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European Journal of Cancer (2013) xxx, xxx– xxx

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Choosing the net survival method for cancer survivalestimation

0959-8049/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.ejca.2013.09.019

⇑ Corresponding author: Tel.: +358 9 135 33 274; fax: +358 9 135 5378.E-mail address: [email protected] (A. Pokhrel).

Please cite this article in press as: Seppa K. et al., Choosing the net survival method for cancer survival estimation, Eur J Cancer (2013)

dx.doi.org/10.1016/j.ejca.2013.09.019

Karri Seppa a,b, Timo Hakulinen a, Arun Pokhrel a,⇑

a Finnish Cancer Registry, Institute for Statistical and Epidemiological Cancer Research, Pieni Roobertinkatu 9, FI-00130 Helsinki, Finlandb Department of Mathematical Sciences, University of Oulu, Oulu, Finland

KEYWORDS

Epidemiologic methodsModelsNeoplasmsPrognosisRelative survivalNet survival

Abstract Background: A new net survival method has been introduced by Pohar Perme et al.(2012 [4]) and recommended to substitute the relative survival methods in current use forevaluating population-based cancer survival.Methods: The new method is based on the use of continuous follow-up time, and is unbiasedonly under non-informative censoring of the observed survival. However, the population-based cancer survival is often evaluated based on annually or monthly tabulated follow-upintervals. An empirical investigation based on data from the Finnish Cancer Registry wasmade into the practical importance of the censoring and the level of data tabulation. A sys-tematic comparison was made against the earlier recommended Ederer II method of relativesurvival using the two currently available computer programs (Pohar Perme (2013) [10] andDickman et al. (2013) [11]).Results: With exact or monthly tabulated data, the Pohar-Perme and the Ederer II methodsgive, on average, results that are at five years of follow-up less than 0.5% units and at 10and 14 years 1–2% units apart from each other. The Pohar-Perme net survival estimator isprone to random variation and may result in biased estimates when exact follow-up timesare not available or follow-up is incomplete. With annually tabulated follow-up times, esti-mates can deviate substantially from those based on more accurate observations, if the actu-arial approach is not used.Conclusion: At 5 years, both the methods perform well. In longer follow-up, the Pohar-Permeestimates should be interpreted with caution using error margins. The actuarial approachshould be preferred, if data are annually tabulated.� 2013 Elsevier Ltd. All rights reserved.

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Table 1The 26 cancer sites included in the analyses and the numbers ofpatients diagnosed in Finland in 1981–1995 by site and sex.

Cancer site InternationalClassification ofDiseases (ICD)-10code

Total number ofpatients

Males Females

Oesophagus C15 1545 1516Stomach C16 8071 7297Colon C18 5905 8449Rectum, rectosigma, anus C19–20 5006 4991Liver C22 1555 1340Gall bladder, bile ducts C23–24 1020 2762Pancreas C25 4266 5166Larynx C32 1672 –Lung, trachea C33–34 25,992 5260Skin, melanoma C43 3331 3577Skin, non-melanoma C44 3538 4236Soft tissues C48–49 901 970Breast C50 – 35,399Cervix uteri C53 – 2420Corpus uteri C54 – 7777Ovary C56 – 6043Prostate C61 21,359 –Testis C62 893 –Kidney C64–65 4626 3867Bladder, ureter, urethra C67–68 7235 2389Central nervous system C70–72 3747 5102Thyroid C73 783 3128Hodgkin lymphoma C81 1007 775Non-Hodgkin lymphoma C82–85, C96 4274 4620Multiple myeloma C90 1625 2035Leukaemia C91–95 3600 3299

2 K. Seppa et al. / European Journal of Cancer xxx (2013) xxx–xxx

1. Introduction

The population-based cancer registries have used rel-ative survival to give estimates of patients’ net survival,i.e. as far as the patients’ cancer is concerned when elim-inating the effects of the other causes of death [1,2]. Inthis way, no information on causes of death has beenneeded as the mortality from the other causes (oftencalled expected mortality) has been estimated from lifetables of the underlying general population. Recently,a recommendation of using the Ederer II relative sur-vival method was made based on both theoretical andempirical arguments [3]. This recommendation has beenalso followed, e.g. by the pan-European EUROCARE-5study (European cancer registry based study on survivaland care of cancer patients).

