Uptake of prostate-specific antigen testing for early prostate cancer detection in Sweden

Uptake of prostate-specific antigen testing for early prostatecancer detection in Sweden

Hakan Jonsson1, Benny Holmstrom2,3, Stephen W. Duffy4 and Par Stattin2

1 Department of Radiation Sciences, Oncology, Umea University, Umea, Sweden2 Department of Surgical and Perioperative Sciences, Urology and Andrology, Umea University, Umea, Sweden3 Department of Surgery, Gavle Hospital, Gavle, Sweden4Wolfson Institute of Preventive Medicine, Queen Mary University of London, London, United Kingdom

The aim of our study was to estimate uptake of prostate-specific antigen (PSA) testing in an entire country, including time

trends and geographical differences. Data from the Swedish Cancer Register on prostate cancer incidence between 1980 and

2007 and published data from the Gothenburg branch of the European randomized study of screening for prostate cancer

(ERSPC), a population-based PSA screening study, were used in two models of changes in incidence of prostate cancer as a

proxy for uptake of PSA testing in all 24 Swedish counties. The estimated annual PSA testing, irrespective of previous years’

exposure, reached a peak of 12% of all men in 2004 and decreased thereafter to 6% in 2007 and varied from less than 5 to

20% between counties. Under the assumption that men who underwent annual PSA testing were previously unexposed to PSA

testing, the cumulated uptake of PSA testing in men aged 55–69 years in Sweden increased from zero in 1997 to 56% in

2007. Our study shows that it is possible to estimate uptake of PSA testing in the population from the prostate cancer

incidence pattern. There were large geographical variations in uptake of PSA testing despite a uniform health care system in

Sweden and there was a substantial increase in the uptake of PSA testing during the study period, despite that there were no

national recommendations for PSA-based prostate cancer screening.

In 1994 the food and drug administration (FDA), in the USapproved the use of prostate-specific antigen (PSA) as ascreening tool for early detection of prostate cancer inasymptomatic men.1 The increased use of PSA testing ofasymptomatic men has resulted in a sharp increase in inci-dence of low risk prostate cancer and it has caused a decreasein incidence of metastatic disease.2–5 In 2009, the Europeanrandomized study of screening for prostate cancer (ERSPC)reported a 20% decrease in the rate of death from prostatecancer in the screening arm after a median follow-up of 9years. There were considerable overdiagnosis and overtreat-ment since, to save one mans life, 1410 men had to beinvited to screening and 48 additional cases had to undergocurative treatment.6 These figures are likely to change withfurther follow-up as indicated by recently published resultsfrom the Gothenburg part of ERSPC.7 There remains noconsensus if population-based screening for prostate cancerby use of repeated PSA testing is appropriate.1

The incidence of prostate cancer in the US increased inthe late 1980s and early 1990s with an incidence peak in1992 with an age standardized incidence of about 240 per100,000.8 In Sweden a similar increase occurred �10 yearslater with an incidence peak in 2004 with an age standar-dized incidence of 236 per 100,000.4,9 The reason for thesharp increase in prostate cancer incidence observed in theUS, Sweden and other western countries, was an increaseduse of PSA testing of asymptomatic men as a part of a healthexamination, and as a part of the work up of lower urinarytract symptoms, mainly among elderly men. In the controlarm of the prostate, lung, colorectal and ovarian (PLCO)screening trial in the US, the proportion of men who hadundergone PSA testing before the study invitation was 40%during the first year of the study and 52% after 6 years.10

The uptake of PSA testing among middle aged Swedish menis unknown and there is no nationwide or regional registerin which the use of PSA testing can be assessed. Several stud-ies derived from databases on results from PSA testing havereported estimates of the proportion of men who have under-gone PSA testing in different parts of the western world.11–19

To the best of our knowledge, no study has reported on esti-mates of the uptake of PSA testing derived from prostatecancer incidence.

The aim of our study was to estimate the uptake ofPSA testing in the 24 Swedish counties as well as in theentire nation by use of models for the relationship betweenthe uptake of PSA testing and incidence of prostatecancer.

