IJC International Journal of Cancer
Cancer incidence, survival and mortality: Explaining the concepts Special Section Paper
Libby Ellis1, Laura M. Woods1, Jacques Este`ve2, Sandra Eloranta3, Michel P. Coleman1 and Bernard Rachet1 1
Cancer Research UK Cancer Survival Group, London School of Hygiene and Tropical Medicine, London, United Kingdom Biostatistics Division, Hospices Civils de Lyon, Universite Claude Bernard, Lyon, France 3 Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden 2
Cancer incidence, survival and mortality are essential population-based indicators for public health and cancer control. Confusion and misunderstanding still surround the estimation and interpretation of these indicators. Recurring controversies over the use and misuse of population-based cancer statistics in health policy suggests the need for further clarification. In our article, we describe the concepts that underlie the measures of incidence, survival and mortality, and illustrate the synergy between these measures of the cancer burden. We demonstrate the relationships between trends in incidence, survival and mortality, using real data for cancers of the lung and breast from England and Sweden. Finally, we discuss the importance of using all three measures in combination when interpreting overall progress in cancer control, and we offer some recommendations for their use.
Measuring the burden of cancer in a population is essential for public health and cancer control. Reliable estimates of the cancer burden can provide a comprehensive picture of how the impact of cancer varies between geographic areas and between population strata. These estimates, in turn, inform the development of cancer control strategies. Increasingly, survival trends are also being used to assess the efficacy of cancer strategies in reducing the impact of cancer over time. Incidence, survival and mortality are commonplace terms in epidemiology. For many years, they have been the principal measures used in population-based research to explore the causes (incidence) and outcomes of cancer (survival and mortality), and to assess its management. In England, for example, population-based estimates of cancer mortality have been published in some form since the 1850s,1 and national population-based estimates of incidence and survival have been published since the 1950s.2 Nevertheless, confusion and misunderstanding still surround the estimation and interpretation of these indicators. One recent examination of the WHO mortality database showed that among 30 European countries, the UK had one of the largest reductions in breast cancer mortality over the period 1989–2006.3 As breast cancer survival in the late 1990s Key words: cancer, mortality, incidence, survival, methods DOI: 10.1002/ijc.28990 History: Received 26 Nov 2013; Accepted 4 Dec 2013; Online 19 June 2014 Correspondence to: Prof. Michel P. Coleman, Cancer Research UK Cancer Survival Group, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, United Kingdom, Tel.: 144-0-20–7927-2478, Fax: 144-0-20–7580-6897, E-mail: [email protected]
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was lower in the UK than elsewhere in Europe,4 the authors postulated that differences in screening intensity between countries had resulted in spurious survival estimates, and concluded that “mortality data are a more realistic measure of successful cancer control than cancer survival, as the latter is influenced by changes in cancer incidence.”3 This despite the fact that mortality is itself affected by incidence and survival. Again, in 2011, controversy followed publication of an international comparison of survival from four common cancers during the period 1995–2007 in Australia, Canada, Denmark, Norway, Sweden and the UK, based on population-based cancer registry data.5 The study found persistently lower survival in Denmark and the UK for all four cancers, particularly in the first year after diagnosis. The authors noted that the trends in incidence, survival and mortality were broadly consistent. They also pointed out that “mortality is a function of both incidence and survival,” a statement that summarises the obvious point that your chances of dying from a disease depend on your chances of getting it in the first place, and then on your chances of surviving it. An accompanying editorial6 nevertheless dismissed this statement on the basis that colorectal cancer mortality in the UK had declined substantially over time, whilst international differences in incidence and survival had remained fairly constant. Other commentators have joined the debate on the relative merits of mortality, incidence and survival, often arguing fervently for one measure over another.7,8 One group of epidemiologists wrote recently9 that 5-year survival from a given cancer can be obtained from the formula: S5ðC2dÞ=C; where S is the survival, C is the number of cancer patients and d is the number of those patients who died from any cause in the 5 years after diagnosis.9 This could be true only
