a Department of Population Health Sciences,
b Department of Virology, National Institute of Public Health, Oslo, Norway.
Reprint requests: Hein Stigum, Department of Population Health Sciences, National Institute of Public Health, PO Box 4404 Torshov, 0403 Oslo, Norway. E-mail: Hein.Stigum{at}Folkehelsa.no
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Abstract |
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Methods A mathematical model was used to calculate the number of cases prevented by the intervention. For a given prevalence of HTLV in the blood donor population, the model calculates the number of recipients infected by transfusion, and the number of partners and offspring that will in turn be infected. The model then calculates the number of subjects with disease due to HTLV-I infection and the number of deaths from disease. From these numbers the measures of cost and effect are calculated.
Results Testing all new blood donors for HTLV is calculated to cost US$ 9.2 million per life saved, or US$ 420 000 per quality adjusted life year gained by the intervention, when the HTLV prevalence among donors is 1 per 100 000. When the prevalence among donors is 10 per 100 000 the intervention will cost US$ 0.9 million per life saved, or US$ 41 000 per quality adjusted life year gained. The same analysis shows that testing blood donors for human immunodeficiency virus (HIV) saves money when the HIV prevalence among donors is above 0.7 per 100 000.
Conclusion For Norway, studies suggest a willingness to pay to save a statistical life of approximately US$ 1.2 million. The costs fall under this value when the number of infected persons is 8 per 100 000 donors. The results are uncertain because of the uncertainty in HTLV infection and disease parameters.
Keywords Cost effect analysis, cost utility analysis, HTLV, HIV, mathematical model, blood donors, transfusion
Accepted 8 May 2000
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Introduction |
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Progressive permanent lower-extremity weakness, spasticity, hyperreflexia, sensory disturbances and urinary incontinence characterizes HAM/TSP. No specific treatment for the myelopathy is known. The HAM/TSP patient survives 2030 years.2 In Japan, West Africa, the Caribbean, North and South America and Melanesia HTLV-I infection is endemic.1 From these countries, infection has spread to Europe by immigration and by sexual contact.
An association between HTLV-II and subsequent disease is still uncertain, but the virus is suspected to be associated with some rare neurological disorders.4 It is endemic in many American Indian populations, and has been found among injecting drug users in North America, Europe and South Asia.
Both HTLV-I and II can be detected by antibody tests. In USA, screening of blood donors started in 1988 and about 0.01% of the donors were found to be infected. About 70% of these were HTLV type II.5 In 1991 testing of blood donors was made mandatory in France followed later by the Netherlands, Denmark, Sweden and Finland. Other countries in Europe have tested parts of their blood donor population. The results of these approximately 5.5 million tests show that the prevalence of HTLV is low among European blood donors, ranging from 0% in Belgium (95% CI : 00.009%) to 0.02% in Greece (95% CI : 0.0020.07).1 The majority of cases were HTLV-I. Both Denmark and Sweden reviewed their screening programme after one year. Denmark found seven HTLV-I positives among 220 000 donors giving a prevalence of 0.003%. Sweden found seven HTLV-I positives among 300 000 donors giving a prevalence of 0.002%.6 Both countries are now testing new donors only.
In Norway a sample of 33 000 donors was tested by January 1998. One HTLV-II positive donor was found.7 On the basis of this it was decided to continue testing until all current donors have been tested, and then re-evaluate the programme.
A cost-effect analysis of the HTLV testing estimated a cost of US$ 36 million per life saved based on the Swedish conditions.8
This paper aims to show how costs and effects associated with testing depend on the HTLV-prevalence among donors and further to see if the effects of anxiety connected to testing will influence the results. The analysis also includes a full sensitivity analysis. For comparison, the cost-effect ratio for tests against human immunodeficiency virus (HIV) infection is calculated.
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Materials and Methods |
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We distinguish between the direct costs of the intervention (cost of screening minus treatment costs for those that would become ill without the intervention), and the indirect costs (consumption minus production of the individuals whose life years are saved). There is controversy as to how indirect effects should be treated in economic analysis.9 Our position is that indirect effects should not be disregarded in a positive (factual) analysis of resource consequences, even if the weight they should have in priority setting is unclear. In the following we therefore present both direct and indirect costs.
