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In recent years, increased attention has been given to guidelines for cost-effectiveness analysis of medical interventions, and some of these guidelines (such as NICE [1]) have become rather influential. In the paper, we present a model of retrieving and processing information to be used for the study of guidelines and their use. Our main result, which relies on a version of the theorem of Blackwell [2], shows that in cases where there are sufficiently many decisions to be made on the basis of the information obtained, there can be no other objective ranking of methods than the trivial one ranking more information is higher than less information. In our context, this means that guidelines may have administrative advantages but cannot be considered as a scientifically based approach to better decision making.

In the course of the last decades, the use of cost-effectiveness analysis as an aid to decision making in healthcare has been increasing steadily, so as to become a standard feature of medical research and medical decision making. Parallel to this, there has been a discussion of methods and foundations (see e.g. Johannesson and Weinstein [

In many cases, the scientific community has been invited to participate in drawing up guidelines, so that the cost-effectiveness analyses which are made in accordance with the guidelines are those that are “best” from a purely theoretical point of view. The question of whether such scientifically correct guidelines can at all be found seems not to have attracted much, if any, attention. However, a similar question has been asked long ago in another field, which however is related, namely that of finding the “correct” accounting standards, rules for how the accounts of a company should be drawn up and presented. As pointed out by Demski [

What is behind this seemingly paradoxical situation―that science cannot point to the right way of doing cost-effectiveness analysis―is a problem, which was considered by statistical information theory even earlier. Indeed, one of the main results of this theory, known as Blackwell’s theorem (Blackwell, [

It might be argued that this dependence of the guidelines on the decision maker is not a real problem; guidelines are indeed established by specified decision makers (public health care organizations, NICE, and others). However, in what follows we can actually sharpen the statement of Blackwell’s theorem slightly, so that it will apply even when the decision maker and her preferences are uniquely specified, as long as there are sufficiently many alternative actions to choose among―as will indeed be the case when the decision maker is in charge of a national health care system. So, even in this case, there is no theoretical foundation of guidelines considered as “golden standard” or best practice. Guidelines may be convenient or useful for many other purposes, but alas, they cannot be the last of science. This result adds another dimension to the skepticism towards the increased emphasis on detailed guidelines, as expressed e.g. by Birch and Gafni [

The paper is structured as follows: In Section 2, we introduce the statistical information theory and explain the relation to cost-effectiveness analysis. This section ends with a formulation and proof of the version of Blackwell’s theorem, which is tailored to our purpose. In Section 3, we connect the abstract result on information methods to cost-effectiveness analysis, and we show why guidelines cannot be scientifically well-founded here, although it may well be so in purely medical decision making. We close the paper with some comments in Section 4.

In the present section, we briefly introduce the background for our model, which is the approach to the theory of information introduced by Marschak, Blackwell, and others, see e.g. Marschak and Miyasawa [

We consider a situation where a decision maker―which in our application may be a health care organization deciding upon the best way of treating the patients under their responsibility―has to make a decision which is subject to some uncertainty. This uncertainty will be modeled in a very simple way, since we assume that there is a finite set of uncertain states,

We shall assume that the decision maker has initial beliefs about the likelihood of each of the underlying states

over all decisions

In our discussion so far, there has been no mentioning of information; decisions were based on assessments of probabilities but not on any observation; to allow for this―and thereby formally introducing “evidence-based medicine” into the model, we should add the option of collecting and processing of information before the decision is made, which is what cost-effectiveness analysis is about. In particular, following the recent guidelines of NICE [

In our simplified formal world, an information method is a pair

set if signals, and

preted as the probability that signal

Given any observed signal

where

babilities over states of nature, conditional on the observed signal

over all

that is the difference between the ex ante expected utility with and without the information method. We call

The value of information, as derived above, depended on the utility function U of the decision maker. Consequently, the choice of information method, if indeed such a choice is open to the decision maker, will in its turn depend on the utility function. In the case we have in mind, where an information method is a particular way of collecting and presenting data on different medical interventions, this means that the method for performing these operations should be chosen in accordance with the desires and goals of the decision maker. Simple and acceptable as this sounds, it carries a controversial message, namely that it is in general impossible to prescribe a single such method, independent of the decision maker who is going to use the results. In other word, ranking different methods of performing cost-effectiveness analysis seems not in general possible without recourse to a concrete decision maker, so that guidelines, which are applicable to all users cannot be constructed in a scientific way. In the following we give the precise formulation of this result.