if (i) all cancer patients die only from their cancer (i.e., there are no competing causes of death), (ii) all patients were followed up for 5 years and (iii) the risk of a cancer patient dying from cancer was constant for the 5 years after diagnosis. None of these conditions is ever fulfilled. The formula was nevertheless used to argue that the results of the EUROCARE study of trends and international differences in cancer survival in Europe10 could not be trusted. These recurring controversies over the use—and misuse— of population-based cancer statistics in health policy suggest the need for further clarification. In our article, we describe the concepts that underlie the measures of incidence, survival and mortality. We illustrate the synergy between these three key measures of the cancer burden, and show how their joint application can be more informative in assessing progress against cancer than the use of any one measure in isolation. This point has been known for decades,11,12 but it has often seemed lost from view in recent years. We also address some of the common misunderstandings. We will only briefly mention the concerns that are sometimes raised about the quality of the various data sources, because they have also been widely discussed.13–17
The Relationship between Incidence, Survival and Mortality The concepts of incidence, survival and mortality represent the probability of a single event occurring at a given point in time: the occurrence of a specific cancer (incidence), occurrence of death from any cause (survival) or occurrence of death from a specific cancer (mortality). The common concept underlying these three random processes is the event rate. The population that is at risk of the event of interest must be carefully defined at each point in time. For incidence and mortality, the population at risk is the general population. For survival, the population at risk is the persons who have been diagnosed with cancer. This distinction has implications for the measurement and interpretation of the three measures (see Appendix for a more detailed explanation). The relationship between the three measures can be described as a multistate model that includes the various possible trajectories of individuals between birth and death, including a possible sojourn in the “cancer” state (see Fig. A1). If we have a good estimate of net survival,18 i.e., survival of cancer patients after adjusting for other causes of death, the three measures of cancer incidence, mortality and survival have a simple mathematical relationship, because the age at death is obviously the sum of the age at diagnosis and the duration of survival.19 However, because of competing risks of death, and differences between the populations at risk of each event and in the timing of the processes, the relationship between the three measures is much more complex. Incidence, survival and mortality are summary measures that provide snapshots of a long-term process that is timedependent. When we interpret these statistics, it is crucial to C 2014 UICC Int. J. Cancer: 135, 1774–1782 (2014) V
account for the dynamic nature of this process. Thus, evaluating progress in cancer control with summary statistics on incidence, survival and mortality for the same chronological year may be misleading, because the cancer mortality rate for a given year depends on both incidence and survival in the past 5, 10, etc. years. These errors are illustrated in the second part of this article.
Application of the Concepts to Real Data We now illustrate the relationships between incidence, survival and mortality by analysing real data for cancers of the lung [10th revision of the International Classification of Diseases (ICD-10)20 C33-C34] and breast (C50; women only) from England and Sweden. For incidence and survival, the measures relate to patients aged 15–99 years who were diagnosed during 1981–2009. For mortality, trends are presented for people who died from one of these cancers aged 15–99 years during the same period. For each sex and broad age group, incidence and mortality rates in a given year are calculated by dividing the number of new (incident) cases or deaths by the mid-year population. The mid-year population is used to approximate the number of person-years lived by persons in that population during the index year. For England, individual data on incident cases and deaths from breast and lung cancer were obtained from the National Cancer Registry and the national registry of deaths at the Office for National Statistics (ONS). For Sweden, the incidence data were obtained from a publicly available database maintained by the National Board of Health and Welfare, whilst mortality rates were taken from the NORDCAN database. In both countries, survival was estimated from the individual records of incident cancers, which are routinely linked to death registrations. The vital status of all cancer patients was ascertained up to the end of 2010. Net survival18 up to 5 years after diagnosis was estimated for each sex and country using a flexible excess hazard regression model in which year of diagnosis and age were modelled as quantitative variables.21,22 Net survival can be interpreted as survival from the cancer of interest, in the absence of deaths from other competing causes.19 It accounts for the mortality from other causes (the expected or background mortality), which is estimated from general population life tables defined by sex, single calendar year and single year of age, for each country.23 Where fewer than 5 years of follow-up were available, the model was used to predict net survival up to 5 years after diagnosis.