The effects of the intervention are measured in three different ways, either in saved lives, gained life years, or in gained quality adjusted life years (QALY10). The concept of QALY builds on the idea that the value of resources spent on treatment or interventions is greater the more quality of life is improved for patients, the longer the improvement lasts, and the more people that benefit from the treatment. Full health is given the health value 1, death is given the value 0, and disease is somewhere in between. Different methods have been used to decide on the health values of different conditions.10,11 A review of empirical studies in Australia, England, Norway, Spain and the US using the person trade-off technique showed that societies like these place very heavy weight on interventions that save lives compared to interventions that improve functioning or relieve symptoms.11 To be consistent with the observed person trade-offs, values for health states must lie in the range of 0.81.0 unless dysfunctioning and/or symptoms are very severe. We are aware that utilities conventionally used in QALY calculations are much lower. There is evidence that conventional utilities are misleading, largely because they are mostly elicited by asking members of the general public to value hypothetical health states. When chronically ill people are asked to value their own conditions by means for instance of the time trade-off technique (willingness to sacrifice life expectancy to become well), most states get values corresponding to those obtained by means of the person trade-off technique.12 In our main analysis we use values that are consistent with these data. Even years lived with full-blown AIDS is assigned a value of 0.9, given that the main losses from the illness are captured by the counting of lost life years. However, we perform a sensitivity analysis using somewhat lower values.
A possible negative effect of the intervention is that subjects with a positive HTLV test may experience reduced life quality knowing they are infected with an sexually transmittable agent that may lead to disease that cannot be treated. The use of QALY makes it possible to include this type of anxiety in the calculations.
The cost-effect ratio equals the costs of the intervention divided by the net effects. Using either direct costs alone or direct plus indirect costs combined with the three effects measures gives six different cost-effect ratios. The ethical considerations underlying each of these measures are given in the discussion.
Model
To calculate the number of cases prevented by the intervention, we used a mathematical model. For a given prevalence of HTLV (or HIV) in the blood donor population, the model calculates the number of recipients infected by transfusion, and the number of partners and offspring that these in turn will infect. Then the model calculates the number of subjects with disease (TSP/HAM and ATL associated with HTLV-I infection, or HIV related disorders and AIDS associated with HIV infection) and the number of deaths from disease. From these numbers the measures of cost and effect are calculated. Future costs and effect are discounted to present values by the same rate. The sum of discounted future values is called the cumulative present value. The model is described in full in the Appendix.
The parameter values used in the model reflect, apart from the infection/disease specific parameters, the Norwegian situation. To calculate the number of recipients infected through transfusions, and the number of partners and offspring infected, we need information on the number of transfusions performed, on sexual behaviour, and on birth rates. These values vary with age and the population is therefore divided into age groups. The values used along with the references are found in the Appendix, Table 3. The diseases associated with infection are divided into stages, and stage-specific transmission rates and durations are given in Table 4
. Transfusion and vertical transmission rates are given in Table 5
.
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Results |
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Counting cumulative present value of deaths, the model predicts for HIV that the majority of cases (deaths) are due to transfusion and only 10% come from infected partners or offspring. The cases are old, 88% are 50 years or older. For HTLV-I, 55% of the cases stem directly from transfusion. The age distribution of the cases is similar to that of HIV, 94% are over 50 years. The majority of the HTLV cases, 87%, are due to adult T-cell leukaemia.
Changing the discount rate greatly influences the results. A lower discount rate for costs and effects leads to a more favourable cost-effect ratio (Table 2). This is because a large part of the costs comes from the screening in the first year. And with a lower discount rate, the longer we look ahead and the better payoff we get for this investment.
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Discussion |
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The model assumes that the intervention will stop all HTLV transmission through transfusion. Since donors are tested only once, repeat donors may become infected after the test and transmit through transfusion. If so, our model overestimates the effects of the intervention, that is, the intervention may be even more costly than estimated here.
Many of the parameters are uncertain, particularly the infection and disease parameters of HTLV-I. The results must therefore be seen as indications of possible costs and effects.
