An overview and some recent advances in statistical methods for population-based cancer survival analysis

Transcription

1 An overview and some recent advances in statistical methods for population-based cancer survival analysis Paul W Dickman 1 Paul C Lambert 1,2 1 Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden 2 Department of Health Sciences, University of Leicester, UK 24 September 2014 Dept. of Statistics, University of Uppsala

2 Overview of today s talk About me and my department. The state of epidemiology and biostatistics as research disciplines. Measures used in cancer control; why study patient survival. Intro to relative survival (excess mortality) and why it is the measure of choice for population-based cancer survival analysis. Flexible parametric models (Royston-Parmar models). Paul Dickman Population-Based Cancer Survival 24 September by a per-caput es, county councils than local health ance of power is nt has been ever nce with defined Sweden, like most llocating a steadily mestic product to 82, at 9-7%. Since e (figure) and the About 1-5% of this ally-defined longare, from county o doubt, however, as one of the most s. Since 1982 we ions at hospital and savings campaigns, or equipment and rts to monitor and nalise services by en units at countysort are likely to one that generated re the watchwords e control, was the o providers and gan doing this in s operate a split of Sweden, with its About me clinical autonomy than their opposite numbers in, say, the USA) to managers. Born in Sydney Australia; studied mathematics and statistics in Newcastle (Australia). Private practice? Traditionally, these services have been integrated with the public system, and practitioners have charged according to a fee schedule that is technically Worked in health services research; attached to national health insurance. dabbled in industrial process control and qualitythus, to limit improvement. public costs, entry into private practice has lately been Arrived in Sweden November 1993 for a 10 month visit to tightly controlled. What happens cancer epidemiology unit at Radiumhemmet. next depends very much Stayed in Sweden on the fate of the for most of my PhD. public system. With the economy faltering and public spending under renewed pressure, we Short Postdoc periods at Finnish Cancer Registry and Karolinska can expect Institutet (cancer a further epidemiology). decline in the proportion of GDP that goes to health care. Although public perceptions of the Joined services MEBremain March favourable, 1999, attractedfurther by strong reductions research may well environment provoke a and flight possibilities into the in register-based private sector-a epidemiology. sensitive issue Not for a mathematical a nation that statistician. has by no means lost its taste for equity. Such a development is very much a function of how much public money is spent Paul Dickman Population-Based Cancer Survival 24 September I found paradise! [1] on health services and how well medical quality is maintained. So far there are no objective signs of a decline in quality as a result of the reforms of the 1990s. We are watching carefully. A paradise for epidemiologists? Hans-Olov Adami The Lancet 1996;2:588 For three reasons-the structure of its health system, the existence of nationwide registers, and the systematic use of national registration numbers-sweden offers exceptional opportunities for epidemiological research. The public medical service is divided into 27 financially and I administratively would add willingness independent of the public to areas contribute (25 counties to research. and 2 cities), each of which provides basic health care at local and county hospitals. A regional hospital in each of the six health-care regions provides highly specialised services to Paul Dickman Population-Based Cancer Survival 24 September several areas. Charges are kept low enough to ensure that

3 at low cost. Indeed, ibitively expensive, participation and the costs for record records are stored research purposes, and supplemented, ted" within registerd to population and all problems in otheses cannot be at existing registers exposures, patient xample, few if any allow dietary studies large representative patient samples, and for follow-up over long periods with regard, for instance, to subsequent hospital admissions, cancer incidence, or outcomes in different time periods, geographical areas, or hospital categories. The final challenge is to initiate large-scale prospective studies. In this respect, Sweden has so far shown a lack of vision and foresight. We have no counterparts to the richly productive cohort studies initiated as early as the 1950s in the UK and later the USA, notably among doctors, nurses, and other health professionals. A large obstacle is the economic factor. In Sweden we have no funding mechanism to cover the costs of initiating a sizeable prospective study. Longstanding barriers need to be We have subsequently met some of the challenges crossed-those between disciplines, between funding bodies, and between laboratory science and observational research. We eagerly await initiatives from the major funding agencies to take us beyond the tradition of smallscale thinking, provincial passivity, and self-sufficiency. Paul Dickman Population-Based Cancer Survival 24 September Paul Dickman Population-Based Cancer Survival 24 September Paul Dickman Population-Based Cancer Survival 24 September