Results Lung cancer in men and women aged 50–69 years
There was a substantial reduction in lung cancer mortality amongst men between 1981 and 2009 in both countries, with a greater absolute decrease in England than in Sweden (Fig. 1a). As a result, mortality rates in 2009 were closer, although still higher in England. Among women, mortality was
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Figure 1. Annual mortality (a) and incidence rates (b) per 100,000 population and 1-year net survival (%) (c): lung cancer, men diagnosed aged 50–69 years in England and Sweden during 1981–2009.
Figure 2. Annual mortality (a) and incidence rates (b) per 100,000 population and 1-year net survival (%) (c): lung cancer, women diagnosed aged 50–69 years in England and Sweden during 1981–2009.
initially low in Sweden and high in England. Because mortality rates increased during this time in Sweden, but decreased in England, mortality rates became similar in both countries by 2005 (Fig. 2a). Examining the trends in mortality alone (Figs. 1a and 2a), we might conclude that the burden of disease due to lung cancer had decreased for both sexes in England, whereas in Sweden it had decreased for men but increased for women. Such an interpretation of the secular trends would immediately prompt inappropriate questions such as “Why are women with lung cancer in Sweden now being treated worse than women in England” or “Why are men in Sweden now obtaining better treatment for lung cancer than women?” Even though the graphics provide an accurate description of the lung cancer mortality trends in England and Sweden, such an interpretation would be entirely misplaced. To interpret these data correctly, we must first understand precisely what the mortality rate in each of these calendar years represents. Let us incorporate the incidence trends into our interpretation of the mortality trends. Trends in incidence closely mirrored trends in mortality over this period (Figs. 1b and
2b). This is because the vast majority of lung cancer patients die shortly after diagnosis. The mortality trends in each population (Figs. 1a and 2a) can therefore be interpreted as mainly due to the changes in incidence over time. Figures 1c and 2c complete the picture with the addition of 1-year net survival. Survival increased slightly for both sexes in both countries during the period 1981–2009, but remained very low. It becomes clear now that the greatest increase in survival from lung cancer during this period was for women in Sweden, with a persisting, if not widening, survival gap between England and Sweden over the study period. These trends in the three indicators are consistent and they directly contradict the initial interpretation we provided on the basis of the mortality trends alone. Breast cancer in women aged 50–69 years
National breast cancer screening programmes were implemented in both England and Sweden during the late 1980s for women of similar age ranges. The purpose of mammographic screening is to detect breast cancers earlier, at a less advanced stage, so that treatment options are greater and the C 2014 UICC Int. J. Cancer: 135, 1774–1782 (2014) V
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management of breast cancer patients, or a more effective screening programme in England than in Sweden. Furthermore, the decline in mortality seen from 1990 is unlikely to be solely due to the introduction of screening: the women aged 50–69 who died in 1990 were in fact diagnosed on average 6 years earlier, and thus would not have had an opportunity to be screened before their diagnosis (data not shown). Screening can also lead to so-called overdiagnosis, i.e., the detection of tumours that would not have been diagnosed clinically or caused death. Incidence and survival are affected by overdiagnosis, whilst mortality is not. However, this is unlikely to be an explanation for the difference in survival between England and Sweden because of the parallel incidence trends in both countries. Mortality rates are a reflection of the survival of persons whose diagnosis dates are back-scattered through time: An example comparing breast cancer and lung cancer deaths among women in England (1981–2009)
Figure 3. Annual mortality (a) and incidence rates (b) per 100,000 population and 5-year net survival (%) (c): breast cancer, women diagnosed aged 50–69 years in England and Sweden during 1981–2009.
