Health Policy 38 (1996) 101-115
The cost-effectiveness of mammography screening: evidence from a microsimulation model for New Zealand Kam Leong Szetoa, Nancy J. Devlinb,* bEconomics
alviinistry of Health, Wellington, New Zealand Department, University of Otago, PO Box 56, Dunedin,
New Zealand
Received 5 December 1995; revised 7 May 1996;accepted 8 May 1996
Abstract Mammography screening currently represents the only means by which the mortality rate from breast cancer can be modified substantially. A national mammography screening programme is being considered for New Zealand, and pilot programmes were established in two regions (Otago/Southland and Waikato) in 1991 to determine the potential costs and benefits of mammography for New Zealand women. The aim of this paper is to explore the cost-effectiveness of mammography screening in New Zealand relative to no screening, and to examine the marginal change in costs and benefits of altering programme characteristics such as the age of women invited and screening frequency. Cost-effectiveness is measured by the net cost (the costs of screening minus the treatment savings averted by the early detection of cancers) per year of life gained, from the perspective of the public health care sector. A microsimulation computer model, MICROLIFE, was developed to facilitate the estimation of mortality reduction and cost-effectiveness. The results show that, while mammography screening does not ‘save money’ overall, the cost per year of life saved for a range of policies compares favourably with other New Zealand health services, and is comparable to the results from economic evaluations of mammography screening overseas. Of those regimes
* Corresponding author. Tel.:
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+ 64 3 4798359; fax:
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considered, screening women 50-64 cost-effective. Keywords:
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years of age at 3-yearly intervals appears to be the most
Breast cancer; Mammography
screening; Cost-effectiveness;
Economic
evaluation
1. Introduction Breast cancer is one of the most common forms of malignancy in New Zealand and, as in much of the developed world, is a leading cause of death in women [ 11. In 1990, approximately 1600 New Zealand women were diagnosed as having breast cancer and 640 women died from this cause [2]. Breast cancer accounts for around 25% of all cancer registrations and 20% of all cancer-related deaths in New Zealand [2]. Although there have been innovations in the treatment of breast cancer, enabling treatment to be less mutilating, the overall survival rates from this disease have not improved to any great degree over the last few decades [3]. Furthermore, there are no primary prevention measures presently available that significantly affect the rate of death from breast cancer [4]. Consequently, attention has focused upon the potential for mass screening to modify the mortality rate from this disease. The efficacy of screening for breast cancer is clear. A meta-analysis [S] of the five major international trials of screening, [6- lo] found areductioninmortality for screened women of 37% (with a 95% confidence interval of 21-49%) at 9 years follow-up. A more recent meta-analysis of the results from these trials, which assessed breast cancer death rates for each year of follow-up in each trial and produced summary estimates of the cumulative mortality rates, indicates an overall reduction in breast cancer deaths of 31% in groups offered’ screening (with a 95% confidence interval of 17-42%) [l 11. The benefits of mammographic screening in terms of reduced mortality arise primarily from the detection of pre-clinical cancer (the detection of cancers before they present with clinical symptoms) and the more favourable prognosis associated with early-stage cancers. There are, however, a number of controversies and uncertainties surrounding mammography screening. First, although the potential reduction in breast cancer mortality is unequivocal for women aged over 50 years, the benefits for younger women are less certain [ 11,because both the incidence of the disease and the accuracy ofdetection by screening is lower. Second, overseas screening programmes differ with regards to the frequency of screening. In most programmes, women are invited for screens with a 2- or 3-year interval. A longer interval (that is, less frequent screening) lowers the costs of screening, but simultaneously reduces the benefits. Both issues can be addressed empirically by reference to the marginal costs and benefits associated with screening programmes of different configurations. The aim of this paper is to explore the cost-effectiveness of mass mammography screening in New Zealand relative to no mass screening, and to examine the ’ There is a distinction between the reduction in mortality evident for women offered screening and that for those who are screened, given that not all those invited for screening choose to participate.
