Cost benefit analysis - project description

A cost-benefit analysis of different treatment programs for drug addicts: Theory and application

Every year billions of dollars are spent on different programs for addicts. In the US, for instance, $1.3 billion (1987 dollars) was spent on treating drug addicts in the US (French, 1995: 113) and in Norway it has been estimated that about 1 billion NOK a year was spent on treatment of alcohol addicts in the late 1980's (Waal, 1996: 10). At the same time very little empirical research has been conducted on the relative efficiency of the many different treatment programs (cost-benefit analyses). Moreover, after a review of some of the few studies available, a leading researcher in the field concludes that "no study" has followed the recommended set of important methodological guidelines - such as tracking patients over time to avoid biased measures of effectiveness due to readmission or examined the possibility that doing program A after program B produces different results than the reverse option (French, 1995: 131, 120). In short, there is a gap between our current knowledge and the knowledge we should have to justify the allocation of large sums of money. The purpose of the dissertation is to make a contribution towards closing this gap.

The starting point of the dissertation is the following simple question: "From a cost-benefit perspective, which treatment for treating drug addicts is the best?" This main question, in turn, leads to a large number of sub-questions: Is cost-benefit analysis the correct way of deciding the matter? How do you define addiction? What should count as costs and benefits, in what units, and are these units interpersonally comparable (so they can be aggregated)? Is it enough to collect data about the different treatment programs and do the appropriate statistical calculations (the black-box approach), or is it necessary to discuss theories about drug-addiction (theory-approach)? Indeed, what is meant by "best?"

It is not the purpose of the dissertation to discuss all the questions above in detail. The dissertation is part of a larger project at the National Institute for Alcohol and Drug Research (SIFA) financed in part by the Norwegian Research Council and different questions are allocated to different researchers in the team. In the proposal below I have therefore indicated which themes which I want to emphasise as opposed to those questions on which I will be strongly guided (although not uncritically) by the research of others.

Some of the questions on the list above can be labelled "conceptual preliminaries". It is, for instance, not obvious that all questions of public policy money should be guided by cost-benefit analysis. As an illustration ask yourself which group of victims you should help after a plane-crash (The example is inspired by Elster, 1992: 92). Should you help those who are most wounded (but likely to die anyway), those who have moderate injuries (who have a greater change of surviving if given treatment) or those with non-lethal but painful injuries which are easily curable? The utilitarian answer is simply to focus on those patients that will maximize social welfare (people in the second category?). Against this a pure "rights" or norm based ethic might tell us to first attend to those who are worst off. It is not obvious that the pure utilitarian solution is the "best." The same kind of logic also applies to drug treatment. Even if cost-benefit considerations tell us that it would be "best" to leave the heavy users to themselves without trying to help, this need not be the policy that is "best" if we include ethical considerations.

A second conceptual preliminary concerns definitions and classifications. The problem of defining addiction may be more acute when it comes to gambling and other forms of claimed addictions (for an overview of possible addictions, see Ainslie, 1992: 3-4), but even with drug addiction there are ambiguities. Is a person who occasionally has used "mild" drugs during the past four months a drug addict? The second problem - that of classifying different treatments - is one of those areas in which I will rely on previous research. Based on this research the project has identified five major different treatments that need to be distinguished: a) traditional inpatient treatment (24 hours); b) hierarchical therapeutic units; c) collectives; d) psychiatric youth teams; e) methadone treatment. This can be collapsed to a distinction between inpatient treatment (a, b, c) and outpatient treatment (d, e) and one of the aims of the research is to examine whether the rather expensive inpatient treatment is better than the less expensive outpatient treatment. Some previous research - for instance on alcohol abuse - suggests that the net benefit from inpatient care is not large enough to justify the heavy emphasis this type of treatment has received compared to outpatient treatment (French, 1995: 121). Whether this is the case in Norway and in the context of drug addicts is an important research question to be answered.