Even more recently, a new method to estimate net sur-vival has been proposed by Pohar Perme et al. [4] as a sub-stitute of the relative survival approach. This method isnot based on a direct comparison of an observed survivalproportion of the patients against an expected survivalproportion in the comparable general population groupas the relative survival methods. It still uses the generalpopulation mortality as an estimate of mortality due tothe other causes, so that no information on the actualcauses of death is needed. This method, unlike the relativesurvival methods, has been shown to provide an unbiasedestimator of the true net survival, if there is no informa-tive censoring of the observed survival (e.g. censoring thatwould vary by patients’ age [5]) and continuous time isused in survival calculations. The international CON-CORD-2 (Global surveillance of cancer survival) studywill use the Pohar-Perme net survival method.

Also the relative survival methods, including the Eder-er II method, aim to estimate net survival. The Ederer IIestimator calculates the cumulative product of the inter-val-specific relative survival ratios, which are based onunweighted observations of patients alive at the begin-ning of the corresponding intervals. Therefore, patientswho have a high probability of dying due to other causesthan cancer get too small weights in estimation of net sur-vival, as a patient’s contribution to net survival is omittedin subsequent intervals after dying. Because net survivaldepends almost always on the same demographic vari-ables as the expected hazard due to other causes than can-cer, the estimator of the Ederer II method becomesbiased. In the classical relative survival methods, strati-fied analyses and their summarisations, e.g. by (age-)stan-dardisation, have been conducted to reduce this bias.

In the method of Pohar Perme et al., a patient’s con-tribution to net survival is weighted on the basis of thepatient’s expected survival, i.e. the probability of beingalive for a healthy person in the national or other pop-ulation (comparable with respect to demographic vari-ables e.g. sex, age and calendar year). The methodmay be viewed also as a generalisation of the gold

Please cite this article in press as: Seppa K. et al., Choosing the net survivdx.doi.org/10.1016/j.ejca.2013.09.019

standard used in an earlier study [3] into a situationwhere each patient makes her own group defined bysex, age and year of diagnosis. The choice of weightsfor each group can also be viewed natural, as in a truegold standard, depending on the cancer-related excesshazard of death only.

The present study investigates systematically, usingdata from the population-based Finnish Cancer Regis-try and the two publicly available computer programs,how crucial these two assumptions (no informative cen-soring of the observed survival and use of continuoustime) are, particularly the latter one, when a change ofmethod from the traditional relative to the new net sur-vival is done. It is important to know, for national andinternational population-based cancer survival analyses,how much results obtained by the two methods differand under which conditions the new method can be rec-ommended in practice.

2. Patients and methods

Patients diagnosed in Finland in 1981–1995 and fol-lowed-up until the end of 2010 were included in the anal-ysis with stratification by the most common 26 sites.Table 1 shows the list of the sites and the numbers of

al method for cancer survival estimation, Eur J Cancer (2013), http://



K. Seppa et al. / European Journal of Cancer xxx (2013) xxx–xxx 3

diagnosed patients by site and sex. Cancer sites with lessthan 500 patients were not included. The effect of cen-soring was studied by using the ends of 1995 and 1999as the alternative closing dates of follow-up. The overallnon-standardised net survival estimates were obtainedby the Ederer II relative survival method [6] and bythe method proposed by Pohar Perme et al. [4]. Theresults of applying the methods were compared at 5,10 and 14 years of follow-up by using exact follow-uptimes as well as by applying annual and monthly fol-low-up intervals as a basis of grouping the data. In addi-tion to the point estimates, also the precision of thepoint estimates was evaluated by investigating thelengths of confidence intervals.

