Interest in health economics has increased considerably over the last several decades 13, motivated by Arrow's pioneering 1963 work 14, which provided economists with a novel framework for analyzing health and healthcare. Greater availability of data and the growing policy process in health care provision have since stimulated a great deal of research. Indeed, an economic approach to health matters has great policy relevance 15, particularly in light of the exponential recent growth in expenditure. In 2003, health costs in Switzerland amounted to 49.9 billion Swiss francs, or 11.5% of the gross domestic product 16. In 1985, health's share of GDP was just 7.7% 17. The U.S., the world's largest consumer of health care, has also experienced intensive growth. Expenditures grew from 5.3% of the GDP in 1960 to 8.9% in 1980, 12.2% in 1990 and 14.1% in 2001 18. Unfortunately, early data on the costs of mental health care in Switzerland are limited. There is, however, reason to believe that mental health costs are increasing. In 2004, psychotherapy costs were roughly 500 million Swiss francs 19, while inpatient psychiatric treatment totaled 1.8 billion 20.

In 1972, Grossman, inspired by Becker's Human Capital Theory 21, formulated a model in which expenditure in health care were treated as an investment in human capital, similar to education 12. Grossman's work implied that a rational individual's investment in current health promotion yields returns to health and longevity in later periods. The individual may optimize his personal lifespan by adjusting for changes in the discount rate 22. There are some crucial differences from traditional demand theory in Grossman's model, because of the particular form of health-related products. Folland, Goodman, & Stano 18 point out that:

• Consumers are not interested in medical care, but rather in health. They request and consume goods that produce health.

• The purchase of health-related goods from the market is not passive. Consumers produce health by investing time in activities that maintain or improve their health status.

• Health, like capital goods, does not depreciate immediately.

• Health is both a consumption and investment good, and investing in health capital leads to future savings. For example, investing in health-promoting activities today may result in greater number of available days of non-illness.

This final point is fundamental to our analysis, because it introduces the concept of investment in health as a way of realizing future economic savings from better mental health status or, correspondingly, to fewer illness days. Hence, the consultation of an online screening tool is interpreted as an investment in human capital.

In a cost-benefit analysis, an individual compares an investment outlay today with the present value of an expected future return from the investment. The investment outlay amounts to the total costs of engaging in the activity that is assumed to subsequently generate a return. The present value (PV) results from:

P V = F u t u r e A m o u n t ( 1 + D i s c o u n t R a t e ) t , MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemiuaaLaemOvayLaeyypa0tcfa4aaSaaaeaacqWGgbGrcqWG1bqDcqWG0baDcqWG1bqDcqWGYbGCcqWGLbqzcqWGGaaicqWGbbqqcqWGTbqBcqWGVbWBcqWG1bqDcqWGUbGBcqWG0baDaeaacqGGOaakcqaIXaqmcqGHRaWkcqWGGaaicqWGebarcqWGPbqAcqWGZbWCcqWGJbWycqWGVbWBcqWG1bqDcqWGUbGBcqWG0baDcqWGGaaicqWGsbGucqWGHbqycqWG0baDcqWGLbqzcqGGPaqkdaahaaqabeaacqWG0baDaaaaaOGaeiilaWcaaa@58E1@

where the denominator discounts the future return in period t to account the time value of money. The cost-benefit comparison is achieved by subtracting the amount currently invested from the calculated present value of future returns. The result is the net present value (i.e. NPV = PV – current investment). If the net present value is greater than zero, then the investment should be undertaken.

The investment in online psychological screening includes two basic types of costs: direct and indirect 23. In our model, two types of direct costs are considered. Initial direct costs (IDC) refer to time costs associated with self-administration of the evaluation. Therapy costs represent the monetary value of mental health intervention and treatment for individuals who seek counseling after assessment. Indirect costs in our model encompass employment losses (e.g., lost work days and decreased productivity) and foregone earnings 24.