Figure 1 shows that the cost of saving a life falls with increasing prevalence of HTLV among donors. As a comparison, estimated values of a statistical life based on willingness to pay for reduction of mortality risk cited in The economics of health care range from US$ 0.5 to 6 million.13 For Norway, Elvik suggests a willingness to pay to save a statistical life of approximately US$ 1.2 million.14 The costs fall under this value when the number of infected people is
8 per 100 000 donors.
The cost-effect ratio is very sensitive to the choice of discount rate. This is because the main costs come at the start of the intervention, whereas the effects come after a long latency period. We have followed the recommendation of the Panel on Cost-Effectiveness in Health and Medicine in using a 3% discount rate.1517
The model assumes a 10-year latency period before the development of tropical spastic paraparesis (TSP). There is some indication that TSP will develop sooner after transfusion than for other modes of infection.18 If so, our cost-effect ratios should be lower because the effects would be less discounted. The short observed latency after transfusion may, however, be an effect of a too short observation period.
The model assumes that the number of infected subjects as well as the rates in the model do not change over time. This is not so much an assumption about time trends as it is a way of looking at the cost-effect problem. We want to know if the present situation calls for action. However, to see the consequences of actions taken today, we need to look far ahead in time due to the long incubation period of the diseases. The question we ask is: given that today's situation would prevail over time, what are the costs and effects of an intervention? We therefore use the number of infected subjects at each stage of disease when the model is in equilibrium.
The sensitivity analysis assumes that the uncertainty of the parameters can be described by triangular distributions (simple distributions with defined minimum, mode and maximum). There is no empirical justification for this choice, nor for the choice of minimum and maximum values in these distributions. Therefore, the uncertainty of the output generated by these parameters is not reported and we only report which parameters the model is sensitive to.
The model does not consider HTLV-II infection. A donor screening would also reveal these cases, and have the extra effect of preventing diseases that may be caused by this infection.
The six different cost-effect ratios used in this paper rest on different value judgements and have different distributional effects. Costs are calculated as direct costs only, or as directs costs plus consumption minus production. Using the former means that we think it is equally valuable to save one person in productive life as one unemployed or retired person. Using the latter means that we place higher value on saving a person in productive life. Effects are measured in lives, life years or QALY. Using lives means that we think it is equally valuable to save one young as one old person. Using life years or QALY means that we think it is more valuable to save a young person representing many potential years, as an older person. In the model most of the infected cases are older than 50 years. In fact each life saved in the model contributes on average 23.92/1.08 22 life years (Table 1
). Using QALY rather than life years means that we also consider the years of disease avoided. Each case of disease lasts on average one year for ATL and 20 years for TSP and leads on average to 22 life years lost. The risk of ATL is five times the risk of TSP. Therefore adding disease years times health value to the life years will not give a large change regardless of the health value used.
The health value and duration used for anxiety are completely speculative. However, we can conclude from the sensitivity analysis that if all subjects who test HTLV positive experience between 1 and 3 years of anxiety with a health value between 0.95 and 1, this has no statistically significant effect on the cost-effect ratio (Table 6).
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Conclusion |
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Appendix |
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Let Ti be the number of subjects infected by transfusion in age group i. A proportion (1 ) will remain healthy carriers throughout their lives (stage 1), the remaining proportion
will go through latency, disease and death (stages 24), Figure 2
. All infected individuals, except in the terminal stage, are subject to ageing at rate
i and death at rate µi from causes unrelated to HTLV. Subjects progress from stage j at a rate
j.
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The number of subjects infected by transfusion in age group i (Ti) equals the number of recipients (Ri) times the number of transfusions per recipient (i) times the HTLV-I prevalence among donors (
) times the transmission rate (ßT). A proportion sTi will survive the first two years after transfusion, for simplicity, only these cases are counted in the model.
![]() | (1) |
The changes in pijt over time as depicted in Figure 1 and Figure 2
are described in equation 2
.
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where
![]() | (2) |
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and
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The dot over the p means derivation with respect to time. The extra groups p0j and pi0 were added to simplify the equations.