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marginal change in cost-effectiveness of altering programme characteristics such as the age eligibility criteria and screening interval. Pilot mammography screening programmes introduced in two regions of New Zealand ~Otago/Southland and Waikato) in 1991 have generated info~ation on the costs associated with screening, assessment and treatment of breast cancer which facilitate this analysis. Cost-effectiveness is measured by the discounted net costs of screening (the costs of screening, plus the costs of follow-on assessment and treatment of screen-detected cancers, minus the costs of assessment and treatment of breast cancers which would be evident without screening) per discounted year of life gained by screening. The costs considered are restricted to those incurred or saved by the public health care sector. Data currently being collected on the private costs incurred by women participating in screening will allow us to extend this analysis to the societal perspective in future research. 2. A microsimulation
model of the benefits from screening
A microsimulation model, MICROLIFE2, has been used to estimate the gains in terms of mortality reduction resulting from screening. This model, which is similar to other models (such as MISCAN [12]) used elsewhere in the evaluation of cervical and breast cancer screening programmes, simulates the life histories of members of the population according to the epidemiology and natural history of breast cancer. The first stage of the model simulates the life history of individuals when no screening is available, and the second stage simulates the life history of those same individuals under alternative screening scenarios. The model incorporates the costs associated with each screening option and allows the calculation of cost-effectiveness ratios (net discounted cost per discounted year of life gained) for each. The model characterises the disease as having four pre-clinical stages when breast cancer is detectable by screening but shows no clinical symptoms (that is, displays no symptoms or signs). The structure of the disease process is shown in Fig. 1. As in MISCAN, the disease model is based on a three-stage division of the development of invasive breast cancer, where each stage represents the size of the tumour: Stage I ( < 10 mm), Stage II (lo-19 mm) and Stage III ( > 20 mm). Five percent of the invasive breast cancers are assumed to be preceded by ductal carcinoma in situ (DCIS) which is screen-detectable, and from which a 100% progression to invasive cancer is assumed [I 31. The relative probabilities on staging and mortality were obtained from van Oortmarssen et al. [14] and are provided in Appendix A. Data on the probability of women developing breast cancer were obtained from the New Zealand cancer incidence statistics for the period 1985-89. Although more recent data were available, the introduction of screening in later periods will have acted to produce an artefactual increase in the number of breast cancer cases. The probability of women dying from other causes was obtained from New Zealand Life Tables (198587) from which breast cancer deaths have been excluded. 2 The MICROLIFE model used here was developed specifically for this evaluation on ‘SAS for Windows’ Version 6.10. and is available to researchers upon application to the authors.
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The model assumes that the screening programme commences in 1996 and ceases in 2025, The SO-year duration of screening was chosen to facilitate comparison of these results with those available from the Australian National Evaluation Report and various MISCAN-based evaluations of screening. Given the potential interest in modelling the effects of screening for women aged 45-69 years of age, the cohort of women included in the simulation was those born between 1927 and 1980. The population of each birth cohort at age zero was estimated using New Zealand Life Tables. The costs and effects of screening that flow on after 2025 are computed until all wamen who may have benefited from screening will have died. The sensitivity of ma~o~ams was taken as 0.70 for cancers < 10 mm and 0.95 for cancers > 10 mm. The specificity of screening was assumed to be 0.92 that is, the chance of a healthy woman having a positive test is 8%. Qf these positive diagnostic tests, 8% were assumed to have a surgical biopsy. The model incorporates a ‘phasing in’ period during which the number of women screened is lower than that in a fully established programme. In the first year, the programme achieves 50% of its full capacity3 screens, 80% in year 2 and full
Pm-clinical Breast Cancer > 2Omm
Fig. 1. The disease process model for breast cancer. 3 ‘Full capacity” refers here only to the maximum throughput level achievable for the programme, given the assumed coverage rate, once fully established. There may still be ‘spare capacity’ in the sense of capital resources being less than fully utilised.
K.L.
Table 1 Mammography
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screening scenarios
Policy
Age eligibility (years)
Screening interval (years)
1 2 3 4
50-64 50-64 50-69 45-64
2 3 2 2
capacity by year 3. The attendance rate (the number screened as a proportion of those invited) is taken to be 75%. Although this is lower than the attendance rates evident to date from the New Zealand pilot programmes of around 80%, 75% was chosen to reflect the possibility that attendance rates may fall as screening moves beyond ‘pilot’ status. The policy options considered in this paper are described in Table 1. Under each screening policy, the model assumes that women in the eligible age group are invited to have a screen every year until they attend their first screen - after which they are invited every 2 years (policies 1, 3 and 4) or 3 years (policy 2). Life years gained (and costs) of screening in each scenario have been discounted at 5%, the rate commonly applied to health sector evaluations in New Zealand at present, although we also report the results from employing a discount rate of 10% instead. Although there continues to be some controversy regarding the discounting of health benefits [15- 181, discounting has been used here both to satisfy the requirements for consistency of treatment with costs [19] and to avoid the ‘paralyzing paradox’ i.e. for any attractive programme, there is a superior delayed programme which should be funded first - the result being that no programme with a finite starting point can be selected [20-221. Discounting also reflects pure tune preference and opportunity cost considerations [21] conventionally applied in economic evaluation, i.e. discounting future health benefits reflects the fact that the resources spent to achieve these benefits precludes their use to produce benefits elsewhere [23].