Key words: early detection, prostate cancer, prostate-specific antigen

Grant sponsors: Swedish Cancer Foundation; Grant number: 0750;

Grant sponsor: Vasterbotten county council, County Council of

Gavleborg

DOI: 10.1002/ijc.25846

History: Received 30 Jun 2010; Accepted 11 Nov 2010; Online 10

Dec 2010

Correspondence to: Håkan Jonsson, Oncological centre, Umeå

University Hospital, Umeå 901 85, Sweden, Tel.: 46-90-7852419,

Fax: þ46-90-127464, E-mail: [email protected]

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Int. J. Cancer: 129, 1881–1888 (2011) VC 2010 UICC

International Journal of Cancer

IJC

Material and MethodsSwedish cancer register

Registration of all cancer cases to the Swedish CancerRegister is mandatory and regulated by law, and the overallcapture rate has been estimated to 96.3% for all tumours andhigher among solid tumours in subjects 70 years oryounger.20 Data on prostate cancer incidence among menaged 55 to 69 years between 1980 and 2007 on county levelwere retrieved from the Swedish Cancer Register. The num-ber of counties in Sweden is currently 21, but we used theformer county division of 24 counties to make optimal use ofhistorical data. Aggregated population data were retrievedfrom Statistics Sweden.

Gothenburg part of the ERSPC

Published data from the Gothenburg branch of the ERSPCtrial, a randomized population-based PSA screening study,were extracted.2 In that study, which started in 1995, a totalof 20,000 men aged 50 to 64 years were randomized in a 1:1ratio to a screening group offered biennial screening or to acontrol group.2 Results from four screening rounds, i.e., 8years, were reported in the study. The number of screeningvisits for a PSA test was 19,290 in the screening group. Anapproximation of the population over time was made byassuming a 1% annual mortality which corresponds to theannual mortality in the Swedish population for the same agecategory at that time. This led to population figures with apossible number of visits to 38,327 giving a mean populationcoverage of 50%. However, since this is the coverage over 2year’s time, 25% was used as the annual coverage of PSAtesting in the screening group. In the screening group, 640prostate cancer cases were diagnosed, out of which 550 caseswere screen detected while 244 prostate cancers were diag-nosed in the control group. The number of person-yearsduring the 8 years was calculated as 76,654 in each of thescreening and control group.

The additive and multiplicative models

Two models were used to describe the relationship betweenthe annual incidence of prostate cancer and the proportion ofmen in the population that underwent PSA testing that year.These models were used to estimate uptake of PSA testingfrom an observed increase of prostate cancer incidence. Themodels were additive; I(p) ¼ I(0) þ CAp, and multiplicative;I(p) ¼ I(0) (1 þ CM p), where I(p) is the annual incidence ina population with the proportion p of PSA tested men duringthe year, I(0) is the annual incidence in an unscreened popu-lation, and where CA and CM are unknown constants.

Since we have an unknown constant in each model theestimation of the coverage p had to be performed in twosteps. In step one a data set consisting of two groups, onewith a certain PSA coverage and the other without any PSAtesting can be used, e.g., a randomized PSA screening trial,where also the prostate cancer incidence is known. The con-

stants can then be estimated as; CA ¼ [I1(p0) � I1(0)]/p0, andCM ¼ [I1(p0) � I1(0)]/[I1(0) p0]. The prostate cancer inci-dence in the group with a known PSA coverage (p0) isdenoted I1(p0), while the incidence in the unscreened groupis denoted I1(0). For step one we used published data fromthe screening trial in Gothenburg described above.2

In step two the unknown uptake of PSA testing (p) inthe Swedish counties was estimated from the additive andmultiplicative model by; p ¼ [I2(p) � I2(0)]/CA, and p ¼[I2(p) � I2(0)]/[I2(0) CM], respectively. The prostate cancerincidence in a county with a certain unknown PSA coverageis denoted I2(p), while CA and CM are the constants esti-mated in step one. See Appendix for further details. If thereis a small difference between I2(p) and I2(0), e.g., when thetrue PSA uptake p is low, it is possible to get p < 0 bychance only. Such estimates can be regarded as similar top ¼ 0. However, confidence intervals are not possible to esti-mate when p � 0.

