With 4 mn people diagnosed with T2D in 2022/3 that implies an average cost of £800 p.a. for diagnosis and management and £1,400 p.a. for treatment of complications. Doyle et al. (2022), in a study of the Irish Republic look at the annual costs of care for five categories of patient, those with optimal blood sugar control, those with suboptimal blood sugar control but no complications, those with kidney disease, those with active foot disease, those at moderate risk of active foot disease and those who have suffered myocardial infarction. In all, 70%–80% of patients fall into the first or second category. In the first case, the treatment cost about €800 per patient year, and in the second case about €1,200 or approximately £1,000 per patient year. We use a figure of £1000 as an annual cost of treating diabetes, noting that the late stage costs are discounted. If we assume that this is incurred for twenty years and discounted at 3 1 2 % $$ 3\frac{1}{2}\% $$ p.a., then the average discounted cost per case is £14,600.

4.2 The Effects of the Program

In assessing the effects of the program, it is necessary to distinguish referral from enrollment and again enrollment from following most or all of the course. NHS England (2016) provides estimates of the costs and benefits of the National Diabetes Prevention Programme in terms of cases of diabetes prevented or delayed by at least four years based on enrollment and participation in at least the first session, while Ravindrarajah et al. (2023) studied the effects of referral to the program on the prevalence of diabetes three years later. They were unable to identify what proportion of referrals were actually enrolled although an earlier study (Valabhji et al. 2020) does provide some estimates of this. It is not possible to say precisely how the estimates of cases delayed by at least three years compared with those delayed by at least four years. But figure 2 in Ravindrarajah et al. (2023) suggests that, while prevalence rises among both the participants in the program and the nonparticipants, the gap between the two values does not change much in the fourth year.

The total cost of the program “excluding implementation, support, and local costs”, was estimated at £105 mn for the anticipated 390,000 participants. Implementation and support costs added £10.34 mn to this, making a cost of £29.6 mn per 100,000 participants rounded to £30 mn per 100,000. It is possible, of course, that some of these costs would fall if the scheme were permanent.

The base assumption made was that 37% of those eligible would enroll (NHS England 2016, page 10)—meaning actually participating in the first session and that 63% of those who enrolled would fail to complete the course. Valabhji et al. (2020) looking at early data, found that 53% of those referred to the program actually participated in an initial assessment and of those who joined the initial assessment 64% went on to at least one intervention session. Given the timing of this study only a fairly small number of referrals were in a position to have completed. But again 53% of those who had attended at least one intervention session completed the course. These last two figures suggest 34% of those who enrolled completed the course—a figure very similar to the initial assumption. Initial enrollment was, however, nearly 50% higher than assumed in the prospective study. Taken in the round, these figures give us a penetration ratio of 0 . 53 × 0 . 64 × 0 . 53 % = 18 % $$ 0.53\times 0.64\times 0.53\%=18\% $$ of the population at risk. Like the example of Section 3.4.1, the program is exclusive. We assume that no costs are faced from those who do not undertake the initial assessment. But we assume that once someone attends the initial assessment, the full costs are incurred. In practice, presumably an allowance can be made for the savings which result from those who do not proceed to the course. We therefore probably overstate the costs.

NHS England (2016) assumed that for every 100,000 participants enrolled in the program 4,500 cases of diabetes would be delayed by at least four years or prevented. It is noted that this is a conservative estimate; in a comparable program in Finland it was estimated that 7,400 cases per 100,000 referrals were delayed or prevented (Lindström et al. 2006). NHS England (2016) also suggested, rather conveniently, that one QALY is generated per case of diabetes prevented or delayed by at least four years. We work with this figure when discussing how the program might be treated in the national accounts.

As noted earlier, the main medical problems associated with diabetes arise often many years after onset of the disease itself. If we assumed that the one year QALY gain came on average twenty years after onset, then discounting at 3 1 2 $$ 3\frac{1}{2} $$ % p.a. would yield a current value QALY gain of 1 2 $$ \frac{1}{2} $$ QALY and, without better guidance as to timing, we work with this figure.