4 on, permit simple and prevalence of by linking exposure term consequences al procedures, and iduals followed up fied in the registers; ently from sources scriptions, payrolls, udies of cancer, the le for rapid case e registers allow on-based. ount two important arch-namely, low ionable validity. The million, defines the ailable for study. In are sufficient for outcomes. Internal of observational lways, facilitated by (occupation, birth l procedure) can be recall that hamper, virtually complete at low cost. Indeed, ibitively expensive, participation and the costs for record records are stored research purposes, and supplemented, ted" within registerd to population and all problems in otheses cannot be at existing registers formally Likewise, factor such as smoking, alcohol intake, physical exercise, or drug use is a potential confounder in an epidemiological analysis, adequate adjustment for the factor in question may be impossible because such data are not recorded. Studies of patients may be hampered by a lack of data on the severity or stage of disease, on the treatment given, or on "soft" outcomes such as remission, relapse/recurrence, or sequelae. Thus, epidemiologists in Sweden have to recognise not only the enormous potential but also the limitations of the existing databases. There is a widespread notion that record linkage studies are an easy and quick way to produce results-and publications. This gross misperception can lead investigators to produce invalid results and deceive readers into accepting them uncritically. The compiling of information from different sources offers just as many challenges, pitfalls, and possibilities as does epidemiological research in general. Any investigator who uses registers needs to be familiar with the broad Paul Dickman Population-Based Cancer Survival 24 September repertoire of epidemiological methods, the systematic errors that threaten validity, and the biological and clinical realities that underlie the diagnostic codes and medical Little progress in other areas interventions. Prospects Evidently, Swedish epidemiologists have exceptional opportunities to add to knowledge in many areas of medicine. They do, however, face some important challenges. The large nationwide registers need to be better characterised-for example, with regard to completeness, agreement with hospital records, validity of diagnoses, and changes in registration over time. This sort of quality control will be much aided by the Epidemiology Centre recently established within the National Board of Health and Welfare, responsible for the maintenance of several registers. So far, registers have been used mostly in the realm of traditional epidemiology-ie, in the search for aetiology. A second challenge, an educational one, will be to foster the Paul Dickman Population-Based Cancer Survival 24 September use of linked register data in clinical research and health care assessment. Clinicians need to be persuaded about the possibilities that are opening, and encouraged to New challenges arise seek training in epidemiological methods. For example, the Inpatient Register is a remarkable resource for selection of large representative patient samples, and for follow-up over long periods with regard, for instance, to subsequent hospital admissions, cancer incidence, or outcomes in different time periods, geographical areas, or hospital categories. The final challenge is to initiate large-scale prospective studies. In this respect, Sweden has so far shown a lack of vision and foresight. We have no counterparts to the richly productive cohort studies initiated as early as the 1950s in the UK and later the USA, notably among doctors, nurses, and other health professionals. A large obstacle is the economic factor. In Sweden we have no funding mechanism to cover the costs of initiating a sizeable prospective study. Longstanding barriers need to be crossed-those between disciplines, between funding Paul Dickman Population-Based Cancer Survival 24 September bodies, and between laboratory science and observational

5 New challenges arise Eur J Epidemiol (2014) 29: DOI /s COMMENTARY The European Parliament proposal for the new EU General Data Protection Regulation may severely restrict European epidemiological research Olof Nyrén Magnus Stenbeck Henrik Grönberg Received: 20 December 2013 / Accepted: 25 April 2014 / Published online: 7 May 2014 Ó The Author(s) This article is published with open access at Springerlink.com About MEB (Dept. of Medical Epidemiology and Biostatistics) Name change in 2002 (adding and Biostatistics ). O. Nyrén (&) H. Grönberg Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden olof.nyren@ki.se M. Stenbeck Division for Insurance Medicine, Department of Clinical Neuroscience, Karolinska Institutet, Stockholm, Sweden Paul Dickman Population-Based Cancer Survival 24 September In January 2012, the European Commission presented the on European data analysis and, in turn, to impede efforts to draft of a new General Data Protection Regulation (GDPR) improve public health and welfare in the union and to the European Parliament and the Council of the European Union. The GDPR is planned to replace the 1995 In October 2013, after a long period of negotiations elsewhere. Directive 95/46/EC, which constitutes the present European legal framework for processing of personal data. mittee voted on its final amendments to the Commission s surrounded by intense lobbying efforts, the LIBE Com- Hence, this new binding Regulation will lay the legal proposal [1]. Alas, although some improvements were foundation for future European epidemiology based on noted, the overall outcome was largely disappointing from personal data, including register-based research. an epidemiological perspective. The main points are summarized in the following. The intentions behind the new GDPR are commendable: [1] to protect the fundamental rights and freedoms of The first Articles with specific relevance for scientific individuals, Established in particular their at KI right1997 to protection as Medical of personal data, in a society where commercial enterprises and and lawfulness (Article 6) of personal data processing. research Epidemiology are concerned(mep) with generalwhen principles (Article 5) authorities Hans-Olov have rapidly increasing Adamicapabilities moved to the collect, Department Article 5b lays ofdown Cancer that personal data shall be collected store and combine personal information; and [2] to facilitate free movement of personal data within the European be further processed in a way incompatible with those for specified, explicit and legitimate purposes and may not Epidemiology from UU. Has grown from 40 to 300 FTE staff. Union through Hans-Olov a uniformadami legislation was/is in all member a very states. strong purposes supporter ( purpose limitation ). of biostatistics This corresponds to an The Commission s proposal is being reviewed and identical principle in the current 95/46/EC Directive. amended and independently invested by in the Council developing of the European biostatistics. However, Collaboration in Directive 95/46/ECwith there was an exemption Union and the European Parliament. In the Parliament, for research, namely that further processing of data for Reinhold Bergström (and others) instilled Hans-Olov with a deep Committee on Civil Liberties, Justice and Home Affairs historical, statistical or scientific purposes is not to be (LIBE) respect was assigned for thebiostatistics/biostatisticians. task of formulating Parliament s amendments. The first draft by the chairman of the long as Member States provide appropriate safeguards. considered as incompatible with the original purpose as Committee, Today, Jan Philipp 4 Professors Albrecht, was criticized and 3for Associate insufficient consideration to the needs of epidemiological matically reducing the scope for data sharing between ThisProfessors exemption was omitted (lektorer) in LIBE s ofamendments, dra- biostatistics at MEB (all foreign). research. The proposed text threatened to restrict currently research groups and severely restraining the use of retrospective (historic) cohort study designs. Such studies existing possibilities to produce scientific evidence based utilize old data collections with exposure information that was collected for other purposes than the current scientific research. Thus, hundreds of thousands person-years of follow-up may have accumulated already at the start of the retrospective cohort study, making it possible to immediately test important public health hypotheses that would otherwise take decades to address. A typical example is the study of long-term health effects of Swedish snus (snuff) in Paul Dickman Population-Based Cancer Survival 24 September My research interests 123 Primary research interests are in the development and application of methods for population-based cancer survival analysis, particularly the estimation and modeling of relative survival. Recent interest has been in presenting information on patient survival in a manner relevant for patients and clinicians. General interest in statistical aspects of the design, analysis, and reporting of epidemiological studies along with studies of disease aetiology, with particular focus on cancer epidemiology and perinatal/reproductive epidemiology. Collaborate closely with Paul Lambert (Biostatistician at University of Leicester) and Magnus Björkholm (Haematologist). Paul Dickman Population-Based Cancer Survival 24 September