In an empirical comparison, a true ‘gold standard’ isnot available, as even an unbiased method with no cen-soring is prone to give estimates with random error.Nevertheless, due to unbiasedness and the recent recom-mendation [7], the results of the Pohar-Perme methodwith exact and uncensored follow-up times (i.e. fol-lowed-up until the end of 2010) were selected as the goldstandard against which the other approaches were com-pared. The other approaches included the use ofmonthly or annually grouped observations, also subjectto empirical patterns of censoring due to earlier com-mon closing dates (1995 or 1999) and the use of theEderer II method instead of the Pohar-Perme method.Results were calculated by site, but the estimates ofsite-specific gold standards are very unstable. Overallsurvival combining patients of all sites is more stablebut a less reasonable measure in practice [8]. Therefore,we focused on results averaged over the various siteswith equal weights. The average gives a summary mea-sure that treats the estimation for each site equallyimportant and has a smaller random error than thesite-specific results. Age-standardised results were pro-duced by using internal age-standardisation [3,9] basedon five age groups: 0–44, 45–54, 55–64, 65–74 and75+ years.

The calculations for the monthly and annuallygrouped observations were conducted by using the bothavailable computer programs: the original program in Rby Pohar Perme [10] (version 2.0-4) and another pro-gram in STATA by Dickman et al. [11] (version 1.3.8).The most accurate follow-up time was called the exactfollow-up time, although it was based on the exact dateat exit (day of death, emigration or the 31st December2010) and an approximated date of diagnosis, as theexact date of diagnosis is not available. The date of diag-nosis was set to be the 15th day of a month of diagnosis,or, if the month of diagnosis and exit were the same, theday in the middle between the 1st day and the day ofexit. As the R program had been designed for exactobservations, in its grouped data application, followingthe traditional life table practice, all the deaths and cen-soring events were placed in mid-points of the respective


follow-up intervals. We slightly modified the variance ofthe actuarial estimator of the Pohar-Perme method inSTATA program to obtain better approximation forthe weighted person-time at risk. Implementations ofthese different approaches in R and STATA are pre-sented in the Supplementary Web Appendix.

3. Results

Colon cancer in males is shown as an example on thecomparisons (Fig. 1). The results depend quite a lot onthe choice of the method, level of grouping of the dataand on patterns of censoring. With annually groupedfollow-up times, the Pohar-Perme and the Ederer IImethods tend to give much higher values in R, particu-larly when the data are censored (closing year 1995). Theactuarial approach in STATA provides estimates thatare much closer to those based on exact follow-up times.Age-standardisation does not remove these differencesalthough it brings the Ederer II and the Pohar-Permeestimates closer to each other when the data are cen-sored. In incomplete follow-up with exact observations,the Pohar-Perme method tends to underestimate long-term net survival, whereas the estimates of Ederer IImethod are closer to the gold standard. The site-specificresults of males are summarised in SupplementaryFigs. 1–3.

Averaged over the sites, the gold standards of net sur-vival for males were 49.9%, 42.6% and 38.9% for the 5-,10- and 14-year follow-up, respectively. Annuallygrouped data in R caused a marked overestimation, par-ticularly when the data were censored and the follow-upwas long (Table 2). At 10 and 14 years, the average over-estimations in the most heavily censored situation were3.4% and 6.0% units, respectively, in the Pohar-Permeestimates and 3.3% and 5.3% units, respectively, in theEderer II estimates. Even with no censoring, the averageoverestimations were 1.5% and 2.5% units in the Pohar-Perme estimates and 1.8% and 2.8% units in the EdererII estimates. The analyses based on the actuarialapproach in STATA virtually removed the large differ-ences to the gold standard observed in R with annuallygrouped data. The use of monthly grouped data mostlyreproduced the same average differences as the exactdata.