Economic benefits of an online screening tool will accrue via early detection of psychological disorder. Early detection increases the likelihood of prompt recovery from mental illness, and decreases its rate of chronicity and disablement in the long term. It also reduces the duration of treatment, due to prompt entry into therapy, when mental illness is still at an early stage. The expected benefits may thus be seen as the financial savings that occur from shortening the duration of costly psychotherapeutic care and moderating adverse labor market effects.

Consider a person A, who has experienced a traumatic event such as the Indian Ocean Tsunami Earthquake on December 26, 2004, and develops psychological symptoms associated with the experience. An online self-evaluation test is available, and the individual can choose whether to take the evaluation or not. We assume the following scenarios:

Scenario 1 – Person A takes the test and has the following cost structure:

IDC₀(A₁) > 0: Initial Direct Costs of person A in period t = 0

STC₁(A₁) > 0: Shot-term Therapy Costs of person A in period t = 1

Scenario 2 – Person A does not take the test and has the following cost structure:

IDC₀(A₂) = 0

LTC₁(A₂) > 0: Long-term Therapy Costs of person A in period t = 1

We further assume that:

(i) There are only two periods. In period t = 0, it is possible to take the test and in t = 1, therapy occurs.

(ii) In order to simplify the model, we chose a one-period therapy. The therapy begun at an early stage of psychological disease is shorter in duration than one entered at a later stage. Consequently, STC₁(A₁) <LTC₁(A₂).

(iii) The indirect costs of performing the test can only be greater than zero if we consider economic opportunity costs (e.g., a loss of productivity at work).

(iv) Individuals make their decisions with perfect information. This assumption implies that every individual knows about the existence of an online screening test and that individuals have equal access to the online screening test.

The scenarios may now be compared. First, we deduce the present value (PV) of costs under the two scenarios. The value of costs under Scenario 1, PV(S₁) includes both initial direct costs, at time 0, associated with Person A's participation in the screening assessment, and the discounted value of short-term therapy costs. The value of costs under Scenario 2, PV(S₂), includes only the discounted appraisal of long-term therapy, as Person A does not complete the online tool under Scenario 2.

Present Value under Scenario 1:

P V ( S 1 ) = I D C 0 ( A 1 ) + S T C 1 ( A 1 ) 1 + i MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemiuaaLaemOvayLaeiikaGIaem4uam1aaSbaaSqaaiabigdaXaqabaGccqGGPaqkcqGH9aqpcqWGjbqscqWGebarcqWGdbWqdaWgaaWcbaGaeGimaadabeaakiabcIcaOiabdgeabnaaBaaaleaacqaIXaqmaeqaaOGaeiykaKIaey4kaSscfa4aaSaaaeaacqWGtbWucqWGubavcqWGdbWqdaWgaaqaaiabigdaXaqabaGaeiikaGIaemyqae0aaSbaaeaacqaIXaqmaeqaaiabcMcaPaqaaiabigdaXiabgUcaRiabdMgaPbaaaaa@48CB@

Present Value under Scenario 2:

P V ( S 2 ) = L T C 1 ( A 2 ) 1 + i MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemiuaaLaemOvayLaeiikaGIaem4uam1aaSbaaSqaaiabikdaYaqabaGccqGGPaqkcqGH9aqpjuaGdaWcaaqaaiabdYeamjabdsfaujabdoeadnaaBaaabaGaeGymaedabeaacqGGOaakcqWGbbqqdaWgaaqaaiabikdaYaqabaGaeiykaKcabaGaeGymaeJaey4kaSIaemyAaKgaaaaa@3F9D@

Investments in early detection methods, such as online screening tests, are cost effective as long as the total costs (i.e., short-term therapy costs plus the economic value of initial costs of self-evaluation) are less than the costs that would result from therapy begun at a later stage. Thus, if PV(S₁) <PV(S₂), then by substituting, we arrive at