6 r year 100,000 per y rate per 1 In ncidence or mortality Incidence Mortality Survival Lung cancer incidence, mortality and survival (age-standardised) England, , by sex Men Women Women Men Five-ye ear relativ ve surviva al (%) Year of death / Year of diagnosis 0 Paul Dickman Population-Based Cancer Survival 24 September Lung cancer incidence in Sweden Paul Dickman Population-Based Cancer Survival 24 September International comparisons of survival are hot! Paul Dickman Population-Based Cancer Survival 24 September

7 Editorials represent the opinions of the authors and not Not everyone is a fan of cancer survival [2] necessarily those of the BMJ or BMA For the full versions of these articles see bmj.com EDITORIALS UK cancer survival statistics Are misleading and make survival look worse than it is RESEARCH, p 335 In the linked article, Autier and colleagues report that (population based) breast cancer mortality rates have fallen over vival calculations based on registry data make UK cancer survival rates seem significantly worse than they really are. Valerie Beral professor the past two decades in many European countries, with a Information in cancer registries on deaths from cancer of epidemiology, Cancer Epidemiology Unit, University of greater decline in the United Kingdom than in any other is virtually complete because every death certificate that Oxford, Oxford OX3 7LF large country. 1 That the UK is leading Europe in the speed mentions cancer is automatically sent to one of the regional pa.valerie.beral@ceu.ox.ac.uk with which national breast cancer mortality rates are falling registries that, between them, cover the UK. That cancer is Richard Peto professor of medical statistics and is in stark contrast to, and at first sight difficult to reconcile then registered, and further information is sought (not always epidemiology, Clinical Trial Service with, claims that survival after breast cancer onset is worse successfully) from medical records. Death certificates have Unit and Epidemiological Studies in the UK than elsewhere in western Europe. 2 for decades played an important role in the way UK registries Unit (CTSU), University of Oxford, Oxford OX3 7LF The unpromising UK cancer survival estimates are, however, identify people with cancer. Without this source of informa- Competing interests: Both misleading. In contrast, population based mortality tion, many such cancers could have been missed; even with authors have completed the trends are reasonably reliable (at least in middle age, for it, many people who die of cancer may have no record other Unified Competing Interest form at example, people aged years) because a death certificate than the death certificate ever traced by the registry ( death (available on request from either is legally required before someone can be buried certificate only cases) or may have had only the later phase author) and declare no competing or cremated. Although the certified cause of death can be of their illness traced by the registry. interests, other than long term funding from the UK Medical wrong, particularly in older people (for example, those over If the first months or years of the illness are never traced, Research Council and Cancer 70 or 80 years), in younger people errors in death certifica- the earliest event registered may be some aspect of cancer Research UK. Paul Dickman Population-Based should have Cancer relatively Survival little effect on 24 the September assessment 2014of recurrence. The date of 17 this recurrence would then be taken Provenance and peer review: breast cancer mortality trends in western Europe or North as the date from which survival rates are calculated. This Commissioned; externally peer reviewed. America. 3 makes short term survival look misleadingly worse in the UK In contrast with death registration, cancer registration than in countries such as Sweden where, in contrast to the Cite this as: BMJ 2010;341:c4112 is not statutory in the UK and is known to be somewhat UK, cancer registration is compulsory and death certificates June 2011 Response to Beral & Peto by doi: /bmj.c4112 incomplete. 4 6 Partly because of this incompleteness, sur- are not used for case finding. Because recurrence and death 80 are often separated by less than a year, such biases could Coleman et al. (including Dickman & Lambert) substantially reduce the calculated one year survival rate in the UK, but not in Sweden; and the main difference between 70 UK and Swedish cancer survival estimates arises during the first year This editorial is unfounded, untenable and inconsistent. For obvious Itreasons, has calculations of UK survival rates conventionally exclude death certificate only cases. Efforts in UK elicited critical responses 50 (refs) but the BMJ editor registries reports to limit such thecases by intensive searching for at least some medical record that mentions the cancer found on the authors were too busy to defend it. In fact, the editorial is 40 indefensible. We suggest you withdraw it. death certificate have reduced their number. 6 If, however, the only medical record found by such searches relates to a recurrence and not to the first diagnosis of the cancer, the The editorial is unfounded. 30 The provocative title recent UKreduction cancer in the proportion of death certificate only cases could actually be aggravating artefacts in UK cancer survival statistics are misleading and make survival look worse 20 statistics on short term survival rates. than it is is pure conjecture. The article slides directly Moreover, from UK survival statistics are further distorted by 10 the absence of any registration at all of some non-fatal cases. assertion to conclusion, with no evidence in between. Unregistered survivors are (again, for obvious reasons) not included the numbers at risk for survival calculations. In 0 The editorial thus undermines research designed to the catchment explainarea the of one UK registry an estimated 23% of UK cancer survival deficit, as well as policy designed cancer survivors were still not registered five years after their Year to reduce disease was first diagnosed. 5 (The proportion missed will the deficit. That Breast cancer is a mortality disservice rates in women to cancer aged in patientsvary inby the region UK. and over time, but no other formal estimate the United Kingdom. *Mean of annual rates in the seven component five year age groups. A mean rate of 60 per was found.) Although electronic hospital admission data corresponds to a 2% risk of death at ages are improving the completeness of UK cancer registration, Paul Dickman years. Calculated from World Health Organization mortality the currently available electronic records do not distinguish Population-Based Cancer Survival 24 September estimates and United Nations population estimates explicitly between the first diagnosis and later events. 8 C ancer Death rate/ women, age standardised* BMJ 14 AUGUST 2010 VOLUME Beral & Peto arguments debunked [3] FULL PAPER British Journal of Cancer (2013) 108, doi: /bjc Keywords: cancer registration; registration errors; relative survival; population-based data; simulation A comprehensive assessment of the impact of errors in the cancer registration process on 1- and 5-year relative survival estimates M J Rutherford*,1, H Møller 2 and P C Lambert 1,3 1 University of Leicester, Department of Health Sciences, Leicester LE1 7RH, UK; 2 Section of Cancer Epidemiology and Population Health, Division of Cancer Studies, King s College London, Medical School, London SE1 9RT, UK and 3 Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm SE , Sweden Paul Dickman Population-Based Cancer Survival 24 September Background: When making international comparisons of cancer survival, it is essential reported differences are real effects and not an artefact of potential errors in cancer registration.