3. costs 3.1. Screening and assessment costs The costs of recruiting, screening and further assessing women participating in screening have been drawn from those reported for the pilot programmes [24]. Unit assessment costs from that study were also used to attribute costs to assessments occurring in the absence of screening. The cost per woman screened of the screen (excluding the costs of follow-on assessments, but including recruitment and health promotion costs) is estimated to be $100 (all costs are reported in 1991 New Zealand dollar terms). This is the cost
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evident from the ~tago/Southland pilot programme by year 3 of its operation [24]. During years 1 and 2, the co~esponding cost was $161 and $102, respectively. The cost of further diagnostic assessment per woman assessed was approximately $200 and the cost per biopsy $1379. The costs per woman screened have been estimated on the basis of capital costs being annuitised over the operation of the programme [25] assuming a useful life of the screening programme capital assets of 10 years and no resale value, and a discount rate of 5%:As also appears to be the case in MISCAN-based analyses, the total costs of screening in each period have been aggregated up from the cost per woman screened. Given the treatment of capital costs unde~inning these estimates, the overall cost of the screening programme in year 1 estimated by the model is substantially lower than that which applies in practice when capital costs are incurred as lump sums, and in subsequent periods costs appear higher than that which would apply in practice when only variable costs are incurred. While this affects the overall discounted costs of the programmes, in the New Zealand context the approach has a sound rationale. Health services in New Zealand are funded, but not necessarily provided, publicly. Under a national programme, screening services will be purchased by Regional Health Authorities from contracted providers on the basis of a negotiated unit cost. From the perspective of the public health fun&r, the lumpiness of fixed costs therefore ceases to be relevant. 3.2. Treatment assumptions and costings There is little consensus regarding the treatment regime to be applied to cancers of various stages, and no protocols were adopted either formally or info~ally by the New Zealand pilot programmes. In New Zealand, as in Australia and the UK, most women are treated by general rather than specialist surgeons and the possibility exists that treatment decisions are idiosyncratic and vary widely between clinicians [26,27]. The costs associated with treating cancers of each stage were based upon treatment protocols constructed by Salkeld and Gerard 1271 in their study of treatment cost savings from mammography screening in Australia. Malignancies are classified into two categories: non-invasive (DCIS) and invasive. Ten treatment profiles are considered, each representing a key combination of treatments for each category - two for DCIS and eight for invasive cancers, as shown in Table 2. In other studies (including that by Salkeld and Gerard [27]), treatment costs and cost savings generated from screening have been estimated on the basis of the probability of women receiving treatments of each type under the screening and no-screening scenarios [27]. However, given the variability in treatment patterns which has been apparent within the New Zealand pilot programmes, it was instead deemed approp~ate to conduct extensive sensitivity analysis for a range of alternative assumptions regarding treatment costs. The main results reported in Tables 3-6 are based on an assumption that all non-invasive cancers are treated using the least expensive and all invasive cancers treated using the most expensive of their respective treatment profiles; results from reversing this assumption and for a range of other possible assumptions are also reported.