treatment itself is more effective. However, there is debate regarding the best measure to evaluate the effectiveness of a screening programme. Screening had a short-term effect on the incidence rate of breast cancer because it led to the detection of small prevalent cancers, many of which would have been diagnosed symptomatically within the next few years. This effect is known as the “prevalent wave” and it can be clearly seen during the period 1988–1994 in both countries (Fig. 3b). Breast cancer mortality rates (Fig. 3a) decreased rapidly in England for women aged 50–69, by about 40% during the period 1981–2009 while in Sweden, the reduction was much smaller (around 25%). Nevertheless, in 2009, breast cancer mortality was still higher in England (57 per 100,000 person-years compared to just below 50 in Sweden), whilst the incidence rates remained very similar in the two countries (Fig. 3b). The only viable explanation for the persistently lower mortality rates in Sweden, matched with similar incidence to that seen in England, is that survival in Sweden is persistently higher than in England (Fig. 3c). Such trends cannot be interpreted as better C 2014 UICC Int. J. Cancer: 135, 1774–1782 (2014) V
The dates of diagnosis associated with the cancer deaths observed in any given year are back-scattered through time. The degree of this back-scattering is dependent on prognosis, i.e., survival: the higher the survival, the further back in time the dates of diagnosis will be scattered. Figure 4 shows, for women who died in 2009, the year in which they were diagnosed with lung cancer (a) or breast cancer (b). It is clear that the back-scattering is far greater for breast cancer (good prognosis) than for lung cancer (poor prognosis). For example, 55% (N 5 7,000) of the women diagnosed with a lung cancer in 2009 died in the same calendar year as their diagnosis: for breast cancer, the figure was only 10% (N 5 1,500). This back-scattering highlights the fact that mortality rates are a confusing indicator when it comes to evaluating how changes in cancer diagnosis and management have influenced prognosis. This is crucial when comparisons are being made between groups of patients with very different prognoses. This confusion arises because the deaths occurring in a given year are not deaths among patients who were diagnosed around the same time (and would thus have received similar medical treatment). For breast cancer, these deaths consist of a mixture of women diagnosed quite recently, combined with those who were diagnosed a number of years earlier. Lung cancer deaths in the same year, however, occur among patients diagnosed much more recently, with the majority in the previous 2 years (Fig. 4). This back-scatter also changes over time. Figure 5 displays the percentage of patients who were diagnosed within the 5year period preceding their death for those who died between 1986 and 2009. Because the prognosis of lung cancer remained poor in England throughout this period, the percentage is high and has remained fairly constant: nearly 100% of women with lung cancer who died in 1986 were diagnosed within the preceding 5 years, and this figure remained as high as 95% for those who died in 2009. By contrast, survival from breast cancer has improved rapidly, so
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Figure 4. Women with lung cancer (a) or breast cancer (b) who died in 2009: back-scatter of the year of diagnosis. The bars represent the number of women diagnosed in a given year, while the curves represent the percentage of the total number of women diagnosed in a given year.
interpreting overall progress in cancer control by the use of all three measures in combination. Trends and contrasts in any one of these three measures cannot be appropriately interpreted alone. We have demonstrated the mathematical derivation of each of these measures and proved their interdependence. We have illustrated the concepts with data on lung and breast cancer. We chose these malignancies because the prognosis of lung cancer has remained very poor over the past three decades, whereas the prognosis of breast cancer has improved substantially. We now summarise the merits and limitations of each measure. Mortality Figure 5. Women who died of lung cancer or breast cancer in England, 1986–2009: percentage of patients who were diagnosed within the 5 years preceding their death.
that a progressively larger proportion of women who died in a given year were diagnosed more than 5 years earlier. The progressive increase in the time between diagnosis and death has therefore led to a slow decline in breast cancer mortality rates: as a result, the mortality rate from breast cancer increasingly reflects the experience of a group of women who were diagnosed progressively further in the past.