8 From Dickman & Adami (2006) [4] Interpreting trends in cancer patient survival Until primary prevention programmes succeed to the point of eradicating cancer, doctors must effectively diagnose and treat the cancers that arise and require a means of measuring progress in this specific area. Patient survival rates provide such a measure whereas population mortality rates may not as they also reflect changes in incidence. For example, lung cancer mortality rates are decreasing in many countries, not because we have become better at diagnosing and treating those individuals that develop lung cancer butcancer becausein Norway 2012 successful primary prevention has reduced lung cancer incidence. Paul Dickman Population-Based Cancer Survival 24 September Figure 10-M: Breast (ICD-10 C50) Breast cancer in Norway [5] 100 PURPOSE AND AIMS Primary aims To identify women at high risk of breast cancer in need of preventive 70interventions, such as risk-reducing medications Incidence 70 To identify the dose of tamoxifen with the highest benefit vs. harm ratio Overall purpose of the project To reverse the increase in number of women diagnosed with breast cancer 40 using a primary preventive strategy. 40 Rates per (World) Trends in incidence and mortality rates and five-year rel 30 SURVEY OF THE FIELD PRISMA A RANDOMIZED CLINICAL TRIAL FOR PREVENTION OF BREAST CANCER Females APPLICATION TO VETENSKAPSRÅDET, SEPTEMBER 15, 2014 Survival Mortality The number 20 of women diagnosed with breast cancer is increasing all over the 20world. In Europe more than 360,000 women are diagnosed and 90,000 die from the disease annually 10 [1]. In Sweden, one woman in eight will be diagnosed with breast 10 cancer, corresponding to nearly one woman being diagnosed with breast cancer every hour [2]. 0 0 In contrast to breast cancer incidence, the incidence of myocardial infarction in women is at a constant decrease 1975 (Figure ) The 1990 decrease 1995 in 2000 myocardial 2005 infarction 2010 is due to the ability Paulto Dickman identify Population-Based risk factors Cancer and Survival the possibility 24 September to influence 2014 them in a primary 21 preventive setting. High cholesterol and blood pressure, increased body mass index (BMI), low physical activity and tobacco are well known risk factors for cardio-vascular disorders. They are Trends in incidence Figure easily detected 10-O: and in Prostate relatively Sweden(ICD-10 easily to influence C61) with beta-blockers, weight loss, increased physical activity, etc year relative survival (%) Rates per (World) Figure Figure 10 FIGURE 1: INCIDENCE OF BREAST CANCER AND MYOCARDIAL INFARCTION AMONG SWEDISH WOMEN < 80 YEARS [NATIONAL BOARD OF HEALTH AND WELFARE] Males Rates per (World) Risk factors 12.5 for breast cancer are not as strongly associated with the disease 10 and much more difficult to detect and influence. An amalgamation of lifestyle factors, genetic 0.0 determinants, so-called mammographic density and plasma biomarkers 0 forms the basis Paul of Dickman future complex Population-Based risk prediction Cancer Survival models. 24 September year relative survival (%) Rates per (World)