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The costs associated with death from breast cancer have been addressed by dividing the possible outcomes for women diagnosed with breast cancer (under both screening and no-screening) into three groups: those cured by primary treatment, those who die within 1 year of diagnosis despite primary treatment, and those who die more than 1 year after diagnosis despite primary treatment. The results reported here show cost-effectiveness under the assumption that only women who die more than 1 year after initial diagnosis receive both primary treatment and palliative care. The method of estimating treatment costs adopted here does not distinguish between the treatment of invasive cancers of different stages of invasive disease. Butler et al. [ZS] have demonstrated a significant relations~p between stage of cancer and treatment costs in Australia - a finding with obvious implications for the cost-effectiveness of screening. In the absence of New Zealand evidence on this issue, the treatment costs averted by the introduction of mammography screening in Table 2 Primary treatment profiles for non-invasive and invasive cancers under screening and no-screening scenarios, and the cost per unit or episode of treatment in 1991 New Zealand dollars Cost per unit or episode of treatment ($ in 1991) Non-invasive
cancer
(DCIS)
1. Mastectomy (plus reconstruction) 2. Conservative surgery (local excision) + Radiotherapy (Stages I, II and III) I. Mastectomy (plus r~nstruction) 2. Mastectomy + Chemotherapy Invasive
$4315 $3496 $2748 Total
$6244
cancers
3. Mastectomy + Radiotherapy 4. Conservative surgery (local excision) 5. Conservative surgery + Radiotherapy 6. Conservative surgery f Radiotherapy + External boost I. Conservative surgery + Radiotherapy + Hormone therapy 8. Advanced palliative care (inclu~ng chemotherapy, hormone therapy, radiation therapy, surgical ctearance)
$4315 $4315 $3536 Total $4315 $2748 Total $3496 $2748 Total $3496 $2748 $1048 Total $3496 $2748 $578 Total
$7851 $7063 $3496
%244
$6822 $13 636
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Table 3 MICROLIFE results regarding the number of screens performed, number of cancers detected, net cost and net discounted cost per life year gained under each screening policy Policy 1[5O-64 years, 2-yearly] No. screens (000) No. cancers detected No. lives ‘saved’ Life years gained (LYG) per life ‘saved Net costs (NC) ($) NC per cancer detected ($) NC per life saved (8) NC per LYG ($) Discounted net costs (DNC) (9 DNC per discounted LYG 01
Policy 2f50-64 years, 3-yearly]
Policy 3150-69 years, 2-yearly]
Policy 4[45-64 years, %-yearly]
3986 15390 4060 18.18
2771 11750 2950 19.79
4815 20 360 5050 17.06
5375 18 660 4810 20.82
451 m 29 275 110973 6104 241 m
312 m 26 541 105 714 5339 170 m
546 m 26 804 108 067 6334 292 m
615 m 32 974 127 918 6144 333 m
14 510
12668
14 597
15 169
Table 4 The estimated cost of services used by the cohort (from 1995 onwards) under each screening policy (including ‘no screening’)
Screening (Sm) Assessment ($m) Biopsy ($m) Treatment ($m)
No screening
Policy 1
Policy 2
Policy 3
Policy 4
nia 22 148 1274
401 8.5 184 1223
279 66 173 1238
485 98 192 1214
542 107 196 1214
Table 5 The estimated net cost of services used by the cohort (from I995 onwards} under each screening policy
Screening (Sm) Assessment (gm) Biopsy ($m) Treatment ($m)
Policy 1
Policy 2
Policy 3
Policy 4
401 64 36 -51
279 44 25 -36
485 77 43 -60
542 86 48 -60
this study arise principally from the shift of cancers detected from invasive to non-invasive categories. Data on the costs of each treatment procedure or episode of care were provided by A. Menon from his ongoing research on the New Zealand pilot programmes. These data were derived primarily from the Resource Utilisation System (RUS) of HealthCare Otago (the host institution for the Otago/Southland pilot programme), and were based upon observations for all breast cancers in the period 1993-94. It
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is assumed that the cost of each procedure is independent of the means of detection (that is, screening or symptomatic). The RUS system, which is widely used in New Zealand hospitals, aims to capture all costs associated with the provision of services (both direct inputs and shared institutional services) [24]. Limitations to the ability of RUS to track treatment costs by diagnostic category required these data to be supplemented with information on case management obtained from Oncology Department notes and records. Treatments costed included surgical procedures (mastectomy and local excision), and adjuvant therapies such as radiotherapy, chemotherapy and hormonal treatments (tamoxifen), and outpatient visits. Breast reconstructive surgery was assumed to be undertaken for all cases in which mastectomy is performed - this added 10% to the cost of mastectomy alone (assuming the two procedures are undertaken concurrently). Radiotherapy includes outpatient attendances for initial consultation, reviews and follow-up; planning for treatment, 23 radiotherapy treatments, and Radiation Monitoring System (RMS) checking. Chemotherapy included outpatient attendances for initial consultation, reviews and follow-up, six cycles of either CMF (Cyclophosphamide, Methotrexate and Flurouracil) or FAC (Flurouracil, Adrimycin and Cyclophosphamide), preparation and treatment administration (including consultant inputs and Oncology day-unit nursing and bed costs). Advanced invasive cancers receive palliative care (treatment undertaken to relieve symptoms rather than with the expectation of cure) which included a combination of chemotherapy, radiotherapy, surgical clearance, radiotherapy, and hormonal treatments. The ‘episode of treatment’ for palliative care shown in Table 2 is defined as the period from diagnosis until death.