For this, we need the notion that one information method is more informative that another. Let

signal

An equivalent formulation of this condition is that there is an

where

Theorem 1. Let

(i)

(ii)

Proof: (ii)

By separation of convex sets, there must then be

Now we use the assumption on

since

Assessing the value of the information method

It follows that

(i)

Therefore, if

where we have used that

and summing over

and it follows that

In the previous section, we established a version of Blackwell’s theorem tailored to our problem, dealing with cost-effectiveness analysis in general and rules for conducting such analyses in particular. In the present section, we draw the lines from the abstract world of information systems to the more relevant context of guidelines for cost-effectiveness analysis―as well as to guidelines for other aspects of medical decision-making.

For this, we take a closer look on the conditions on

For this, we consider the environment in which a cost-effectiveness analysis is carried out. We outline briefly its theoretical background (or rather, one possible theoretical background, as there may be several, cf. Brouwer and Koopmanschap [

In the standard approach (Hansen, Hougaard, Keiding, Østerdal, [

an approach often termed as “welfarist”. In our present setup, we do not insist that allocations are ranked exactly in this way, but only that the decisions in society are made in accordance with a utility function of the type

To make this setup fit with our model of the previous section, we assume that the changes in allocation are subject to random displacements, so that

Theorem 2. Let A be a set of interventions of the form

(i) A allows for all possible money compensations of health effects: For each intervention

(ii) for each

If the cost-effectiveness methodology

Proof: The theorem is basically a reformulation of Theorem 1 and all that is needed is to show that A contains interventions such that for each vector

But this follows easily from the assumptions (i) and (ii), which together show that there is an intervention, constructed from the original one combined with suitable commodity displacements in each state, such that the final utility level in each state corresponds to the vector

It may be noticed that our assumptions in Theorem 2 are stronger than what is really needed; indeed, we need not compensate everybody, what matters is only that some compensations can be made which make up for any loss and gain that the decision maker would experience from the uncompensated intervention. Also, it suffices to consider very small displacements since what mattered in Theorem 1 was not the absolute values of the utilities in each state but only their relative values.

The implications for practice of the results are that guidelines for cost-effectiveness are of dubious value., at least when considered as a source of information. Given that the assumptions of Theorem 2 are reasonably weak and seem satisfied in practical situations where cost-effectiveness analysis is performed, the conclusion is that there can be no “best” way of setting up such an analysis. The reference case approach, specifying that observations on medical and other outcomes of an intervention should be carried out according to a standardized scheme, may have administrative merits but it has no scientific basis. The only rule that can be stated is that more detailed observation is better than less detailed information, which indeed is trivial.

Why, then, are guidelines so widespread and estimated? Again, Theorem 2 points to an answer: For purely medical interventions, the setup differs considerably from that of cost-effectiveness analysis, since there is no economic component, and obviously monetary transfers are irrelevant for the medical outcome. In such cases, information methods may indeed by ranked to an extent which permits a choice of a best one, singled out as a reference case.

What makes perfect sense in one context may however not necessarily work in another. Guidelines may be useful in medical practice and misleading in economic practice. The arguments of the present paper should indicate why this may be the case.

Hans Keiding, (2016) On the Foundations of Guidelines for Health Economic Assessment. Open Journal of Social Sciences,04,20-26. doi: 10.4236/jss.2016.45004