S T C 1 ( A 1 ) 1 + i + I D C 0 ( A 1 ) < L T C 1 ( A 2 ) 1 + i . MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqWGtbWucqWGubavcqWGdbWqdaWgaaqaaiabigdaXaqabaGaeiikaGIaemyqae0aaSbaaeaacqaIXaqmaeqaaiabcMcaPaqaaiabigdaXiabgUcaRiabdMgaPbaakiabgUcaRiabdMeajjabdseaejabdoeadnaaBaaaleaacqaIWaamaeqaaOGaeiikaGIaemyqae0aaSbaaSqaaiabigdaXaqabaGccqGGPaqkcqGH8aapjuaGdaWcaaqaaiabdYeamjabdsfaujabdoeadnaaBaaabaGaeGymaedabeaacqGGOaakcqWGbbqqdaWgaaqaaiabikdaYaqabaGaeiykaKcabaGaeGymaeJaey4kaSIaemyAaKgaaiabc6caUaaa@4F5F@

Rearranging terms yields the following comparison:

L T C 1 ( A 2 ) − S T C 1 ( A 1 ) 1 + i > I D C 0 ( A 1 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqWGmbatcqWGubavcqWGdbWqdaWgaaqaaiabigdaXaqabaGaeiikaGIaemyqae0aaSbaaeaacqaIYaGmaeqaaiabcMcaPiabgkHiTiabdofatjabdsfaujabdoeadnaaBaaabaGaeGymaedabeaacqGGOaakcqWGbbqqdaWgaaqaaiabigdaXaqabaGaeiykaKcabaGaeGymaeJaey4kaSIaemyAaKgaaOGaeyOpa4JaemysaKKaemiraqKaem4qam0aaSbaaSqaaiabicdaWaqabaGccqGGOaakcqWGbbqqdaWgaaWcbaGaeGymaedabeaakiabcMcaPaaa@4ABF@

According to equation 1, if the cost reduction resulting from the difference between the therapy costs (left-hand side of the equation) is greater than the direct costs generated by early detection (right-hand side), then the investment in the online screening test should be made.

The next step is to build in indirect costs to the model. A person affected by mental illness after a disaster, such as depression or PTSD, is assumed to be either unable to work or to function at an impaired level productivity. To represent this condition, we add the discounted value of lost earnings to the therapy costs previously estimated, denoting foregone wages with W₁(A_t), where i = 1, 2.

Present Value with Indirect Costs under Scenario 1:

I D C 0 ( A 1 ) + S T C 1 ( A 1 ) + W 1 ( A 1 ) 1 + i MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemysaKKaemiraqKaem4qam0aaSbaaSqaaiabicdaWaqabaGccqGGOaakcqWGbbqqdaWgaaWcbaGaeGymaedabeaakiabcMcaPiabgUcaRKqbaoaalaaabaGaem4uamLaemivaqLaem4qam0aaSbaaeaacqaIXaqmaeqaaiabcIcaOiabdgeabnaaBaaabaGaeGymaedabeaacqGGPaqkcqGHRaWkcqWGxbWvdaWgaaqaaiabigdaXaqabaGaeiikaGIaemyqae0aaSbaaeaacqaIXaqmaeqaaiabcMcaPaqaaiabigdaXiabgUcaRiabdMgaPbaaaaa@4858@

Present Value with Indirect Costs under Scenario 2:

L T C 1 ( A 2 ) + W 1 ( A 2 ) 1 + i MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqWGmbatcqWGubavcqWGdbWqdaWgaaqaaiabigdaXaqabaGaeiikaGIaemyqae0aaSbaaeaacqaIYaGmaeqaaiabcMcaPiabgUcaRiabdEfaxnaaBaaabaGaeGymaedabeaacqGGOaakcqWGbbqqdaWgaaqaaiabikdaYaqabaGaeiykaKcabaGaeGymaeJaey4kaSIaemyAaKgaaaaa@3F2A@

If we assume that wage losses for persons who enter therapy later are greater than wage losses for those who begin therapy earlier, after pursuing self-evaluation with the online assessment (i.e., W₁(A₂) > W₁(A₁)), then by differencing equations 2 and 3, subject to the inequality suggested by equation 1, we get the following:

[ L T C 1 ( A 2 ) + W 1 ( A 2 ) ] − [ S T C 1 ( A 1 ) + W 1 ( A 1 ) ] 1 + i > I D C 0 ( A 1 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=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@5C95@

Rearrange terms gives us

[ L T C 1 ( A 2 ) − S T C 1 ( A 1 ) ] + [ W 1 ( A 2 ) − W 1 ( A 1 ) ] 1 + i > I D C 0 ( A 1 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=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@5CA0@

Once more, as both numerator terms in square brackets are positive, this suggests that early mental illness detection systems are cost saving.

The aggregate model can now be constructed. This model differs from the 1-person model in that it also accounts for those people who take the screening assessment, but do not develop posttraumatic disorders or a need for therapy. Consequently, in period t = 1, the proportion π individuals will initiate psychological treatment, and the proportion (1-π) will not.

The following statistics offer some insight into the potential range of π. Immediately after a disaster, 54% to 59% of all individuals affected develop psychological disorders 252627. These numbers decrease to 41% by week 10 and to 22% one year after the disaster 2528. In the medium term after a disaster, a variety of disorders may be found, including major depression (20%–41%) 2529, posttraumatic stress disorder (14%–59%) 252629, different subtypes of anxiety disorder (20%–29%) 2529 and substance-abuse disorders (14%–52%) 253031. A potentially traumatic experience (PTE), traced below in Table 1, is a necessary, but not sufficient, cause of chronic PTSD, since pre-traumatic, peri-traumatic, recovery environment and post-trauma lifespan conditions affect the risk of developing posttraumatic difficulties 32. Therefore, a screening test helps to select and treat those people who suffer from more than a transitory stress response and are predisposed to develop chronic PTSD.

Table 1 illustrates the cost paths of the two previously presented scenarios for the n-person model. In Scenario 1, n people (i.e., the whole population who experienced the trauma and was potentially at risk for PTSD) take the available online self-evaluation test in period t = 0. Of the n individuals, only the proportion π requires therapeutic intervention at period t = 1. Individuals who do not manifest any mental disease will not need treatment and thus generate no additional costs. The total costs resulting from Scenario 1 are reported in the bottom row of the table.

In Scenario 2, none of the n persons performs the test at time t = 0. However, in period t = 1, the same number of people, π, as in Scenario 1 require psychological treatment. The aggregate model continues to maintain that the delayed therapy initiated under Scenario 2 carries on longer than under Scenario 1 and is therefore more costly. As a result, investments in the test reduce the total costs of mental illness following a traumatic experience.

Beginning with equation 4, this additional assumption can be modeled. We multiply both the left and the right equation by n. Since in period t = 1, only π individuals need therapy, we also multiply the left side of the equation by π. We consider π as a probability, which takes the value 0 when no one needs therapy and 1 (equal to 100%) when every one needs therapy. Thus, π ∈ [0; 1].

n ⋅ π [ L T C 1 ( A 2 ) − S T C 1 ( A 1 ) ] + [ W 1 ( A 2 ) − W 1 ( A 1 ) ] 1 + i > n ⋅ I D C 0 ( A 1 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=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@65C2@

Dividing both sides by n·π yields

[ L T C 1 ( A 2 ) − S T C 1 ( A 1 ) ] + [ W 1 ( A 2 ) − W 1 ( A 1 ) ] 1 + i > I D C 0 ( A 1 ) π MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=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@5ED8@

Equation 5 differs from equation 4 in one important aspect, seen in the term on the right-hand side of the inequality. In the aggregate state, the initial investment costs must be adjusted for the probability of therapy, π, to be compared to the discounted value of total future expenditures. Given that π cannot be greater than 1, the resulting adjusted initial direct costs IDC₀ in the aggregate state will be greater than or equal to the investment costs without the adjustment for probability of therapy. Analogous to the former result, investment in early detection methods is cost saving as long as the inequality holds.