With censored observations, the Pohar-Permemethod using exact follow-up times tended to underesti-mate net survival at 10 and 14 years. With the heaviestcensored data (closing year 1995), the underestimationwas 2.0% units at 14 years (Table 2). The Ederer IImethod based on exact follow-up times did not givethe same negative differences to the gold standard asthe Pohar-Perme method, particularly when the fol-low-up was long and the data heavily censored. Butwhen there was no censoring, this approach




0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14Years from diagnosis

Anl, R (EdII)Anl, STATA (EdII)Exact, R (EdII)Anl, R (PP)Anl, STATA (PP)Exact, R (PP)

Non-standardised

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70



Age-standardised

Cum

ulat

ive

net s

urvi

val

Closing year 1995

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70



Non-standardised

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70



Age-standardised

Cum

ulat

ive

net s

urvi

val

Closing year 2010

Fig. 1. Cumulative net survival curves of male colon-cancer patients diagnosed in Finland 1981–1995 and followed-up until the end of 1995 anduntil the end of 2010 by using the Pohar-Perme (solid lines) and the Ederer II method (dashed lines), two different levels of grouping the data(annually grouped (Anl) and exact follow-up times (Exact)) and the programs in R and STATA. In R, all the events have been placed in the mid-points of the follow-up intervals. Both non-standardised and internally age-standardised curves are shown.


overestimated the gold standard on average with 1.0%and 1.8% units at 10 and 14 years of follow-up,respectively.

Lengths of confidence intervals (CIs) of the gold stan-dard of net survival for males were, on average, 4.1%,5.7% and 8.1% units at 5, 10 and 14 years, respectively.With censored data, the Pohar-Perme method tended togive longer confidence intervals than the gold standard


(Table 2). The Ederer II method did so only with theheaviest censored data, whereas otherwise the confi-dence intervals were shorter than those of the gold stan-dard. Within data of the same closing year, the averagelengths of the confidence intervals of the Pohar-Permemethod were 5–8%, 28–39% and 66–75% longer at 5,10 and 14 years, respectively, than those of the EdererII method.




Table 2Differences (in % units, average of 20 sitesa) to the point estimate and the length of confidence interval of gold standard of net survival (PoharPerme, exact follow-up times for closing year 2010) at 5, 10 and 14 years by method, program and level of data grouping, for male cancer patientsdiagnosed in Finland in 1981–1995 and followed-up until the end of three different closing years.

Follow-up time(years)

Closingyear

Ederer II Pohar Perme

Annualb Monthly Exact Annual Monthly Exact

R STATA R STATA R R STATA R STATA R

Difference to the point estimate of gold standard (49.88%, 42.60% and 38.91% at 5, 10 and 14 years, respectively)

5 1995 1.93 �0.20 0.15 0.00 �0.02 1.82 �0.36 �0.14 �0.32 �0.321999 0.95 0.26 0.45 0.42 0.39 0.76 0.03 0.11 0.06 0.042010 0.74 0.23 0.40 0.40 0.37 0.51 �0.02 0.05 0.02 0

10 1995 3.27 �0.37 0.35 0.10 0.08 3.41 �0.95 �0.51 �0.85 �0.861999 2.49 0.42 0.97 0.86 0.82 2.36 �0.35 �0.06 �0.27 �0.292010 1.77 0.60 1.11 1.07 1.04 1.45 �0.15 0.13 0.01 0

14 1995 5.33 �0.24 0.68 0.27 0.19 6.02 �1.77 �1.24 �1.91 �2.021999 4.14 0.92 1.75 1.55 1.49 4.35 �0.35 0.01 �0.36 �0.422010 2.80 1.21 1.94 1.89 1.84 2.48 �0.15 0.22 0.03 0

Difference to the length of confidence interval of gold standard (4.11%, 5.66% and 8.09% units at 5, 10 and 14 years, respectively)

5 1995 �0.16 0.17 0.15 0.18 0.18 0.13 0.42 0.45 0.49 0.481999 �0.54 �0.24 �0.27 �0.23 �0.24 �0.29 �0.03 �0.01 0.03 0.022010 �0.54 �0.26 �0.28 �0.25 �0.25 �0.29 �0.05 �0.03 0.01 0