The prostate cancer incidence without any PSA testing,I2(0), was predicted using historical data. Since hardly any PSAtesting was performed between 1980 and 1990, the prostatecancer incidence during this 11-year period was used to predictI2(0) for each year until 2007. We used all 24 counties for theprediction to take into account the different incidence patternsin the counties. The estimates of the incidence trends weremade with a log-linear Poisson model with calendar year (con-tinuous) and county as covariates. Separate intercepts wereused for all counties but a common slope for calendar year.

The county specific coverage and the population size wereused to calculate the total number of PSA tests in eachcounty. Based on these data total coverage per year in thecountry was calculated.

ResultsIn the end of the 1990s the age standardized incidence ofprostate cancer increased very steeply and over a period of 7years the age standardized prostate cancer incidence for menaged 50–74 years increased by more than 100% (Fig. 1). Thetotal number of incident prostate cancer cases increased from5,903 in 1997 to 9,880 in 2004 and thereafter a markeddecrease in incidence was observed.

For step one in the estimation procedure, the prostatecancer incidence in the Gothenburg trial was estimated to 8.3per 1000 in the screening group, I1(0.25), and to 3.2 per 1000in the control group, I1(0). The constants were estimated to0.0207 for CA, and 6.63 for CM. For step two the observedincidence for men aged 55 to 69 years and the predicted inci-dence based on the observed incidence between 1980 and1990 were calculated using a Poisson model (Fig. 2). A smallincrease in prostate cancer incidence was observed during thefirst decade. From the mid 1990s, the increase became steeperin a majority of the counties but the start and size of theincrease varied considerably between counties. For somecounties, e.g., the counties of Kronoberg, Ostergotland, andSodermanland, the slope of the trend may have been

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1882 Uptake of prostate-specific antigen testing


overestimated with an ensuing underestimation of the uptakeof PSA testing.

The Poisson model used for prediction of the prostatecancer incidence in absence of PSA testing showed an over-dispersion (residual deviance 343 with 239 df). Thus, a moreindividual modeling may have improved the estimates in step

two. However, an alternative extended model with differentslopes for all counties seemed to give an over-fitting resultingin extreme results in many counties while over-dispersionstill remained (residual deviance 285 with 216 df). A sensitiv-ity analysis was not performed since p is inverselyproportional to the constants CA and CM, and it is easy toconsider how an error in these constants would influence theestimated proportion.

The estimated annual PSA testing varied between coun-ties from a maximum of less than 5% of all men to morethan 20% (Fig. 3). In many of the counties where a highlevel was reached early, the proportion of PSA testsdecreased during the most recent years. The total number ofPSA tests was dominated by counties with both high PSAuptake and a large population, e.g., the counties of Stock-holm, and Gothenburg and Bohus (Fig. 4). For the entirecountry the PSA uptake reached a top level of 11 to 12% ofall men in 2004 and decreased during the most recent yearsto between 6 and 7% of all men in 2007 in the multiplica-tive model (Fig. 5), and the additive model (not shown)gave very similar results. The corresponding figures, cumu-lated over time, increased from 0 to 56% and 59% duringthe last decade for the multiplicative and additive model,respectively (Fig. 6).

Figure 2. Observed (dotted line) and predicted prostate cancer incidence in absence of PSA testing in men aged 55 to 69 years in Swedish

counties 1980 to 2007. The predicted incidence was based on the years 1980 to 1990 using a Poisson model. G&B ¼ Gothenburg and

Bohus county. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 1. Age standardized prostate cancer incidence in men aged

50 to 74 years in Sweden 1980 to 2007.

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DiscussionA large regional variation in prostate cancer incidence wasobserved in Sweden. In some counties an early and steepincrease in prostate cancer incidence was observed while inother counties hardly any increase was observed. The twodifferent models used to estimate the annual proportions ofmen who had undergone a PSA test showed similar propor-tions that varied between counties from a maximum of lessthan 5% of all men to a maximum of over 20%. Dependingon the model used the estimated cumulated uptake of PSAtesting in Swedish men increased from 0 to 56% and 59%between 1997 and 2007.