It is unclear what the long-term prognosis is for those for whom onset is delayed by four years. NHS England (2016) suggest that the benefits may be over-stated if there is a ‘catch-up’ effect. Equally, however, one might think that, at least for those who eventually die of some cause not related to diabetes, the costs saved are the higher costs associated with the late stages of the disease. NHS England (2016) simply assume that the average costs are saved and we follow that approach.

Ravindrarajah et al. (2023) studied the effects of referral, not initial participation, three years after referral. They found that the probability of not converting to diabetes from prediabetes was 87.3% for those who were referred to the course and 84.6% for those who were not referred to the course—a reduction in the prevalence of diabetes at three years from 15.4% to 12.7%, a drop of 18.5% or 2.7 percentage points, as noted earlier. Those referred had higher body mass index and were more likely to have smoked at some time in their lives. Analyzing the data using Cox's proportionate hazard model suggests that referral to the program reduces the risk of progression to diabetes by 20%—a number not very different from the result inferred directly by comparing crude conversion rates at three years. We also note that the drop of 2.7 percentage points contrasts with the drop of 4.5 percentage points assumed by NHS England (2016). However, that figure of 2.7 percentage points was based on referrals, not enrollment. If we use the enrollment ratio of 53% from Valabhji et al. (2020), it implies a drop of 2.7/0.53 = 5.1 percentage points or 5,100 per 100,000 among the enrolled population—slightly higher than that anticipated by the prospective study, suggesting a result slightly better than had been assumed. The key program statistics are summarized in Table 3.

TABLE 3. Key program statistics per thousand patients referred.
Referred 1000
Attended initial assessment 530
Attended at least one session 340
Completed Course 180
Diabetic at three years 127
Cases of diabetes delayed 27
Value of QALYs generated £810,000
Discounted saving in cost of treatment £394,200
Total discounted benefit £1,204,200
Cost per thousand participants £300,000
Cost per thousand referrals £159,000

5 Implications for the National Accounts

It might be tempting to take the discounted benefit of £1.204 mn per 1000 participants and simply add this to the output of the health service and the estimates of consumption of health services. But this is inappropriate for a number of reasons.

First, the national accounts show financial costs and benefits separated in the years in which they are incurred or realized. So in the current price accounts in the first year it is necessary to show an increase in spending of £300,000 per 1000 participants, or, with a participation ratio of 0.53, £159,000 per thousand referrals and not an unrealized benefit. The subsequent reductions in spending on treatment also need to be shown when they occur.

In volume terms, the gross output figures need to reflect the increase in QALYs in the year in which the DPP takes place. The reason for this is as follows. The changes in QALYs are seen as changes in the quality of medical services. But the services themselves are provided when the program runs and not when the benefits are realized and quality adjustments should therefore be made when the services are produced.

To derive the proportional effect of the program on the QALY output of the public sector, we largely follow the assumption of Cutler et al. (2022) that its output is measured by half the number of QALYs enjoyed by the population aged 65 and over. We estimate the total number of QALYs enjoyed by the population aged 65 and over using the self-reported health assessment data compiled by the Office for National Statistics. This shows, for the whole of the United Kingdom as well as for much smaller geographic units, period life expectancy and also period life expectancy in good health. Someone is categorized as being in good health if they report their health as being good, very good or excellent. Those who report their health as fair or poor are counted as being in poor health. The ONS focus on healthy life expectancy, effectively, and with no justification, putting a zero weight on time spent in poor health. Palmer et al. (2021), however, explore the impact of health state on a measure of life satisfaction, and suggest that time in poor health is valued at about 75% of time in good health. The ONS provides the relevant data at five-year intervals and we use these to estimate the total number of expected QALYs by sex and age. The maximum age shown is 90 and we assume that for people older than 90 the mortality rate is independent of age. This gives a total of 126.1 mn undiscounted QALYS accruing to the population aged 65 and over; with discounting the figure is 88.8mn. With each QALY valued at £60,000, the total value of QALYs for those aged 65 and over is £5,326 bn. More details of the QALY calculations are provided in online Appendix B and in the reproduction package.

We are now in a position to calculate the impact, looking first at the main-stream accounts and secondly at the satellite account calculation proposed by Cutler et al. (2022).