9 How might we measure the prognosis of cancer patients? Total mortality (among the patients). Our interest is typically in net mortality (mortality associated with a diagnosis of cancer). Cause-specific mortality provides an estimate of net mortality (under certain assumptions). When estimating cause-specific mortality only those deaths which can be attributed to the cancer in question are considered to be events. cause-specific mortality = number of deaths due to cancer person-time at risk The survival times of patients who die of causes other than cancer are censored. Paul Dickman Population-Based Cancer Survival 24 September Need to consider competing risks [6] Figure 1 The competing risks multi-state model. Paul Dickman Population-Based Cancer Survival 24 September Many synonyms for the same concept Net probability of death due to cancer = Probability of death in a hypothetical world where the cancer under study is the only possible cause of death Crude probability of death due to cancer = Probability of death in the real world where you may die of other causes before the cancer kills you Net probability also known as the marginal probability. Crude probability also known as the cause-specific cumulative incidence function (Geskus) or the cumulative incidence function. Paul Dickman Population-Based Cancer Survival 24 September

10 Net (left) and crude (right) probabilities of death in men with localized prostate cancer aged 70+ at diagnosis (Cronin and Feuer [7]) Paul Dickman Population-Based Cancer Survival 24 September Should we use crude or net survival? 1 Comparing patient survival between countries. 2 Studying temporal trends in patient survival. 3 Communicating prognosis to patients. Paul Dickman Population-Based Cancer Survival 24 September Cause-specific survival can estimate net survival (assuming conditional independence) Using cause-specific methods requires that reliably coded information on cause of death is available. Even when cause of death information is available to the cancer registry via death certificates, it is often vague and difficult to determine whether or not cancer is the primary cause of death. How do we classify, for example, deaths due to treatment complications? Consider a patient treated with radiation therapy and chemotherapy who dies of cardiovascular disease. Do we classify this death as due entirely to cancer or due entirely to other causes? Paul Dickman Population-Based Cancer Survival 24 September

11 All-cause mortality for males with colon cancer and Finnish population Mortality Rate (per 100,000 person years) General population Colon cancer patients Age Paul Dickman Population-Based Cancer Survival 24 September Relative survival aims to estimate net survival (still need conditional independence) We estimate excess mortality: the difference between observed (all-cause) and expected mortality. excess = observed expected mortality mortality mortality Relative survival is the survival analog of excess mortality the relative survival ratio is defined as the observed survival in the patient group divided by the expected survival of a comparable group from the general population. relative survival ratio = observed survival proportion expected survival proportion Paul Dickman Population-Based Cancer Survival 24 September Cervical cancer in New Zealand Life table estimates of patient survival Women diagnosed with follow-up to the end of 2002 Interval- Interval- Effective specific specific Cumulative Cumulative Cumulative number observed relative observed expected relative I N D W at risk survival survival survival survival survival Paul Dickman Population-Based Cancer Survival 24 September