There is no basis for the assumption that there would bea real difference in the prostate cancer incidence betweenSwedish counties. The population is rather homogenousover the country with similar age structure and geneticbackground,21 and the Gothenburg area, in which the PSAscreening trial was conducted, is the second largest city inSweden. Hence the observed differences and steep increase inprostate cancer incidence in some counties have to beexplained by other factors.

The increase in prostate cancer incidence started in severalcounties in the mid 1990s after the introduction of PSA test-ing. There are several likely explanations for the observed

differences including regional differences in the use of PSAtesting in the work-up of lower urinary tract symptoms andin health check-ups. The access to urologists in differentcounties may vary because prostate cancer incidence washighest in urban regions and in counties with university hos-pitals.22 Several steps precede a prostate cancer diagnosisafter the detection of an elevated PSA value and the numberof cancers detected will not only depend on the use of PSAtesting. The readiness of general practitioners to refer thepatient to a urologist, his/her willingness to perform prostatebiopsies, the number of cores taken at a biopsy session, thenumber of biopsy sessions undertaken, and the intensity ofthe search by pathologist for cancer will all affect the detec-tion rate.23 One factor that may affect both cancer incidenceand cancer mortality is the access to health care.24

The influence of the aforementioned factors may varydepending on local clinical practise or guidelines in theabsence of national guidelines on best practise for prostatecancer care, which were published in 2007 in Sweden.25

Several studies based on regional databases have reportedon the uptake of PSA testing. A study from the United King-dom estimated the proportion of men older than 45 yearswith no diagnosis of prostate cancer having a PSA testto 3.5% in 1999.11 A later follow-up estimated the overall

Figure 3. Estimated annual proportion (with 95% CI) of men aged 55 to 69 years in Sweden who had a PSA test using the multiplicative

model. G&B ¼ Gothenburg and Bohus county. Confidence intervals were given from 1995 and onwards if the estimated proportion was

>0.02 for two consecutive years or more. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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annual rate of PSA testing to 6%, out of which one third wasamong asymptomatic men.12 Several studies from Italy haveestimated the proportion of PSA tested men to between 6and 34% depending on age, year of estimation, and geo-graphical area.13–15 In the US, the proportion of men 65years or older who had undergone PSA testing, estimatedfrom Medicare claims, was between 31 and 38% in 1998.16 Ina recent publication from the PLCO screening trial, the pro-

portion of men PSA tested at least once in the control armincreased from 40 to 52% during 6 years.10 There has been aclear increase in the uptake of PSA testing over timealthough there are large differences in the uptake of PSA test-ing between countries and regions.

The concordance between the results from the additiveand multiplicative model is an important strength of ourstudy. The additive model gave slightly higher proportions

Figure 4. The estimated total number of PSA tests (with 95% CI) in men aged 55 to 69 years in Sweden using the multiplicative model.

G&B ¼ Gothenburg and Bohus county. Confidence intervals were given from 1995 and onwards if the estimated proportion was >0.02 for

two consecutive years or more. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 5. Estimated annual proportion (with 95% CI) of men aged

55 to 69 years in Sweden who had a PSA test, based on the

multiplicative model 1990 to 2007.

Figure 6. Annual proportion of Swedish men aged 55 to 69 years

who had a PSA test cumulated over time.

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and narrower confidence intervals. Since prostate cancer inci-dence is strongly related to age, the constant CA, used in theadditive model, is expected to be age dependent. However,the corresponding constant in the multiplicative model, CM,is probably not age-dependent to the same extent and themultiplicative model is therefore probably more flexible forapplications on different age groups in step two.

The data set available for the estimate in step one is a li-mitation of our study. To estimate the constants CA, and CM

we used published data from a randomized PSA screeningtrial.2 The trial can be seen as an aging cohort with an 8 yearfollow-up where age at start was 50 to 64 years while in steptwo annual prostate cancer incidence for men aged 55 to 69years was used. However, the average age during follow-upin the trial was similar to the age interval in step two. Datafrom all four screening rounds in the trial were used sincethe interval cancers and prostate cancers among nonrespond-ers were only reported for the 8 year follow-up. The coveragethen also better represented the age interval in step two.However, the influence of uptake of PSA testing on the inci-dence is probably most comparable to the situation in thefirst screening round. Only small differences in cancer detec-tion rates were seen between visits in the trial but to somedegree it can be explained by the increasing age with follow-up time. An advantage by using all four screening roundsinstead of round one only, is that the number of cases wasconsiderably larger and thereby the standard error of theestimated constants was reduced.