5.1 Data on Health Spending

The value of QALYs for those aged sixty-five and over provides a basis for gross output calculations, while to look at the impact on net output, we need to deduct the relevant discounted costs of medical treatment. Government expenditure on health in fiscal year 2018/19 amounted in total to £151,573 mn according to ONS data consistent with the national accounts. The data set Effects of Taxes and Benefits allocates this collective consumption to households on the basis of what is known about use of health services by different individuals. This shows, for 2018/9, expenditure, of £144.7bn in total and £53.6bn attributed to retired households. If we take the ratio of these, the implication is that 37% of total spending is undertaken on behalf of retired households, and applying this ratio to the national accounts figure for spending, we have £56.1bn of spending on retired people. Applying a multiplier of ten faut de mieux to derive discounted future costs gives discounted expenditure of £561bn.

We came to a figure of 88.8 mn discounted QALYs as the expected discounted number of QALYs accruing to those aged 65 and over. If each QALY is valued at £60,000 and half of the discounted QALYs accruing to the population aged 65 and over are attributed to health treatment, then the discounted QALY value of the medical system is £2,663bn, or 4.7 times the estimated costs giving a net figure of £2,102bn. It is clear that relatively small revisions to estimates of costs will not have a large impact on the net benefit, calculated as the value of discounted QALYs less discounted costs.

5.2 The Diabetes Prevention Programme in the Main-Stream National Accounts

We set out in Section 3.4.1 the way in which the program can be introduced into the national accounts as a new good whose cost falls from its reservation cost to its actual cost of production. The total benefit of the program stands at £120.4 mn per 100,000 referrals, giving the reservation cost, H r e s $$ {H}_{res} $$ per 100,000 referrals while the actual cost, H $$ H $$ , is £15.9mn, so the log of the ratio of the reservation cost to the actual cost, is
log H H r e s = l o g 15 . 9 120 . 4 = − 2 . 02 $$ \log \frac{H}{H_{res}}=\mathit{\log}\frac{15.9}{120.4}=-2.02 $$ (50)
The share in total expenditure of a program for 100,000 people is given as the cost of the program, £15.9mn, divided by total spending, £151,573mn, giving 1 × 1 0 − 4 $$ 1\times 1{0}^{-4} $$ . We also need to take account of the spending withdrawn from those who do not develop diabetes as a result. Here there is a complication. In calculating the reservation cost, we looked at the discounted sum of treatment saved. But the actual savings happen year by year and need to be reflected as they actually happen. With our assumed treatment cost of £1000 p.a., 2,700 cases avoided per 100,000 referred, and the simplifying assumption that this saving is made in every period including that when the program takes place, this is a saving of £2.7 mn as withdrawn treatment, or a saving of 0 . 18 × 1 0 − 4 $$ 0.18\times 1{0}^{-4} $$ of total health spending. This gives us a change in the log price index of
Δ l o g P 0 , 1 = − 2 . 02 × ( 0 . 18 + 1 ) × 1 0 − 4 2 = − 1 . 2 × 1 0 − 4 $$ \Delta \mathit{\log}{P}_{0,1}=\frac{-2.02\times \left(0.18+1\right)\times 1{0}^{-4}}{2}=-1.2\times 1{0}^{-4} $$ (51)
In the first year, then, we have an increase in the value of spending of 0 . 8 × 1 0 − 4 $$ 0.8\times 1{0}^{-4} $$ and a reduction in the price level of 1 . 2 × 1 0 − 4 $$ 1.2\times 1{0}^{-4} $$ .
The increase in the volume of output is therefore given by
Δ l o g Y 0 , 1 = l o g 151589 151573 − Δ l o g P 0 , 1 = 2 × 1 0 − 4 $$ \Delta \mathit{\log}{Y}_{0,1}=\mathit{\log}\frac{151589}{151573}-\Delta \mathit{\log}{P}_{0,1}=2\times 1{0}^{-4} $$ (52)
so in percentage terms there is an increase in output of 2 × 1 0 − 2 % $$ \times 1{0}^{-2}\% $$ .
In subsequent years, we have to take account of the reduction in nominal spending equaling, before any adjustment for mortality, £2.7mn. But we also need to allow for the fall to its new reservation cost of the withdrawn treatment. Applying Equation (43), the numerator in the first term is the saving in expenditure, £2.7 mn and the denominator is total spending. With log H / H r e s = − 2 . 02 $$ H/{H}_{res}=-2.02 $$ , we find
Δ l o g P t − 1 , t = − 0 . 18 × 1 0 − 4 2 × 2 . 02 = − 0 . 18 × 1 0 − 4 $$ \Delta \mathit{\log}{P}_{t-1,t}=-\frac{0.18\times 1{0}^{-4}}{2}\times 2.02=-0.18\times 1{0}^{-4} $$ (53)
The change in the log of the value of expenditure is similarly − 0 . 18 × 1 0 − 4 $$ -0.18\times 1{0}^{-4} $$ so, to a close degree of approximation, there is no change in the volume measure of output. This result is, of course, not generally true. It arises solely because log H / H r e s $$ H/{H}_{res} $$ is so close to − 2 $$ -2 $$ . More generally, given this, the saving in treatment costs in any year, has to be attributed to a price effect rather than a volume effect.