Discussion We have discussed the differences between measures of cancer mortality, incidence and survival in an attempt to clarify their individual features, but especially the importance of
Cancer mortality rates are vital to inform public health and health-care priorities. The numerator of a mortality rate is the number of deaths for which the underlying cause of death has been coded to a particular cancer in a particular year. This information is often widely available from statutory death registration in high-income countries. Cancer mortality is useful to identify potential bias in measures of cancer incidence and survival, such as overdiagnosis. When a cancer is rapidly lethal, mortality can serve as a rough proxy for incidence, and is closely allied to survival. As shown in the example above, trends in lung cancer mortality closely track trends in incidence. In combination with cancer survival, cancer mortality rates can help evaluate the effectiveness of treatment over time. However, trends in cancer mortality are affected by trends in incidence and survival. We have shown that mortality trends provide a delayed reflection of progress in cancer C 2014 UICC Int. J. Cancer: 135, 1774–1782 (2014) V
control. Trends in cancer mortality rates are also subject to changes and international differences in the accuracy of death certification, and in the selection and coding of the underlying cause of death, especially in older patients, who represent about one-third of all cancers. Incidence
Measures of incidence are most commonly used in the study of cancer aetiology. Population-based measures of cancer incidence are often derived from regional or national cancer registry data, which are subject to strict quality control procedures. The numerator of a cancer incidence rate is the number of newly diagnosed cases in a given year, and is therefore unaffected by events occurring after the cancer diagnosis, such as changes in treatment or trends in survival. The cancer incidence rate is, however, affected by events that occur before diagnosis, such as screening. As shown by the example above, there was a clear increase in the incidence of breast cancer in both England and Sweden following the introduction of a national breast cancer screening programme. Improvements in diagnostic techniques, such as the increased use of endoscopy in the diagnosis of gastrointestinal tumours, or of computed tomography and magnetic resonance imaging in the diagnosis of brain tumours, will lead to increased estimates of cancer incidence. Trends in cancer incidence can also be affected by the way in which the underlying data are collected, such as improvements in the completeness of cancer registration, or any change to the definition of a particular malignancy. For example, major changes in the coding of benign and in situ bladder tumours between the first and second editions of the International Classification of Disease for Oncology in 1998 led to their removal from estimates of incidence of invasive, malignant disease. This artificially altered the pattern of bladder cancer incidence, both between regions and over time.24 Survival
Survival completes the triangle of cancer measures, summarising, on an individual basis, the elapsed time between diagnosis and death for particular groups of patients diagnosed with a particular cancer. It is crucial to understand that survival is a dynamic measure, aiming to reflect the course of the disease from its diagnosis. Survival is the most accurate measure of disease prognosis at a given time, because it is derived from data on all the individuals diagnosed in the same period of time and followed up until death. Survival estimates derived from cancer registration data are population-based, and the records of cancer cases derive from a number of different sources of information, such as pathology reports, GP notes and hospital records. Cancer registrations also undergo a number of quality control checks before a cancer is registered and the date of diagnosis determined, such as whether the cancer was morphologically verified. That is not the case for mortality data, which are derived from a single source, the death certificate. Death cerC 2014 UICC Int. J. Cancer: 135, 1774–1782 (2014) V
tificates are very rarely validated against any pathological or clinical information. Survival is susceptible to misinterpretation when patterns in incidence are forgotten or ignored, particularly when those incidence patterns have changed over time. For example, the rapid increase in the incidence of breast cancer detailed above was associated with a rapid increase in survival: but part of this increase will have been due to the diagnosis of small, localised breast cancers (including the so-called overdiagnosed tumours) via the screening programme. Earlier diagnosis of tumours without an ultimate improvement in prognosis will also affect measures of short-term survival because of the lead-time effect.25 However, long-term survival and estimates of population “cure” (the point at which cancer patients have the same overall mortality as the general population26) will remain unchanged. Therefore, because of substantial changes in diagnostic investigation, is important to estimate cancer survival by tumour stage for better interpretation, in particular in international studies27,28 or when temporal changes in survival are investigated.29 Mortality/Incidence ratio