The third, and perhaps most crucial conceptual preliminary, is an identification of the costs and benefits. This depends among other things on the type of analysis one wants to conduct: Cost-benefit, cost effectiveness and cost-utility analysis (see Nygaard, 1996). This is an area in which much theoretical work has been done, but fewer studies actually follow up to do applied work. Regardless of the type of analysis, there are some obvious costs and benefits associated with the different treatments (and non-treatment). The direct costs include the salaries to the staff involved and the fixed cost of buildings and so on. The benefits of treatment (to the extent it works) include improved ability to participate in work, reduced health expenses, and reduced outlays to prison incarceration (for a full list of possible costs and benefits, see French, 1992: 115)

Even if we ignore the practical problems of identifying and estimating the size of the costs and benefits, there are many difficulties at this stage. One example is the problem of including non-monetary costs and benefits. For instance, how should we include the utility of a cured addict as a benefit? This is difficult to measure in monetary terms (willingness to pay?) and as economists we might even believe that removing drug from an addict reduces her utility; Since she used it voluntarily her utility must be higher with drugs than without (revealed preference theory). Alternatively one might invoke some theory of a multiple self or hyperbolic time-discounting to explain why a person does something he "really" does not want.

Another problem related to the measurement of costs is that we should use opportunity costs, not monetary outlays. Thus, the true cost of the staff is not their salary, but the best use we could make of the staff if they were not occupied treating drug addicts. Usually it is much more difficult to find the true opportunity cost than the monetary outlays.

A third problem is the tendency to ignore the difference between marginal costs/benefits and overall costs/benefits. When faced with an institution that simply cannot be closed for a few years, then it is irrelevant in the short run that the overall net benefits in this program is lower than in an alternative treatment program. The relevant variable in the short run is marginal net benefit: Can we get a better result by moving some resources from one program to another. To give an example: Institution A might have unavoidable high fixed cost due to a housing-contract. This implies that A has a low overall net benefit compared to another institution (B). It does not, however, imply, that it is better to give an additional 100 000 to B rather than A. It is perfectly possible that institution A has a higher marginal net benefit at the same time it has a lower overall net benefit compared to institution B. Although this reasoning is rather obvious to economists who have a rich appreciation of the different cost concepts (fixed, variable, opportunity, accounting), it has not been obvious to the professions that have dominated research on addiction so far (medics, psychologists, sociologists). In sum, more applied research on the relevant marginal net benefits in contrast to the more common overall net benefits, can produce valuable knowledge for policy makers.

Important as they may be, the conceptual preliminaries mentioned above will not be the main focus of the thesis. Some of the questions are well covered by other research (different cost-benefit frameworks and variables), some are fixed parameters outside my control (like the fivefold division of treatments in the larger project) and some are simply too peripheral to be the main focus, although they do need to be discussed. Instead the main focus will be on the following two issues: A critical analysis of original survey data and a discussion of how to model addiction.

As mentioned the dissertation is part of a larger project that has already started. One of the main elements of this project is a large survey of 400 drug addicts in different treatment programs. The participant will be interviewed every year for four or five years. The respondents are asked questions about the treatment they receive, the severity of the addiction (measured by the Europ-ASI - Addiction Severity Index), psychopathological profile (using standardised indexes such as such as MIO, MCMI, BCI and BDI) and important life events like marriage, religious conversion, pregnancy and childbirth.

One of the main dangers when working with surveys of this kind, is that of drawing policy conclusions based on spurious correlation. For instance researchers in the 1940s found a strong correlation between cirrhosis of the liver and vitamin deficiency (the example is from Skog, 1992: 49). Based on this they claimed that liver cirrhosis was not caused by alcohol (since after controlling for vitamin deficiency alcohol intake explained very little). The conclusion also implied that taking vitamins (without reducing alcohol intake) would prevent cirrhosis. Today we know that their conclusion was wrong and based on spurious correlation. Because of the importance of this phenomenon, I propose to make the problem of how correlation can lead to wrong conclusions a major focus in this section. This necessitates, first, a conceptual discussion about the difference between causation and correlation. Second, for every important correlation found in the survey it is necessary to test and examine whether it is spurious. Third, the reasons for spurious correlation found in the second part should be systematised with the aim of creating a more general theory of the reasons why reliance on correlation leads to wrong results (and how it can be avoided).