5.3 The Diabetes Prevention Programme in a Satellite Account

We follow Cutler et al. (2022) in assuming that the QALY output of health services is equal to half the number of discounted QALYs enjoyed by the population aged sixty-five and over. We are unable to offer any justification for this except that it makes it possible to compare Cutler's approach with one based on the main-stream national accounts. We start with the observation that the gain in discounted QALYs per 100,000 referrals is worth £81 mn (see Table 3). The proportionate increase in gross output is given by the ratio of this to the stock of medically-generated QALYs which was valued at £2663 bn. The increase in gross output per 100,000 referrals which would be recorded in a satellite account is therefore
81 2663000 = 3 × 1 0 − 3 % $$ \frac{81}{2663000}=3\times 1{0}^{-3}\% $$ (54)
In terms net of costs, the increase in output is calculated by adding back the saving in the treatment costs but deducting the cost of the program.
81 + 39 . 4 − 15 . 9 2102000 = 5 × 1 0 − 3 % $$ \frac{81+39.4-15.9}{2102000}=5\times 1{0}^{-3}\% $$ (55)

6 Conclusions

This article has shown how it possible to consider new and improved medical treatments including public health and other forms of preventative medicine when producing estimates of the consumption of health services in the national accounts. It should be noted that the approach adopted here, in contrast to Jones and Klenow (2016), does not involve adding directly an estimate of the value of life years generated by public health measures. Rather, following the proposal of Castelli et al. (2007) and the approach adopted by Cutler et al. (2022), it assumes that the increase in the number of QALYs associated with medical and public health services represents a change in the outcomes of these services.

These outcomes can be used to derive reservation costs so as to incorporate the effects of new treatments including preventative public health measures directly into the national accounts. When looking at a quality improvement, the approach is consistent with the System of National Accounts (2008) and Schreyer (2012) in adjusting measures of output to reflect the quality of the good or service provided. Alternatively, the increase in QALYs can be used directly in a health satellite account as suggested by Cutler et al. (2022). The impact of the Diabetes Prevention Programme on the output of medical services is small, although larger when incorporated into the main-stream national accounts than when put into a satellite account.

In concluding, it is important to note that the Diabetes Prevention Programme is a public health measure whose effects are particularly well defined. It is possible to identify who participates and to examine the impact on the participants. Many public health measures are more diffuse than this, with the implication that it is harder to assess their impact. But that does not provide a good reason for assuming implicitly that impact is very low. Imprecise estimates provide a better guide to outcomes than does ignoring the issue.

Conflicts of Interest

The author declares no conflicts of interest.