12 Relative survival example (skin melanoma) Table 1: Number of cases (N) and 5-year observed (p), expected (p ), and relative (r) survival for males diagnosed with localised skin melanoma in Finland during Age N p p r Relative survival controls for the fact that expected mortality depends on demographic characteristics (age, sex, etc.). In addition, relative survival may, and usually does, depend on such factors. Paul Dickman Population-Based Cancer Survival 24 September Breakthrough paper in 2012; Biometrics 68, An unbiased estimator for net survival [8] March 2012 DOI: /j x On Estimation in Relative Survival Maja Pohar Perme, 1, Janez Stare, 1 and Jacques Estève 2 1 Department of Biostatistics and Medical Informatics, University of Ljubljana, Vrazov trg 2, SI-1000 Ljubljana, Slovenia 2 Université Claude Bernard, Hospices Civils de Lyon, Service de Biostatistique, 162, Avenue Lacassagne Lyon Cedex 03, France maja.pohar@mf.uni-lj.si Summary. Estimation of relative survival has become the first and the most basic step when reporting cancer survival statistics. Standard estimators are in routine use by all cancer registries. However, it has been recently noted that these estimators do not provide information on cancer mortality that is independent of the national general population mortality. Thus they are not suitable for comparison between countries. Furthermore, the commonly used interpretation of the relative survival curve is vague and misleading. The present article attempts to remedy these basic problems. The population quantities of the traditional estimators are carefully described and their interpretation discussed. We then propose a new estimator of net survival probability that enables the desired comparability between countries. The new estimator requires no modeling and is accompanied with a straightforward variance estimate. The methods are described on real as well as simulated data. Key words: Age standardization; Cancer registry data; Competing risks; Net survival; Relative survival; Survival analysis. 1. Introduction observed hazard is larger than the population hazard. Survival probability Paul Dickman of cancer patients Population-Based has been used Cancer for many Survival Under 24 September this assumption, 2014 we use the term excess hazard for the hazard due to the disease and we have the 33 years as one of the main tools for evaluation of therapeutic advances. With improved treatments and prognosis, studies relation often now have long follow-up times and it is common to have observed hazard = population hazard+ excess hazard. a substantial proportion of deaths from causes other than the cancer under study. In the usual situation, the cause of death (1) is unavailable or unreliable. Hence the field of relative survival has developed in which observed deaths are compared with A survival function derived from the excess hazard alone is termed the net survival. those expected from general population life tables. We distinguish two goals: In this article, we shall focus on three estimators in widespread use in relative survival. We will refer to them (1) To compare the observed survival (SO) tothesurvival as Ederer I (Ederer, Axtell, and Cutler, 1961), Hakulinen of a disease-free group having the same demographic (Hakulinen, 1982), and Ederer II (Ederer et al., 1961, p. 110) characteristics as the study group. If the expected general population survival is SP, the comparison is made and define them in Section 3 below. Although all three were proposed as variants for estimating the denominator of the relative survival ratio, they have using the ratio also been interpreted as estimators of net survival. We will SO (t) SR (t) = SP (t). show that this is not generally correct. When the excess and the population hazard are not affected by any common covariates, all methods to be discussed in this article estimate the same population quantity. In practice, however, excess hazard almost always depends on demographic variables In the relative survival setting, which approach should one use for estimating net survival? This has been named the relative survival ratio. (2) To estimate survival in the hypothetical situation where the disease under study would be the only possible cause of death. This estimation is made possible by decomposing the observed hazard into the hazard due to the disease and that due to other causes. This decomposition can be carried out if the time to death due to the disease and the time to death due to other causes are conditionally independent given a known set of covariates. We then assume that the hazard due to other causes is given by the population mortality and, therefore, that the A hot topic in our field and a focus of our current research. I won t bore you with the details. (e.g., age) and one of the aims of this article is to find the population quantities that the estimators are estimating in such situations (Sections 2 and 3). Although the concept of net survival may seem too hypothetical to be of interest by itself, it becomes crucial when trying to compare cancer burden between countries, because it is independent of the general population mortality. Up to now, most authors who have produced large sets of survival statistics (Sant et al., 2009, and references therein) C 2011, The International Biometric Society 113 Paul Dickman Population-Based Cancer Survival 24 September

13 Relative survival was estimated to be 50%. Paul Dickman Population-Based Cancer Survival 24 September What does a relative survival of 50% mean? 10-year probabilities of death Measure Age 40 Age 60 Age 80 Net prob. of death (1-rel surv) Crude (actual): cancer death Crude (actual): non-cancer death Crude (actual): any cause death Paul Dickman Population-Based Cancer Survival 24 September European Journal of Cancer 40 (2004) Review Period analysis for up-to-date cancer survival data: theory, empirical evaluation, computational realisation and applications H. Brenner a, *, O. Gefeller b, T. Hakulinen c,d a Department of Epidemiology, German Centre for Research on Ageing, Bergheimer Str. 20, D Heidelberg, Germany b Department of Medical Informatics, Biometry and Epidemiology, University of Erlangen-Nuremberg, Waldstrasse 6, D Erlangen, Germany c Finnish Cancer Registry, Liisankatu 21 B, FIN Helsinki, Finland d Department of Public Health, University of Helsinki, FIN Helsinki, Finland Received 6 August 2003; received in revised form 3 September 2003; accepted 21 October 2003 Abstract Long-term survival rates are the most commonly used outcome measures for patients with cancer. However, traditional longterm survival statistics, which are derived by cohort-based types of analysis, essentially reflect the survival expectations of patients diagnosed many years ago. They are therefore often severely outdated at the time they become available. A couple of years ago, a new method of survival analysis, denoted period analysis, has been introduced to derive more up-to-date estimates of long-term survival rates. Paul WeDickman give a comprehensive Population-Based review of the Cancer new methodology, Survival its 24statistical September background, 2014 empirical evaluation, computational realisation and applications. We conclude that period analysis is a powerful tool to provide more up-to-date cancer sur- 37 vival rates. More widespread use by cancer registries should help to increase the use of cancer survival statistics for patients,

14 Modelling excess mortality Relative Survival Model h(t) = h (t) + λ(t) Observed Mortality Rate = Expected Mortality Rate + Excess Mortality Rate Cox model cannot be applied to model a difference in two rates. It is the observed mortality that drives the variance. Can use Poisson regression (Dickman et al. 2004) [9]. Even better: flexible parametric models (Royston and Parmar 2002 [10], Nelson et al. [11]). Paul Dickman Population-Based Cancer Survival 24 September Flexible Parametric Survival Models [10, 13, 14] First introduced by Royston and Parmar (2002) [10]. Parametric estimate of the baseline hazard without the usual restrictions on the shape (i.e, flexible). Applicable for standard and relative survival models. Can fit relative survival cure models (Andersson 2011) [12]. Once we have a parametric expression for the baseline hazard we derive other quantities of interest (e.g., survival, hazard ratio, hazard differences, expectation of life). Paul Dickman Population-Based Cancer Survival 24 September This paper has been cited over 27,000 times [15] Paul Dickman Population-Based Cancer Survival 24 September