On the conceptual issue, the starting point is Hume's theory of causation as "constant conjunction" (The following discussion draws upon Beauchamp & Rosenberg [1981], Elster [1989, ch. 1] and Skog [1992]). Hume knew, however, that this was not enough since a third variable can make two variables appear together without being causally related. This led Hume to propose two criteria for separating correlation and causation. The first is inductive support; that is whether the relationship holds under a great variety of circumstances. Second there is predictive confidence, which includes the degree of theoretical support behind the correlation (knowing why there is a correlation as opposed to simply knowing that there is a correlation makes us more confident that the correlation is not spurious).

One problem for Hume could be the following (based on information in Dawkins 1995): In 1973 Karl von Frish's won a Nobel prize for his discovery that the complex bee-dance communicated where the bees could find food. Against this Adrian Wenner argued that it was a mistake to believe that the dance was a form of communication. He did not deny than the dance showed both the direction and the distance to the food source, but he denied that the other bees were able to understand this. The last - and final - participant in this debate was James L. Gould who designed an experiment that proved that the dance in fact transmitted information to the other bees (by blinding the dancing bee and using a light bulb to fake the sun's position). To make a long story short (for more, see Melberg, 1997), the flight path of the bees after these experiments showed that the dance transmitted information. How many examples of this do we need to generalise? Although we do not have enough examples to claim that there is a "reliable constant conjunction" a few (even only one?) experiment of this type is enough to convince working scientist of the "communication hypothesis" as opposed to the "no communication hypothesis." (Melberg, 1999a and Skog, 1992: 39-40, provides additional examples of "generalisations based on one example")

Where does this leave us when it comes to distinguishing between causation and correlation? The main conclusion is simply that more research is needed. The bee-dance example may lead us to a Bayesian theory of belief formation, in which the "degree of surprise" is given importance when new information makes us update our beliefs. Whether it is possible (and desirable) to use Bayesian theory to form beliefs about causation remains to be proved, but it is one of the issues I intend to explore.

Consider the second and third point mentioned above - using the survey to develop a list if possible causes of spurious correlation and then using this to create a more systematic theory. As a preliminary categorisation, I have listed 18 reasons why an emphasis on correlation may lead to wrong conclusions (see Melberg, 1996a). These causes, in turn, can be categorised in the following four groups:

(8. wrong direction inferred, 9. ignored joint relationship, 10. wrong kind of causation, 11. self-confirming correlation, 12. confusion between short run and long run effects)

(13. few observations, 14. not enough variation, 15. too much noise, 16. flawed assumptions about underlying distribution, 17. measurement errors, 18. ignored non-quantifiable variables)

This is very much a draft and further work may well demonstrate more useful categorisations and different examples. It would require more space than I have to list examples of all 18 problems, but some of those which are most relevant to the current project are listed below (see the already mentioned paper - Melberg 1996a - for examples of all).

Imagine that the survey shows that outpatient treatment is generally associated with better result than inpatient care. It could be very wrong to conclude from this that inpatient treatment should be closed and all addicts assigned to outpatient care. The reason the conclusion is most likely wrong is that the "heavy" addicts may be assigned to inpatient care, while the "light" addicts are assigned to outpatient treatment. Given this sorting mechanism there is no wonder why outpatient treatment performs better; they receive the easiest cases to treat. In this case the reason behind "strong correlation no causation" is obvious, but in other cases it is much less obvious and it is an important task to try to sort the spurious from the more reliable correlation.

Even less obvious are the mistakes we make by assuming that no correlation means no causation. Take the following example (from Dawes, 1994: 59): Research has shown (weakly) that the compatibility of the therapist's and the client's views on the causes of alcoholism is important for the effect of therapeutic treatment. If both the client and the therapist believe alcoholism is caused by genetic disposition (the disease model) or if they both believe it is a "bad habit" (no genetic disposition), there is a greater chance of success than if they have different views. Schematically we have the following (Diagram 1):

Diagram 1: Compatibility of therapists and clients views and outcome of treatment

If we assigning a random sample of clients to a random set of therapists, we might end up with no correlation between treatment and successful outcome. Still, it would be wrong to conclude from this that treatment is a waste with no effect. In fact, there are strong but opposing causal forces at work. The positive effect of treatment when the views are compatible is balanced by a negative causal effect when the views are incompatible. Ignoring this produces the wrong conclusion, while taking it into account can lead to a dramatically improved result - that we begin to assign clients to the therapist that is most likely to produce success with that particular client. When it comes to drug addiction, Edle Ravndal (1986) has described some potential reasons why the same treatment may have different effects on different clients - such as the age and gender of the client, whether there is a record of criminal activity, the degree of personality disorders and other characteristics. In the dissertation I intend to follow up on these suggestions and test empirically whether the aggregate "no correlation" really hides "strong causation" at a lower level of aggregation. One simple way of doing this is to perform multiple regression analysis of the characteristics against an index that measures success in treatment, but more complex analysis is also necessary (by subdividing the sample based on the variables we believe are important).