We assumed that changes in prostate cancer incidencewere due to PSA testing which made the models insensitivefor the influence from other factors and both the annual

uptake of PSA testing and the corresponding cumulateduptake of PSA testing were estimated and not directlyrecorded in our study. The interpretation of the cumulatednumber as the proportion of men who ever had a PSA testassumes that men underwent PSA testing only once duringthe study period. However, an unknown proportion of menhad undergone multiple PSA testing and therefore the esti-mate is likely somewhat exaggerated. In a recent study basedon the incidence of T1c tumours in Sweden and an assump-tion on the occurrence of cancer among men with elevatedPSA, Bratt et al. estimated that at least 33% of men inSweden had undergone PSA testing.19

Our data together with data from other sources stronglyindicate that a large proportion of middle aged men in Swedencurrently undergo PSA testing. If this nonorganized PSA test-ing has an effect on the prostate cancer specific mortality isunknown, however, there have been very small changes in theprostate cancer specific mortality over time in Sweden.

ConclusionIt is possible to estimate the uptake of PSA testing in a popu-lation from the prostate cancer incidence pattern. Under theassumption that there were no PSA testing before 1997 andthat men who underwent PSA testing had not previouslyundergone PSA testing, the cumulated proportion of PSAuptake in men aged 55 to 69 years increased from 0 to 56%between 1997 and 2007 in Sweden using the multiplicativemodel. There were large regional differences in the uptake ofPSA testing with maximum levels in the counties varyingfrom less than 5% of all men to over 20%.

References

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2. Hugosson J, Aus G, Lilja H, Lodding P,Pihl CG. Results of a randomized,population-based study of biennialscreening using serum prostate-specificantigen measurement to detect prostatecarcinoma. Cancer 2004;100:1397–405.

3. Makinen T, Tammela TL, Stenman UH,Maattanen L, Aro J, Juusela H,Martikainen P, Hakama M, Auvinen A.Second round results of the Finnishpopulation-based prostate cancerscreening trial. Clin Cancer Res 2004;10:2231–6.

4. Adolfsson J, Garmo H, Varenhorst E,Ahlgren G, Ahlstrand C, Andren O,Bill-Axelson A, Bratt O, Damber JE,Hellstrom K, Hellstrom M, Holmberg E,et al. Clinical characteristics and primarytreatment of prostate cancer in Swedenbetween 1996 and 2005. Scand J UrolNephrol 2007;41:456–77.

5. Aus G, Bergdahl S, Lodding P, Lilja H,Hugosson J. Prostate cancer screeningdecreases the absolute risk of beingdiagnosed with advanced prostatecancer—results from a prospective,population-based randomizedcontrolled trial. Eur Urol 2007;51:659–64.

6. Schroder FH, Hugosson J, Roobol MJ,Tammela TL, Ciatto S, Nelen V,Kwiatkowski M, Lujan M, Lilja H, ZappaM, Denis LJ, Recker F, et al. Screening andProstate-Cancer Mortality in a RandomizedEuropean Study. N Engl J Med 2009;360:1320–8.

7. Hugosson J, Carlsson S, Aus G, Bergdahl,S, Khatami A, Lodding P, Pihl CG,Stranne J, Holmberg E, Lilja H. Mortalityresults from the Goteborg randomisedpopulation-based prostate-cancerscreening trial. Lancet Oncol 2010;11:725–32.

8. Jemal A, Siegel R, Ward E, Hao Y, Xu J,Thun MJ. Cancer statistics, 2009. CACancer J Clin 2009;59:225–49.

9. http://www.roc.se/prostata/rapport/rapport_03_07.pdf.

10. Andriole GL, Grubb RL, 3rd, Buys SS,Chia D, Church TR, Fouad MN, GelmannEP, Kvale PA, Reding DJ, Weissfeld JL,Yokochi LA, Crawford ED, et al. MortalityResults from a Randomized Prostate-Cancer Screening Trial. N Engl J Med2009;360:1310–9.