4. Results The model used in this research predicts that screening would generate a reduction in mortality from breast cancer (over the period 2001-2030), of 19% under policy 1, 14% in policy 2, 23% under policy 3 and 22% under policy 4. The results on costs, outcomes and cost-effectiveness of each screening policy are summarised in Table 3. The cost per year of life gained from the screening policies Table 6 Marginal change in net costs, life years gained and cost effectiveness of each screening policy relative to policy 2 Policy 1 Total discounted net cost (%m) [I = 5%] Marginal addition to discounted net costs (%m) of moving from policy 2 Total discounted life years gained [r = 5%] Marginal addition to discounted life years gained of moving from policy 2 Marginal cost ($) per life year gamed
241 71
Policy 2 170 -
Policy 3
Policy 4
292 122
333 163
16 609 3189
13420 -
20 004 6584
21 953 8533
22264
-
18 530
19 102
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considered ranges from $12 668 to $15 169. Screening women aged 50-64 years 3-yearly (policy 2) appears to be the most cost-effective option, although the current policy adopted by the pilot programmes of screening women aged 50-64 years 2-yearly (policy 1) compares favourably to both policies 3 and 4 (extending the age of women eligible for screening to include either younger or older women). Cost-effectiveness appears to be robust to changes in assumptions regarding treatment costs. For example, by reversing the initial assumption and instead assuming that all non-invasive cancers are treated using the most expensive treatment profile and all invasive cancers using the least expensive treatment profile, the cost per year of life gained was $14440, $12637, $14473 and $15 107 for policies l-4, respectively. These results are within 1% of the results shown in Table 3 for every policy4. The variation in overall cost-effectiveness of each of the policies appears to be relatively small. For example, the difference in cost per year of life gained for policy 1 ($14 510) and policy 2 ($12 668) is $1842 (Table 3). However, focusing instead upon marginal cost-effectiveness highlights important differences between these policies. Table 6 shows the marginal change to net costs and life years gained and marginal cost per life year gained of each policy relative to the most cost-effective policy - policy 2. The results indicate that the addition to net cost for each additional year of life gained from choosing policy 1 over policy 2 is $22 264. The results shown in Table 3 are sensitive to the choice of discount rate. Increasing the discount rate to 10% lowers the cost effectiveness of all policy options. For example, the cost per year of life gained for policy 1 with a discount rate of 10% was $28 403, compared to $14 510 where Y = 5%. The sensitivity of the results to this parameter arises from the differential timing of benefits and costs from screening - whereas costs are incurred immediately, the benefits in terms of lives saved, and the stream of life-years gained from each death averted, occur in later time periods. The ranking of screening policies is also sensitive to the choice of discount rate. For example, at a zero discount rate the net cost per life year gained produces a ranking of policies from most to least cost-effective of 2, 1, 4, 3 compared with a ranking of 2, 1, 3, 4 where r = 5% (Table 3).
5. Discussion and conclusions Mammography screening does not ‘save money’ - that is, for the mass screening scenarios considered here, the resource savings arising from the early treatment of cancers only partially offset the cost of screening itself. This finding concurs with the results from all economic evaluations of mammography screening undertaken internationally. For the screening policies considered in this study, 4 The sensitivity of cost-effectiveness to further sets of treatment cost assumptions was also explored, and results are available from the authors upon request. These results confirm that cost-effectiveness is not sensitive to assumptions regarding this variable.