One of the aims of the survey, as stated in the original project description, is to reveal whether the different combinations of treatment produce significantly different results. This aim may run into the last problem mentioned on my list - data problems. Briefly, when we have five different treatments there are at least 120 different possible combinations.[1] With a set of 400 respondents and 120 possible combinations there is not enough data to tell whether the different combinations produce significantly different results. In practice, however, one might expect that not all combinations are equally likely, and this may make it possible to test at least some different combinations. On the other hand (as explained in the footnote) 120 is really a minimum of theoretical possibilities and if we include "no treatment" as a possible option at all times, then the number of possible combinations increase to 720. This leads to two conclusions - one challenge and one warning. The challenge is to devise statistical methods to reduce the problem - for instance, if we can assume that the "BC" in "ABC" can be compared to "BC" in DBC" we will increase the number of observations. The warning (both to the politicians and academics that want these results) is not to expect too many strong results to emerge from this kind of analysis.

It is well known that a focus on correlation can lead to wrong conclusions. Indeed, it is about 75 years since Yule published the first article dealing with spurious correlation. The topic was then "lost" for a period of time, but recent development in econometrics have renewed the interest in the topic of how we should proceed to avoid spurious correlation. For instance, David Hendry's strong criticism of Milton Friedmans theory of inflation - which Hendry claims is based on a spurious correlation - has led to the development of a set of systematic methodological recommendations to avoid spurious correlation (for more on Hendry's specific recommendations, see Gilbert, 1986). Another examples of the renewed interest, is McCloskey and Ziliak (1996) article in which they warn against confusing statistically significant correlation with practically significant correlation. Yet, although it has long been known that correlation and causation are different, this general knowledge is often not matched by specific effort at the applied level of testing whether the correlation is spurious or not. Moreover, this failure is likely to lead to bad policy recommendations. That is why I will make it a major focus in the dissertation, both when it comes to applied and theoretical work. Hopefully this can lead to some novel techniques to reveal spurious correlation as well as improved knowledge about the problem of spurious correlation in drug research (For an overview of existing techniques to reveal spurious correlation in research on addiction, see Skog, 1988).

As mentioned above, there are two approaches to cost-benefit analysis. The first was labelled "the black box" approach i.e. one simply tries to measure the costs and benefits without discussing the theory of addiction. The section above then described some of the weaknesses of this approach and this leads to the second alternative - that of basing your cost-benefit analysis and policy recommendations on a model of addiction and treatment (the "theory approach"). The reason for focusing on this approach is not that the first approach "fails" and that this leaves us with the second (as if theoretical and empirical work is incompatible). Rather the argument is that knowing why a correlation exists reduces the risk of accepting a spurious correlation (see Melberg, 1996b). This was already emphasised by Hume (in his criterion of confidence to distinguish between correlation and causation), and it was emphasised by Hendry who, as one of his methodological demands, require that variables we included in the model must be "theory consistent" i.e. we do not add variables when we have no theoretical reason to believe they are relevant. Thus, one reason why we want to model addiction is to make sure that our correlations are not spurious.

Given that we want to model drug addiction, how should we do so? There are several models available (see Godfrey [1989] for a review of economic models of addiction), but it is possible to categorise these models along two key dimensions. The first is whether they model addiction as the outcome of rational choice or not. This, in turn, has important policy consequences - if addiction is viewed as rational then the "treatment" is simply to change the incentive system facing the agent. The second distinction is whether the model emphasises interaction as opposed to assuming a "representative agent." There are, of course, other relevant distinctions (such as models based on brain chemistry vs. those who view addiction as a "psychological problem"), but this is outside my competence.