Endnotes

  • 1 There is a degree of international trade in medical services, but our focus is on government consumption of health services which are provided free or nearly free at the point of use, and we treat this as synonymous with the gross health service output of the public sector.
  • 2 QALYs form a key part of health service management in the United Kingdom; the National Institute for Clinical Excellence decides what treatments the National Health Service should make available, by comparing the QALY gain with the cost. As Wikepedia at https://en.wikipedia.org/wiki/Quality-adjusted_life_year shows, the approach remains controversial and there may be considerable uncertainty about both the price put on a year in excellent health and the effects of illness and treatment.
  • 3 I am grateful to Joe Grice for helpful conversations on this issue. The problem may be even more acute in the United Kingdom where the value of the output of the National Health Service is measured by the cost of production. Joe Grice has pointed out that the current income/expenditure account could be reconciled only by the use of a new form of factor income whose value is derived as a balancing variable.
  • 4 The time spent waiting for treatment might seem to be an additional quality factor, but if QALYs are counted from the time of diagnosis, then the impact on quality of life resulting from delays to treatment will be reflected in the QALY measure. With suitable discounting, the QALYs lost from delay will be deducted from the QALY gain resulting from treatment without delay.
  • 5 It is important to remember, however, that, despite the appeal of the Törnqvist index as a symmetric price index which is a good approximation to an exact measure when preferences are homothetic, medical treatment does not fit happily into conventional consumer demand theory. The choice is typically between receiving and not receiving a given treatment rather than deciding how much treatment to buy. It is hard to imagine a utility function which includes medical treatment and is also homothetic.
  • 6 Counting year 1 as the year of exposure and assuming exposure takes place at the start of the year.
  • 7 The issue of the treatment of nonexclusive programs like broad anti-smoking campaigns is a topic for future research.
  • 8 The simplifying assumption is made that death occurs at the end of each period.
  • 9 Reflecting the point that it is withdrawn from a fraction ρ − ρ p $$ \rho -{\rho}_p $$ of the population, as the analysis of Section 3.2.1 explains.
  • 10 For example, Reidy et al. (1998) found that three quarters of cases of glaucoma in a North London population aged sixty-five years and older, were not known to the relevant medical services. Glaucoma is a disease which untreated can lead to eventual blindness and whose early stages are largely asymptomatic. This discovery led to a policy of encouraging all old people in the United Kingdom to have their eyes examined free by high street opticians every two years.
  • 11 https://digital.nhs.uk/data-and-information/publications/statistical/health-survey-for-england/2021-part-2.
  • 12 All forms but T2D was much the most common.
  • 13 http://digital.nhs.uk/pubs/hse2018.
  • 14 http://healthsurvey.hscic.gov.uk/data-visualisation/data-visualisation/explore-the-trends/weight/adult/bmi.aspx.
  • 15 In the United Kingdom, a level of glycated hemoglobin (HbA1c) in the range 42–47 mmol/mol is regarded as prediabetic and was the main criterion for referring patients to the DPP. A value of 48 mmol/mol is regarded as diabetic while a level of 41 mmol/mol or lower is regarded as normal.
  • 16 https://www.diabetes.org.uk/about-us/about-the-charity/our-strategy/statistics/#::text=Our%20data%20shows%20that%204.4,by%20167%2C822%20from%202021%2D22.
  • 17 Chris Whitty has kindly pointed out that the course has benefits beyond those of delaying or preventing diabetes. It focuses on obesity and this can cause other medical problems in addition to those related to diabetes.
  • 18 This is a very cautious assumption. Taking the figures on diabetes incidence by age provided by Holden et al. (2013) and the impact on survival from Emerging Risk Factors Collaboration (2023) leads to the approximate calculation that the average diabetes patient loses nearly four years of life. The number of life years lost declines sharply with age at diagnosis. It is estimated at 15 for someone diagnosed at age 40 but at 1.4 years for someone diagnosed at age 80. These figures obviously reflect the fact that the 80-year old is much more subject to mortality risk from other causes than is the 40-year old.
  • 19 Valabhji et al. (2020) and Ravindrarajah et al. (2023).
  • 20 https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/healthandlifeexpectancies/datasets/healthstatelifeexpectancyallagesuk.
  • 21 https://www.ons.gov.uk/peoplepopulationandcommunity/populationandmigration/populationestimates/datasets/populationestimatesforukenglandandwalesscotlandandnorthernireland.
  • 22 https://www.ons.gov.uk/economy/grossdomesticproductgdp/datasets/breakdownofgeneralgovernmentfinalconsumptionexpenditure.

    • Data Availability Statement

    The data that support the findings of this study were derived from the following resources: “Office for National Statistics, ons.gov.uk” NOMIS, https://www.nomisweb.co.uk/default.asp. The files are available from the Office for National Statistics and NOMIS and are in the public domain. The data and calculations can be found at www.openicpsr.org at project “Weale Preventative Medicine Data and Programmes” as project 224841.

      The full text of this article hosted at iucr.org is unavailable due to technical difficulties.