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treatment costs averted by screening offset, at most, 13% of the costs of screening. This is considerably lower than the 20-30% reported from the Netherlands 129,301, although some of this difference is likely to be related to the inclusion in those studies of hospice and nursing care costs for advanced cancers, which in New Zealand fall outside the domain of the public health care sector. Whether mammography screening represents a worthwhile use of public resources requires some basis for comparison with the evidence on cost-effectiveness presented here. There are, however, a small number of economic evaluations available on New Zealand health services, and differences in method limit the validity of comparisons. Where comparisons can be drawn, these suggest that mammography screening represents a relatively efficient means of generating health outputs. Converted to 1991 dollar values using the Consumers Price Index (CPI), the results from a study of treatment of end-stage renal failure indicated a range of costs per year of life gained from $39 943 for in-centre kidney dialysis to $20 909 for kidney transplantation [31]. The results reported here are comparable to those apparent from evaluations of breast cancer screening programmes internationally - although it must be noted that overseas estimates of screening cost-effectiveness are characterised by variations of some magnitude, even within one given country. This is due both to the characteristics of the programmes being evaluated, and the exact nature of the methodologies used - particularly in the estimation of mortality benefits [30]. For example, in their evaluation of mammography screening in Australia, Hall et al. [26] estimate a cost per year of life saved of A$10 560 (in 1988/89 prices) for screening women aged 45-69 years of age 2-yearly5. Carter et al. [34], in a MISCAN-based evaluation of mammography screening in Australia, report a cost per year of life gained of A$20 300 (in $1990 prices) for 2-yearly screening of women over 40 years of age and note the difference between this result and that of the Australian National Evaluation report, $11 000, for the same screening age and interval [35]. The latter result was obtained by using the KNOX [36] model, which assumes an immediate and ‘steady state’ mortality benefit from mammography screening. Exact comparison of the results reported here for New Zealand with regard to the effects of age and screening frequency with those from other studies is limited by differences in age-group aggregation. For example, Carter et al. [34] find that screening Australian women 50-69 years of age 3-yearly is more cost-effective than screening that same group 2-yearly, and is more cost-effective than screening women younger than 50 years for a range of screening intervals. Rosenquist and Lindfors [37] find that 2-yearly screening of 50- to 79-year-old American women was more cost-effective than screening women aged 40-49 year@. De Koning et al.
5 Other evidence on cost per year of life saved from screening includes: for Britain, The Forrest Report (1986): f3044 (1984 prices) [32], for the Netherlands. De Koning et al.: US$3400-5385 (1990 prices) [29] and Van der Maas et al.: US$4850 (year of prices not stated) [13]; and for Japan, Okubo (1991): US$14 300 (year of prices not stated) [33]. 6 However, it should be noted that neither costs or mortality benefits in that study were discounted.
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[38] report that screening women aged 50-65 years at 3-year intervals was more cost-effective than screening 50- to 70-, 40- to 70- or 50- to 75year-olds 2yearly. These findings are broadly consistent with those reported here for New Zealand, although clearly there remains scope to consider a still wider range of possible age/screening interval combinations. The treatment costs and net screening costs calculated in this study rest upon a number of assumptions regarding the treatment of breast cancer. Further research on breast cancer treatment patterns in New Zealand and the relationship between stage of cancer detected and treatment costs, would improve the info~ation we currently have on treatment costs and their influence on screening cost-effectiveness. The difficulty experienced in constructing treatment profiles for use in this analysis also suggests the importance of putting in place clearer guidelines for the treatment of breast cancer before a national screening programme is implemented. Finally, while this study focuses on the benefits from screening in terms of mortality reduction, screening also has important effects upon the quality of life of women screened, diagnosed and treated for breast cancer. Further research on the cost per qua~ty-adjusted life year gained under various screening options would provide valuable additional information to New Zealand pohcymakers.
Acknowledgements We are grateful to the Hugh Adams Cancer Epidemiology Group for providing a grant-in-aid to facilitate this research, and to Dr Arun Menon for providing access to treatment cost data. We are also indebted to Harry de Koning for making available unpublished details regarding the MPSCAN model, and to Paul Hansen in the Economics Department and colleagues in the Ministry of Health for helpful comments. Remaining errors are the authors’ responsibility.
Appedix
A: Made1 parrmeters
The following parameters upon which this model has been based, unless otherwise indicated, were obtained from van Oortmarssen et al. [14]. A. f . CfiPlicuf stage distribution
20 mm
10% 22% 68%
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course of the disease
Transition between stages are described by transition probabilities P,; the dwelling time distribution in a stage is conditional on the next stage and follows an exponential distribution. The mean duration m, is age-dependent according to the formula:
ma = 0.3m,,/(l
- 0.9a)2
where a = age/loo.
From
To
pt
m50
Preclin < 10 mm Preclin < 10 mm Preclin lo-19 mm Preclin lo-19 mm Preclin > 20 mm
Preclin lo- 19 mm Clin < 10 mm Preclin > 20 mm Clin lo-19 mm Clin > 20 mm
0.9 0.1 0.75 0.25 1.0
0.58 0.59 0.85 0.85 1.00
A.3. Survival rates and times
The probability of a cancer patient being cured depends only on the size of the tumour. The survival tunes for those who die from breast cancer were taken from a study which estimated a log-normal model for the survival of 2432 patients diagnosed with breast cancer in New Zealand [39]. The following table shows the estimates of the parameters of the model.
<50 years 50-69 years 270 years
A.4. Proportion
Mean survival time
Standard deviation
1.18 1.29 1.23
1.14 1.20 1.43
of patients
cured
83% 68% 51%
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