The classic argument in favour of the rational addict model, is presented by Gary Becker and Kevin Murphy (1988). In short, people decide to use drugs when the expected utility of doing so is larger than the expected utility of not doing so (the possibility of addiction is included in the calculation). The original project description presents a model of addiction that comes close to this view (SIFA, 1997). In that paper addicts are viewed as acting on a Lancaster-type consumption function with preferences for two types of characteristics: basic needs (food, housing) and experiences (whatever produces self-esteem, feeling of community). The "experiences" can be produced by taking drugs, but it can also be produced by friends, family and important life events. In this perspective the demand for treatment need not be motivated by a desire to really quit, but rather to satisfy basic needs for a period of time (since they receive free housing and food).

Becker's theory of rational addiction is useful as a starting point, but there are also important weaknesses in his theory. One could, for instance, attack his definition of rationality. As I have discussed elsewhere (Melberg 1998, 1999b, ch. 2) rationality demands not only that the action be optimal for a given set of beliefs. It also demands that the beliefs must be optimal for the given set of information AND that the amount of information must be optimal. Hence, although one might agree with Becker that taking drugs may be rational for some people given their beliefs (e.g. if she believes she is strong enough to quit whenever she wants), but one might question whether these beliefs are optimal given the evidence and even if this is the case one could ask whether the amount of information used to form the belief was optimal. Unless all three conditions are satisfied it is not correct to label addiction "rational" in any substantive sense.

Even if we ignore the conceptual problems related to Becker's definition of rationality, Elster has presented one key criticism that goes to the heart of the model (see Elster 1997 and 1999: 160-164). Becker argues that non-monetary sources of utility, such as guilt and shame, should be included when agents calculate the expected utility of various actions. This is fairly standard reasoning for those who include "psychic" utilities. In the words of Elster (1999: 160): "Among economists, the most common way of modelling the interaction between emotions and interests is to view the former as psychic costs or benefits that enter into the utility function on par with satisfactions derived from material rewards." Elster believes this is fundamentally wrong and presents the following example to support his argument: "If guilt were nothing but an anticipated or experienced cost, an agent whose guilt deters him from stealing or retaining the book should be willing to buy a guilt-erasing pill if it were sufficiently cheap. I submit that no person capable of being deterred by guilt would buy the pill. … For him, taking the pill in order to escape guilt and be able to steal the book would be as morally bad as just stealing it … A person willing to take the guilt-erasing pill does not need it." (Elster, 1999: 161, emphasis in the original).

Where does this argument lead us with respect to how we should model addiction? According to Elster (1999: 161) we "need a model that can account for the trade-off between guilt and interest and yet does not imply that a reluctant agent would buy the guilt-erasing pill. I conjecture that the model would involve some kind of nonintentional psychic causality rather than deliberate choice." As an example of such causality, Elster mentions how the psychic mechanism of cognitive dissonance can be introduced to explain asymmetries that rational choice theory cannot deal with.

I do not want to conclude at this early stage that Elster is correct and Becker is wrong. I simply want to indicate that this is one of the issues where more research is needed. Elster's argument must be scrutinised closer and in any case his model can be viewed as an extension rather than a radical new approach. Both Becker's and Elster's starting point is that agents are mainly rational. The difference is that Elster also wants to include non-intentional causal forces in the model to capture psychic costs/benefits, while Becker wants to model this in the usual cost-benefit framework. And, even if Elster's approach is best, there is still the challenge of formalising his verbal arguments.

Since the assumption of a representative agent usually makes it much easier to handle models mathematically, this has traditionally been preferred above explicit modelling of interaction (see Kirman [1992] for more on this and a harsh attach on the representative agent assumption). Although this may work fine in some situations, there are some phenomena which seems to require the incorporation of interaction. An early example of this recognition is Schelling's (1978: 147-155) model of the housing market. Another example is S. Bikhchandani, D. Hirschleifer and I. Welch's (1998) theory of fashion, fads and customs. Until recently, however, addiction had not been modelled using this approach, although important aspects of addiction clearly depend on social interaction. An agent's decision to use drugs may be heavily influenced by whether his friends use drugs (if there is a desire to conform) and the social stigma attached to the drug (which in turn may depend on how many people use the drug).