10 1995 �0.07 0.06 0.10 0.13 0.12 2.13 2.13 2.26 2.36 2.271999 �1.10 �0.93 �0.90 �0.88 �0.89 0.63 0.67 0.80 0.85 0.822010 �1.47 �1.34 �1.31 �1.29 �1.30 �0.12 �0.12 �0.01 0.02 0

14 1995 0.54 0.90 1.11 0.54 1.18 7.00 6.83 7.49 7.96 7.601999 �2.14 �2.07 �1.97 �2.64 �1.96 2.53 1.95 2.38 2.46 2.322010 �3.41 �3.37 �3.31 �4.02 �3.30 0.12 �0.28 0.01 0.07 0

a Cancers of the liver and gallbladder not included as no results were estimable for them at 14-year follow-up with closing date at the end of 1995.b Levels of data grouping: annually grouped, monthly grouped and exact follow-up times. In R, all the events (deaths and censorings) were placed

in mid-points of the respective follow-up intervals.


The results obtained for females were quite compara-ble with those obtained for males (available from thefirst author on request).

4. Discussion

The recommendation [7] to use the Pohar-Permemethod [4] is based on the fact that, unlike the tradi-tional relative survival methods, it gives unbiased esti-mates. This, however, holds true provided that thefollow-up times are recorded accurately and used assuch and when there is no informative censoring of theobserved survival. The former condition cannot alwaysbe met in practical applications due to, e.g. non-avail-ability or confidentiality of the data whereas the lattercondition can be guaranteed only with a complete fol-low-up. Fortunately, with the Finnish Cancer Registry’sdata, both of these two conditions can be met, and thusit is possible to study the importance of these conditionswhen they are not met in practice.

The site-specific gold standards were prone to ran-dom variation. Therefore, it was more difficult to assessthe magnitude of bias by site. Averaging the net survivalestimates over the sites retains the unbiasedness of the


gold standard and gives case-mix (site) adjusted compar-isons, in which each site has the same weight.

As the computer program [10] in R requires accuratefollow-up times it was necessary to decide how to pro-duce data grouped into follow-up intervals by year ormonth of follow-up. The old actuarial choice was toplace all the events in the middle of the interval. Withannually grouped data, this approach proved to beclearly unacceptable. There were many ties betweenobserved and censored survival times, and patientswhose survival times were censored at the mid-point ofthe interval were assumed to remain at risk of dying atthe mid-point according to the practice suggested origi-nally by Breslow [12] for handling tied survival observa-tions in the Cox proportional hazards analyses.

Exact dates of deaths and diagnosis may not be avail-able or accessible (e.g. due to confidentiality and dataprotection regulations). On the other hand, the closingdate of the study is known allowing more accurate fol-low-up times for censored patients. In an alternativeanalysis, ties were removed by using exact follow-uptimes for patients alive at the end of follow-up. The esti-mates of this alternative were very close to those basedon the exact data in the heaviest censored situation.However, the corresponding estimates were deviating,





when there was no censoring. It seemed that the R pro-gram worked better, when event times were more heter-ogeneous and not centred at the mid-points of follow-upintervals. A feasible solution in R might be to drawevent times of each interval from a uniform distribution.In a routine use of the net survival method, however,these kinds of tricks are not really applicable.

Censoring of the observed survival was informative,because patients were diagnosed over a long calendarperiod during which the distributions of covariates thataffect survival (e.g. age at diagnosis) have changed. Thisemerges, e.g. in ageing populations, when the mean ageof diagnosed patients increases over the period of diag-nosis, and therefore, older patients have on averageshorter times from their diagnosis to the end of thestudy. The impact of this type of informative censoringon various net survival methods has been studied usingsimulated accurate follow-up data under various scenar-ios [13]. Recently, Rebolj Kodre and Pohar Perme pro-posed a method of inverse probability weighting thatallows this type of informative censoring [14]. Themethod requires estimating probabilities of censoringtimes and was not used in our study, as it is not availablein the current computer programs. Moreover, the Eder-er II method was not considered in that paper.