15 The Cox model[15] h i (t x i, β) = h 0 (t) exp (x i β) Advantage: The baseline hazard, h 0 (t) is not directly estimated from a Cox model. Disadvantage: The baseline hazard, h 0 (t) is not directly estimated from a Cox model. Paul Dickman Population-Based Cancer Survival 24 September Quote from Sir David Cox (Reid 1994 [16]) Reid What do you think of the cottage industry that s grown up around [the Cox model]? Cox In the light of further results one knows since, I think I would normally want to tackle the problem parametrically.... I m not keen on non-parametric formulations normally. Reid So if you had a set of censored survival data today, you might rather fit a parametric model, even though there was a feeling among the medical statisticians that that wasn t quite right. Cox That s right, but since then various people have shown that the answers are very insensitive to the parametric formulation of the underlying distribution. And if you want to do things like predict the outcome for a particular patient, it s much more convenient to do that parametrically. Paul Dickman Population-Based Cancer Survival 24 September Example: survival of patients diagnosed with colon carcinoma in Finland Patients diagnosed with colon carcinoma in Finland Potential follow-up to end of 1995; censored after 10 years. Outcome is death due to colon carcinoma. Interest is in the effect of clinical stage at diagnosis (distant metastases vs no distant metastases). How might we specify a statistical model for these data? Paul Dickman Population-Based Cancer Survival 24 September

16 Smoothed empirical hazards (cancer-specific mortality rates) sts graph, by(distant) hazard kernel(epan2) Empirical hazard Not distant Distant Paul Dickman Population-Based Cancer Survival 24 September Smoothed empirical hazards on log scale sts graph, by(distant) hazard kernel(epan2) yscale(log) Empirical hazard Not distant Distant Paul Dickman Population-Based Cancer Survival 24 September Fit a Cox model to estimate the mortality rate ratio. stcox distant No. of subjects = Number of obs = No. of failures = 7122 Time at risk = LR chi2(1) = Log likelihood = Prob > chi2 = _t Haz. Ratio Std. Err. z P> z [95% C.I.] distant Paul Dickman Population-Based Cancer Survival 24 September

17 Fitted hazards from Cox model with Efron method for ties stcox distant, efron Hazard Hazard ratio: 6.64 Not distant Distant Paul Dickman Population-Based Cancer Survival 24 September Hazard Fitted hazards from parametric survival model (exponential) Not distant Distant Hazard ratio: Hazard Ratios Cox: 6.64 Exponential: Paul Dickman Population-Based Cancer Survival 24 September Fitted hazards from parametric survival model (Weibull) Hazard Hazard ratio: 7.41 Hazard Ratios Cox: 6.64 Exponential: Weibull: 7.41 Not distant Distant Paul Dickman Population-Based Cancer Survival 24 September

18 Fitted hazards from parametric survival model (Weibull) Not distant Distant Hazard Paul Dickman Population-Based Cancer Survival 24 September Fitted cumulative hazards from Weibull model Not distant Distant Cumulative Hazard Paul Dickman Population-Based Cancer Survival 24 September Demography and epidemiology: Practical use of the Lexis diagram in the computer age. or: Who needs the Cox-model anyway? Annual meeting of Finnish Statistical Society May 2005 Revised December Bendix Carstensen Steno Diabetes Center, Gentofte, Denmark & Department of Biostatistics, University of Copenhagen bxc@steno.dk Paul Dickman Population-Based Cancer Survival 24 September

19 Hazard Fitted hazards from Poisson model (yearly intervals) Hazard ratio: 6.89 Hazard Ratios Cox: 6.64 Exponential: Weibull: 7.41 Poisson (annual): 6.89 Not distant Distant Paul Dickman Population-Based Cancer Survival 24 September Hazard Fitted hazards from Poisson model (3-months) Hazard ratio: 6.65 Hazard Ratios Cox: 6.64 Exponential: Weibull: 7.41 Poisson (annual): 6.89 Poisson (quarter): 6.65 Not distant Distant Paul Dickman Population-Based Cancer Survival 24 September Hazard Fitted hazards from Poisson model (months) Hazard ratio: 6.64 Hazard Ratios Cox: 6.64 Exponential: Weibull: 7.41 Poisson (annual): 6.89 Poisson (quarter): 6.65 Poisson (months): 6.64 Not distant Distant Paul Dickman Population-Based Cancer Survival 24 September

20 Hazard Hazard ratio: 6.64 Poisson (rcs 5df for ln(time)) Hazard Ratios Cox: 6.64 Exponential: Weibull: 7.41 Poisson (annual): 6.89 Poisson (quarter): 6.65 Poisson (months): 6.64 Not distant Distant Poisson (spline): 6.65 Paul Dickman Population-Based Cancer Survival 24 September Hazard Fitted hazards from flexible parametric model (5df) Hazard ratio: 6.63 Hazard Ratios Cox: 6.64 Exponential: Weibull: 7.41 Poisson (annual): 6.89 Poisson (quarter): 6.65 Poisson (months): 6.64 Not distant Distant Poisson (spline): 6.65 Flexible parametric: 6.63 Paul Dickman Population-Based Cancer Survival 24 September Flexible Parametric Models: Basic Idea Consider a Weibull survival curve. S(t) = exp ( λt γ ) If we transform to the log cumulative hazard scale. ln [H(t)] = ln[ ln(s(t))] ln [H(t)] = ln(λ) + γ ln(t) This is a linear function of ln(t) Introducing covariates gives ln [H(t x i )] = ln(λ) + γ ln(t) + x i β Rather than assuming linearity with ln(t) flexible parametric models use restricted cubic splines for ln(t). Paul Dickman Population-Based Cancer Survival 24 September