The first formal model that captured some of the social interaction effects in research on addiction, was created by Karl Ove Moene (1999) who explicitly says that he "focuses on long-range equilibria of social interaction within a group of persons and neglects additive dynamics within each person separately" (Moene, 1999: 30). The key feature of the model is that one person's utility depends on what the other people do; all other things constant an agent has higher utility if she does what the others do (drink when they drink; abstain when they abstain) i.e. there is a desire to conform. The agent's utility also depends on his pain or pleasure from the drug itself and the size of this pleasure/pain differs from agent to agent. Based on this Moene shows that the model most likely has multiple self-enforcing equilibria, that there is hysterese (the history of drug addiction matters to explain the current number of addicts) and that there may be a tendency for drug addiction to go easier up than down.

What are the implications of including interaction effects in our models for conclusions about treatment? One conclusion is that the aggregate effects of small changes may be difficult to predict. If the system is non-linear (exhibits hysterese) and there are thresholds beyond which the system switches to a new equilibrium, then small changes can have large effects (and large changes may not have any effect - depending on the staring point). It becomes almost impossible to estimate and predict the aggregate costs and benefits of treatment based on (linear) correlation alone (see Skog, 1992: 54). There is, however, a large step from a pure theoretic and stylised model to a policy conclusion like this. The model has not been tested or quantified (although it is compatible with some basic facts - such as changes in consumption patterns for no apparent reason except "fads"). This implies that more work should be done on the formal modelling of these systems and whether they are compatible with the central historical facts about addiction.

Exactly how should one go about modelling systems in which agents interact? As mentioned it is often difficult to model complex interaction in a mathematical model. One alternative that could be explored in a dissertation is computer simulations (see Skog, 1980, for a review of computer simulations in the field of addiction). This, in turn may provide valuable lessons for modelling beyond the field of addiction. By using computer programs we can specify the characteristics of the agent, the nature of the environment, rules for interaction and watch as different scenarios unfold. This approach allows for a richer characterisation of the agent (e.g. allowing agents to be influenced by mechanisms like wishful thinking or cognitive dissonance). In short, computer modelling allows the agent in our models to be more like real individuals and it enables us to capture more realistic aggregation procedures than merely assuming that one agent is representative for all. One area in which this approach could be useful (beyond addiction), is to explain economic fluctuations which seems to involve important interaction effects as well as not perfectly rational agents. This does not imply that I believe computer modelling necessarily will succeed or that it will "solve all our problems." It does mean, however, that I believe the approach deserves to be investigated further in a dissertation dealing with addiction.

To create the dissertation I intend to write several articles that can be published separately, but at the same time be united in a coherent thesis. The planned list of articles is: 1. The limitations of cost-benefit analysis; 2. Reasons for spurious correlation and how to avoid them; 3. Modelling drug addiction using computer simulations; 4. Addiction - rational or not, and is that the question? This is, of course, a preliminary plan and if future research throws up more interesting questions or reveals that some of the topics are not very fruitful (this applies particularly to article 3) the plans will be changed.

The work on the dissertation will start in January, year 2000. Whether the dissertation will take three or four years depends on the workload imposed by SIFA. I intend to spend at least one term abroad - more specifically at York University which has a department that is engaged with a project very similar to that at SIFA. During my stay there I also intend to take a course in health economics. Finally, I intend to continue my education is statistics by taking courses at the University of Oslo.

Research on addiction poses important questions. From a policy perspective it is important to know more in order to determine what kind of treatments the state should provide. From an academic perspective it poses important statistical challenges - such as how to avoid conclusions based on spurious correlation. Finally it raises important questions of modelling - about how we can capture complex social interaction and less than perfectly rational agents and still retain the discipline and precision of rigorous modelling. I am aware that to some extent there is a conflict between the need for policy recommendations and a focus on the problem of spurious correlation conflict (Why focus on the problems, we want answers!). When faced with this conflict it is important to be willing to admit that "I do not know" is sometimes the scientifically correct answer. The main purpose is not to produce policy relevant conclusion, but to produce conclusions that are scientifically valid.

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[1] This number is arrived at by using the rule of permuations . There are two reasons why this is a minimum. First, it assumes that no client receives more than five treatements (among the five possible) during our period. Second, it does not adjust for the possibility that doing program A once is different from doing program A at all five times (it assumes that all clients are in treatment at all five times).