If the number of subjects infected by transfusion (Ti) is constant over time, the number of subjects in stage 1 to m-1 will approach an equilibrium (pij*) given by the recursive formulae:
![]() | (3) |
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The number of infected partners (i) is given in equation 4. We assume that the age group of the partner equals that of the infected recipient, and that subjects with disease (stage m-2) do not transmit to their partners. The transmission rate per intercourse is ßj, while
i and
i are the partner- and intercourse frequencies.
![]() | (4) |
The number of infected offspring (Bi) is given in equation 5. Here bi is the birth rate, and ßv the vertical transmission rate. The group with disease (stage m-2) is assumed not to give birth.
![]() | (5) |
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The changes in qijt (infected partners and offspring) over time is described in equation 6. It is analogous to equation 2.
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where
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and
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The extra groups q0j and qi0 were added to simplify the equations. If i and Bi are constant over time, the number of infected partners and offspring in stage 1 to m-1 will approach an equilibrium (qij*) given by the recursive formulae:
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Intervention
All current blood donors (D) will be tested in the first year, thereafter all new blood donors. These are renewed by a rate r. The numbers screened will be D in the first year, and then D*r per year in the following years.
Time horizon
It is reasonable to give less weight to costs and effects that are far into the future. In the model, future costs, bt, are discounted by a value given by the interest rate, d, and the distance in years, t, equation 8, first part. Here t0 is the timelag from the intervention to the effect occurs. B is called the cumulative present value. If costs are constant over time, they can be taken out of the integral and the cumulative present value is equal to the costs per year times a constant that depends on the interest rate, equation 8, second part.
Future effects measured as lives saved or QALYs can be discounted in the same fashion, except now, the discount rate measures society's time preference or impatience. There are, however, theoretical grounds for using the same discount rate for both costs and effects16
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The timelag before costs or effects associated with a particular stage occurs, is equal to the expected time to reach the stage:
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Result measures
Direct costs
The screening costs are equal to the number of donors, D, plus the cumulative present number of future tests times the average cost per test, c1, equation 10. The treatment expenses equals the discounted number of infected subjects times expenses per treatment (c2,j). The direct costs equals screening costs minus the treatment costs saved by the intervention.
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![]() | (9) |
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Indirect costs
The indirect costs measure the effects the intervention will have on the amount of money available to society. It equals consumption minus production for the life years saved by the intervention. The value of production has two parts: The first part is based on the prevalence of infection and equals the average salary times the proportion in each age group that is normally employed (wi) times the discounted number of infected subjects times the reduction of productivity due to disease (1 ). The second part is based on the incidence of death and equals the salary times the discounted number of new deaths times the expected work years left in each age group. The value of consumption equals the potential years saved defined in equation 11 times the yearly consumption per person.
![]() | (10) |
consumption =potential years consumption per person per year
indirect costs =consumptionproduction
Effects
The three different effect measures are given below. The number of lives saved is calculated from the cumulative present number of infected in stage m-1 times the progression rate to death. The life years saved equal the number of lives times the average expected years left in age group i, ei. The QALYs gained equal the cumulative present number of infected from each stage times the change in health value, 1 j, plus the life years won, equation 11. The QALYs lost in anxiety from a positive test equal the number of tests times the prevalence of infection among donors,
, times the period of anxiety, a, times the change in health value due to anxiety, 1
0. The net QALYs gained equal the quality adjusted life years gained by the intervention minus the QALYs from anxiety.
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![]() | (11) |
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QALYs lost in years of anxiety = (D + D r hd,0)a(1
0)
net QALYs = QALYs gained QALYs lost in years of anxiety
Cost-effect ratios
The cost-effect ratios (CE) are defined in equation 12. The combination of two measures of costs with three measures of effects gives six cost-effect ratios. The distributional effects and different ethical implications of these measures are taken up in the discussion.
![]() | (12) |
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The model was programmed in Mathematica.19
Parameters values
The parameter values used in the calculations are in part specific to Norway. The blood donor population in Norway consists of approximately 100 000 people, and about 12 000 of these are replaced by new donors each year. The price of a test was calculated to be US$ 2.86 per test kit plus US$ 1.10 of labour costs per test = US$3.95.