11. Melia J, Moss S. Survey of the rate of PSAtesting in general practice. Br J Cancer2001;85:656–7.

12. Melia J, Moss S, Johns L. Rates of prostate-specific antigen testing in general practicein England and Wales in asymptomaticand symptomatic patients: a cross-sectionalstudy. BJU Int 2004;94:51–6.

13. Zappa M, Visioli C, Crocetti E, BuonamiciC, Baccini A, Taddei S, Ciatto S. Practiceof opportunistic PSA screening in theFlorence District. Eur J Cancer Prev 2003;12:201–4.

14. Russo A, Autelitano M, Bellini A, BisantiL. Estimate of population coverage withthe prostate specific antigen (PSA) test to

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screen for prostate cancer in ametropolitan area of northern Italy. J MedScreen 2002;9:179–80.

15. D’Ambrosio G, Samani F, Cancian M, DeMola C. Practice of opportunisticprostate-specific antigen screeningin Italy: data from the Health Searchdatabase. Eur J Cancer Prev 2004;13:383–6.

16. Etzioni R, Berry KM, Legler JM, Shaw P.Prostate-specific antigen testing in blackand white men: an analysis of medicareclaims from 1991–1998. Urology 2002;59:251–5.

17. Drummond FJ, Carsin AE, Sharp L,Comber H. Trends in prostate specificantigen testing in Ireland: lessons from acountry without guidelines. Ir J Med Sci2010;179:43–9.

18. Smith DP, Supramaniam R, Marshall VR,Armstrong BK. Prostate cancer and

prostate-specific antigen testing in NewSouth Wales. Med J Aust 2008;189:315–8.

19. Bratt O, Berglund A, Adolfsson J,Johansson JE, Tornblom M, Stattin P.Prostate cancer diagnosed after prostate-specific antigen testing of men withoutclinical signs of the disease: a population-based study from the National ProstateCancer Register of Sweden. Scand J UrolNephrol 2010;44:384–90.

20. Barlow L, Westergren K, Holmberg L,Talback M. The completeness of theSwedish Cancer Register: a sample surveyfor year 1998. Acta Oncol 2009;48:27–33.

21. Schaedel C, Hjelte L, de Monestrol I,Johannesson M, Kollberg H, Kornfalt R,Holmberg L. Three common CFTRmutations should be included in a neonatalscreening programme for cystic fibrosis inSweden. Clin Genet 1999;56:318–22.

22. Stattin P, Johansson R, Lodnert R, AndrenO, Bill-Axelsson A, Bratt O, Damber JE,Hellstrom M, Hugosson J, Lundgren R,Tornblom M, Varenhorst E, et al.Geographical variation in incidence ofprostate cancer in Sweden. Scand J UrolNephrol 2005;39:372–9.

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24. Jones AP, Haynes R, Sauerzapf V,Crawford SM, Forman D. Geographicalaccess to healthcare in Northern Englandand post-mortem diagnosis of cancer. JPublic Health 2010;32:532–7.

25. Bratt O, Damber JE, Karvinge C, Malm T,Hensjo LO, Hyttsten E. [The NationalBoard of Health and Welfare’s guidelinesfor prostatic cancer care. PSA testscreening—only for well-informed men].Lakartidningen 2008;105:524–8.

APPENDIX

The two models were estimated in two steps as

described in Table A1 where I(p) is the incidence with the

proportion p of PSA uptake. Incidence was based on dif-

ferent data sets in step one and two which is indicated

by an index. In step 1 the PSA coverage is known ¼ p0.

We assume that I1(p0), I1(0), I2(p) and I2(0) are

independent. Since CA and CM were estimated using the

incidences in step one they are independent of the inci-

dence used in step two.

To calculate confidence intervals the variance of p is nee-

ded. However, it is more convenient to calculate an appr-

oximation of the variance of log(p). It is calculated below

using the delta method. Confidence intervals can then be

estimated as; elogðpÞ61:96ffiffiffiffiffiffiffiffiffiffiffiffiffiffiVðlogðpÞÞ

p.