A second reason for informative censoring was thatthe prognosis of the patients changed over the periodof diagnosis: patients whose follow-up times were cen-sored earlier had often better prognosis than earlierdiagnosed patients who remained under follow-up. Thistype of informative censoring cannot be corrected forwithout extrapolation of survival beyond the closingdate, and therefore, it is not a problem of the methods,as any corrections are subject to pure guessing [14]. Thedifferent sources of bias can be controlled for in simula-tion-based studies. In empirical data, the second type ofinformative censoring cannot be eliminated withouteliminating the first type of informative censoring, too.

In this study, results are based on real data with realprogressive censoring owing to early closing dates of fol-low-up. These real patterns of censoring may well be dif-ferent in different countries, but a good net survivalmethod should be resistant against biases any patternof informative censoring might cause. As opposed tosimulated data, however, the targeted gold standardunder complete follow-up and accurate follow-up timesis still a random quantity with a standard error.

When the data are censored, the Ederer II methodcould be preferred as it gives results closer to the goldstandard. This may, however, be a characteristic dueto the particular censoring pattern in the Finnish data,as the positive bias in the Ederer II method was compen-sated by the negative bias due to informative censoringof the observed survival.

In the setting of cause-specific survival, deaths due toother causes than cancer are considered as censoring


events. The Kaplan–Meier estimator is biased underinformative censoring but can be corrected for by fol-lowing the idea of inverse probability weighting [15] thatwas adapted to the framework of relative survival byPohar Perme et al. [4]. Of course, informative censoringcaused by changes in patients’ prognosis cannot be cor-rected for in cause-specific survival, either. In cause-spe-cific survival, cause of death is not always correct,whereas, in the framework of relative survival, theexpected survival estimated from the mortality rates ofnational population may not always be relevant forthe patients [8]. This is the main reason for differencesbetween results of the two approaches which both aimto estimate net survival.

In the Pohar-Perme method the few observations inthe old age groups get large weights, because the com-peting risks of death do not leave for older ages suf-ficiently sizable materials on which to base reliableestimation [16]. This can be seen in the standarderrors and the confidence intervals based on them.The Ederer II method gives estimates that have dis-tinctively narrower confidence intervals than thosederived by the Pohar-Perme method. It is likely thatin this respect the gold standard is far from a truegold standard.

The age-standardisation is not a solution for remov-ing biases related to the level of grouping and informa-tive censoring or inaccuracies related to intervalestimation. Statistical modelling [17–19] is capable offinding the essence also in net survival analyses andshould be developed into a standard for routine use ona large scale. Otherwise, it is crucial to report in whichway the net survival results have been obtained.

Net survival is especially useful for evaluating differ-ences in cancer survival between population groups andover time, when the expected mortality differs across thegroups we wish to compare. Thus, in future studies, itwould be important to assess whether the choice of theapproach could actually affect results of comparisonsbetween population groups.

A clear recommendation to use the net survivalmethod by Pohar Perme et al. is conditional on the com-pleteness of follow-up and the time point of follow-up atwhich the net survival is wished to be estimated. Bothmethods perform well in the estimation of net survivaluntil 5 years. In complete follow-up, the Pohar-Permeestimator can be preferred in terms of bias but point esti-mates of the long-term net survival should be interpretedwith due caution, because the estimator becomes prone torandom variation. In incomplete follow-up, the estimatorof the Pohar-Perme method may be biased if censoring ofthe observed survival is informative, even if the recentlydeveloped weighting method [14] was used. Irrespectiveof the method, the actuarial approach in STATA shouldbe utilised, if data are grouped into annual follow-upintervals. Following this recommendation, the results





given by different approaches differ on average by 1–2%units depending on the context.

Conflict of interest statement

None declared.

Acknowledgement

This work was supported by a grant from the FinnishCancer Foundation.

Appendix A. Supplementary data

Supplementary data associated with this article canbe found, in the online version, at http://dx.doi.org/10.1016/j.ejca.2013.09.019.

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