The population was grouped into four age groups (01, 217, 1850 and 5190 years) to pick up variation in transfusions and sexual behaviour over age. The number of recipients per year, the number of transfusions per recipient and the proportion surviving the two first years after transfusion, shown in Table 3, are based on information from the Norwegian blood banks. The mortality and birth rates, the expected years left, the proportion employed in each age group, and the expected work years, are based on Norwegian vital statistics.20 The number of new partners per year and the number of sexual contacts per year are estimated from the Norwegian sexual surveys.21,22 The values for the oldest age group are estimated for subject between 51 and 60 years, and are assumed to apply to subjects 5165 years in the model. This group makes up 60% of the oldest age group.
The biological parameters for HTLV-I, shown in Table 4 and Table 5
, are based on information in the MMWR report on recommendations for counselling persons infected with HTLV-I and II.3 The transmission rate was estimated as follows: In a report from Japan, cited in ref. 3, 60.8% of women married to HTLV-I positive men were infected after 10 years. Assuming
= 97 contacts per year, as in the Norwegian sexual survey data, leads to a transmission rate of ß = 1 (1 0.608)1/10
= 0.001. The proportion developing disease, given by
, is on the high side of that given in ref. 3. The treatment expenses cover all hospital costs for the given diagnose. They are based on costs of diagnose-related groups23 and on the number of hospital admissions per year for the diagnose group.24 The average salary used was US$ 30 000 and the consumption was US$ 12 000 per person per year.20 The health values used in Table 4
and Table 5
were determined according to suggestions by Nord.11 The number of years with anxiety caused by one positive test was set to 2 years for HTLV and 10 years for HIV without any empirical justification.
The transmission rates and duration of infectivity for HIV were based on refs 2528. The vertical transmission rate for HIV was based on empirical studies of infection from mother to child cited in ref. 29.
Throughout the calculations, both economical measures and measures of suffering were discounted at 3% per year.
Sensitivity analysis
A multivariate sensitivity analysis of the cost-effect ratio for the intervention against HTLV infection was employed using a Latin hypercube sampling scheme combined with ranked correlations.3032 In this method each (of the K) parameters is assigned a probability distribution expressing the uncertainty. The investigator decides on a number of simulations (N). Then each distribution is divided into N equiprobable intervals, and a value is chosen at random within each interval. The N values of the first parameter are combined with random permutations of the values from the other distributions producing an N*K matrix. Then the output of the model is calculated using each row of this matrix as input values. The sensitivity of the model output to the variance in each parameter is assessed by ranked correlation coefficients.
The effects of changes in donor HTLV prevalence and discount rate are shown in Table 2. The sensitivity analysis applies to the central cell in this Table, that is an HTLV prevalence = 5/100 000 and a discount rate = 3%. The parameters in Table 3
and the cost parameters of Table 4
are assumed fairly certain and are not included in the analysis. The remaining nine parameters, ß, 1/
2, 1/
3,
3,
, ßT, ßV, a, and
0 were assumed to follow triangular distributions with mode equal to the respective values in Table 4
or Table 5
. The minimum and maximum values were set equal to the mode ±50%, with three exceptions. For the transmission rate the variance was set greater than this: The minimum, mode and maximum were 0.0001, 0.001, and 0.01, respectively. For the health values the variance was set smaller: For the health value in stage 3 the minimum, mode and maximum were 0.9, 0.98, and 1, respectively. For the health value of anxiety the minimum, mode and maximum were 0.95, 0.99, and 1, respectively.
The two diseases associated with HTLV, ATL and TSP were analysed separately, using both cost per life and cost per QALY as output. We performed two hundred runs of the model (N = 200) and calculated the ranked correlations between the output and the parameters. Using cost per life or cost per QALY made no difference. Four parameters were selected as sensitive for ATL, the same four parameters plus duration in stage 3 were selected as sensitive for TSP.
Table 6 shows the result of 200 runs for each disease. The monotonicity between output and parameters assumed in the rank correlation was checked using generalized additive model regressions. The sensitivity analysis was repeated three times of 200 runs each to look at the variation of the correlation coefficients. The same parameters were selected as sensitive each time, but their correlation coefficients and ordering varied somewhat. The sensitivity analysis was programmed in Splus.33
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