A Poisson model based on incidence for the years 1980

to 1990 was used to predict I2(0). r22ð0Þ is the estimated

variance for this predicted incidence.

Additive model

First we have; VðCAÞ ¼ V I1ðp0Þ�I1ð0Þp0

8:

9;¼ 1

p02I1ðp0ÞP1ðp0Þ þ

I1ð0ÞP1ð0Þ

8:

9;

where P1( ) is the person years corresponding to I1( ).

VðlogðpÞÞ ¼ VðlogððI2ðpÞ � I2ð0ÞÞ=CAÞÞ¼ VðlogðI2ðpÞ � I2ð0ÞÞÞ þ VðlogðCAÞÞ

� VðI2ðpÞ � I2ð0ÞÞEðI2ðpÞ � I2ð0ÞÞ2

þ VðCAÞEðCAÞ2

¼ 1

ðI2ðpÞ � I2ð0ÞÞ2I2ðpÞP2ðpÞ þ r2

2ð0Þ

8>>:

9>>;

þ 1

CA2p02

I1ðp0ÞP1ðp0Þ þ

I1ð0ÞP1ð0Þ

8>>:

9>>;

Multiplicative model

We have

VðlogðCMÞÞ ¼ V logI1ðp0ÞI1ð0Þ � 1

8>>:

9>>;

8>>:

9>>;

� VðI1ðp0ÞÞðE½I1ðp0Þ� � E½I1ð0Þ�Þ2

þ VðI1ð0ÞÞ E½I1ðp0Þ�E½I1ð0Þ�ðE½I1ðp0Þ� � E½I1ð0Þ�Þ

8>>:

9>>;2

and

VðlogðpÞÞ ¼ V logI2ðpÞ � I2ð0ÞI2ð0ÞCM

8>>>:

9>>>;

8>>>:

9>>>;

¼ V logI2ðpÞI2ð0Þ � 1

8>>:

9>>;

8>>:

9>>;þ VðlogðCMÞÞ

� VðI2ðpÞÞðE½I2ðpÞ� � E½I2ð0Þ�Þ2

þ VðI2ð0ÞÞ E½I2ðpÞ�E½I2ð0Þ�ðE½I2ðpÞ� � E½I2ð0Þ�Þ

8>>:

9>>;2

þ VðlogðCMÞÞ

¼ I2ðpÞP2ðpÞðI2ðpÞ � I2ð0ÞÞ2

þ r22ð0Þ

I2ðpÞI2ð0ÞðI2ðpÞ � I2ð0ÞÞ

8>>:

9>>;2

þ I1ðp0ÞP1ðp0ÞðI1ðp0Þ � I1ð0ÞÞ2

þ 1P1ð0ÞI1ð0Þ

I1ðp0ÞI1ðp0Þ � I1ð0Þ

8>>:

9>>;2

:

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Total number of PSA tests

The total number of PSA tests added over counties

was estimated asP

i pini where pi ¼ the estimated propor-

tion in county i and ni ¼ the population (person-years). Wehave

VðelogðpiÞÞ � VðlogðpiÞÞðeEðlogðpiÞÞÞ2 ¼ VðlogðpiÞÞðelogðpiÞÞ2¼ VðlogðpiÞÞp2i

And thus

VX

i

pini

8>>>:

9>>>; ¼ V

X

i

nielogðpiÞ

8>>>:

9>>>;

¼X

i

n2i VðelogðpiÞÞ¼X

i

ðnipiÞ2VðlogðpiÞÞ

Table A1. The additive and multiplicative model and parameterestimates

Additive Multiplicative

Model I (p) ¼ I (0) þ CAp I (p) ¼ I (0) (1 þ CM p)

Estimationstep 1

CA ¼ [I1 (p0) �I1 (0)]/p0

CM ¼ [I1 (p0) �I1 (0)]/[I1 (0) p0]

Estimationstep 2

p ¼ [I2 (p) �I2 (0)]/CA

p ¼ [I2 (p) �I2 (0)]/[I2 (0) CM]

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Uptake of prostate-specific antigen testing for early prostate cancer detection in Sweden