21 Fitted cumulative hazards from Weibull model Not distant Distant Cumulative Hazard Paul Dickman Population-Based Cancer Survival 24 September Flexible Parametric Models: Incorporating Splines We thus model on the log cumulative hazard scale. ln[h(t x i )] = ln [H 0 (t)] + x i β This is a proportional hazards model. Restricted cubic splines with knots, k 0, are used to model the log baseline cumulative hazard. ln[h(t x i )] = η i = s (ln(t) γ, k 0 ) + x i β For example, with 4 knots we can write ln [H(t x i )] = η i = γ 0 + γ 1 z 1i + γ 2 z 2i + γ 3 z }{{ 3i } log baseline cumulative hazard + x i β }{{} log hazard ratios Paul Dickman Population-Based Cancer Survival 24 September We are fitting a linear predictor on the log cumulative hazard scale. Survival and Hazard Functions We can transform to the survival scale S(t x i ) = exp( exp(η i )) The hazard function is a bit more complex. h(t x i ) = ds (ln(t) γ, k 0) dt exp(η i ) This involves the derivatives of the restricted cubic splines functions, although these are relatively easy to calculate. Paul Dickman Population-Based Cancer Survival 24 September

22 Paul Dickman Population-Based Cancer Survival 24 September

23 Sensitivity to choice of knots; Simulation study by Rutherford et al. [17] Through the use of simulation, we show that provided a sufficient number of knots are used, the approximated hazard functions given by restricted cubic splines fit closely to the true function for a range of complex hazard shapes. The simulation results also highlight the insensitivity of the estimated relative effects (hazard ratios) to the correct specification of the baseline hazard. Paul Dickman Population-Based Cancer Survival 24 September Simulation Study (Rutherford et al.) [17] Generate data assuming a mixture Weibull distribution. 2.5 Scenario Scenario Hazard rate Hazard rate Time Since Diagnosis (Years) 0.0 Time Since Diagnosis (Years) 2.5 Scenario Scenario Hazard rate Hazard rate Time Since Diagnosis (Years) 0.0 Time Since Diagnosis (Years) Fit models using restricted cubic splines. Paul Dickman Population-Based Cancer Survival 24 September Scenario 3 comparison of Log Hazard Ratios -.4 Cox Model Flexible Parametric Model Paul Dickman Population-Based Cancer Survival 24 September

24 Choice of knots: Scenario 3 8 knots (7 df) 1.0 Survival Function 1.6 Hazard Function S(t) h(t) Time since diagnosis (years) Paul Dickman Population-Based Cancer Survival 24 September Model Selection Estimated hazard and survival functions fairly insensitive to knot location. AIC and BIC can be used as rough guides to choose models. Not crucial (within reason) to inference based on the model. We often present a sensitivity analysis to show this. Could treat number of knots and their locations as unknowns. However, it is an area where more work is still required. Paul Dickman Population-Based Cancer Survival 24 September Implementation in Stata [13] stpm2 available from SSC. ssc install stpm2 All cause survival. stpm2 eng, scale(hazard) df(5) Relative survival. stpm2 eng, scale(hazard) df(5) hazard(rate) Time-dependent effects. stpm2 eng, scale(hazard) df(5) hazard(rate) tvc(eng) dftvc(3) Cure model. stpm2 eng, scale(hazard) df(5) hazard(rate) tvc(eng) dftvc(3) cure Paul Dickman Population-Based Cancer Survival 24 September

25 Example using attained age as the time-scale Study from Sweden [9] comparing incidence of hip fracture of, 17,731 men diagnosed with prostate cancer treated with bilateral orchiectomy. 43,230 men diagnosed with prostate cancer not treated with bilateral orchiectomy. 362,354 men randomly selected from the general population. Study entry is 6 months post diagnosis. Outcome is femoral neck (hip) fracture. Risk of fracture varies by age. Attained age is used as the primary time-scale. Actually, two timescales, but will initially ignore time from diagnosis. Paul Dickman Population-Based Cancer Survival 24 September Estimates from a proportional hazards model stset using age as the time-scale. stset dateexit,fail(frac = 1) enter(datecancer) origin(datebirth) /// id(id) scale(365.25) exit(time datebirth + 100*365.25) Cox Model. stcox noorc orc Incidence rate ratio (no orchiectomy) = 1.37 (1.28 to 1.46) Incidence rate ratio (orchiectomy) = 2.09 (1.93 to 2.27) Flexible Parametric Model. stpm2 noorc orc, df(5) scale(hazard) Incidence rate ratio (no orchiectomy) = 1.37 (1.28 to 1.46) Incidence rate ratio (orchiectomy) = 2.09 (1.93 to 2.27) Paul Dickman Population-Based Cancer Survival 24 September Proportional Hazards Incidence Rate (per 1000 py's) Control No Orchiectomy Orchiectomy Age Paul Dickman Population-Based Cancer Survival 24 September