Mortality/Incidence (M/I) ratios are occasionally presented as a crude surrogate for survival.30 Used in combination with incidence and mortality measures, these ratios can help to understand how the impact of a particular cancer has changed over time. However, with the exception of cancers with a very poor prognosis, the interpretation of the M/I ratio alone is problematic. This is because in any given year, the mortality rate relates to a different group of patients than the incidence rate (Fig. 5). Examining the M/I ratio alone makes no allowance for this “back-scattering” through time. Rapid improvements in prognosis are not observable in the M/I ratio before the time between diagnosis and death has elapsed. In the case of a nonlethal cancer, this period is lengthy, whilst for a lethal cancer the change would be detectable more immediately. Comparison of M/I ratios alone can therefore be very misleading. Second and multiple cancers
For an increasing proportion of patients registered with a cancer in a given organ or tissue, the malignancy is not that person’s first primary cancer.31 The availability of sensitive new diagnostic tests and improved treatments increases the prevalent pool of long-term survivors who remain at risk of developing a new malignancy.32 The introduction of prostatespecific antigen (PSA) testing, for example, has led to a rapid increase in the incidence of prostate cancer in some countries. Many of these cancers have a benign clinical picture, and their diagnosis has resulted in a large number of elderly male survivors who remain at high risk of developing a different cancer. The proportion of cancer patients with a known prior cancer depends largely on the length of operation of the cancer registry. This is simply because cancer
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registries that have been in existence for many years are likely to hold more information on a given patient’s previous cancer diagnoses than a more recently established registry. The presence of multiple primary cancers in cancer registry data can affect the measurement of incidence, survival and mortality. For cancer incidence, it is usual to include first-, second- and higher order primary cancers in the numerator of the rate. Measures of incidence can therefore be affected by the definition of a multiple primary cancers. The Surveillance, Epidemiology and End Results (SEER) programme in the United States and the International Association of Cancer Registries (IACR) have both developed rules to standardise the definition and coding of multiple primary cancers in an individual patient, including cancers that were diagnosed concurrent with or subsequent to a first primary cancer.33,34 The two sets of coding rules are different (the IACR criteria are more conservative), and this needs to be considered when making international comparisons of cancer incidence. Inclusion of all primary cancers, regardless of rank order in a given patient, will reduce the impact of such differences on incidence comparisons. Survival can also be affected, depending on the nature of the study. When survival is analysed separately for each type of malignancy, usually defined by the ICD-O topography code at the three-character level (e.g., colon, rectum and anus), it is reasonable to permit the inclusion of a person with two malignancies at different anatomic sites in the separate analysis of survival from each of those cancers. Survival from a second malignancy is typically shorter than survival from a cancer at the same site when it presents as the first malignancy, so restricting survival analyses only to first primary malignancies may introduce bias in comparisons of survival if the definitions of multiple primary cancer differ between populations.35,36 As the proportion of multiple primary cancers increases, with new diagnostic tests and improved long-term survival, the effect of this bias will also increase. However, multiple primary cancers that arise at the same anatomic site must be excluded from survival analyses because a given individual can only die once. To do anything else would permit inclusion of two deaths (events) for a single person in the same survival analysis; whilst statistically feasible, this is inherently illogical. Similarly, if data are pooled from more than one anatomic site to analyses survival
from all cancers combined, it would again be inappropriate to include a single person more than once in the analyses, which should thus be confined to first primary malignancies that were registered in the period covered by the study. The effect of multiple primary cancers on measures of cancer mortality is perhaps more straightforward. Although a person can have more than one independent cancer in their lifetime, they can die only once, and only one cancer can be selected as the underlying cause of death, i.e., the cause of death for which the death will be counted in the numerator of the death rate. A mortality rate for the “other” cancer, not selected as the underlying cause of death, will not be calculated and is therefore disconnected from the corresponding incidence and survival estimates. In conclusion, incidence, survival and mortality capture different aspects of a dynamic, time-dependent process. Examination of trends in all three metrics is crucial to obtain a fuller understanding of progress in cancer control. Recommendations
1. Examining incidence and survival together provides a more accurate picture of the impact of cancer in a population Cancer incidence can be used to identify the population(s) at highest risk, whilst survival provides a measure of prognosis. Used in combination, these two measures illustrate how the impact of cancer varies between groups and over time. 2. Cancer mortality is essential to inform public health and health-care priorities Examining mortality rates enables bias in cancer incidence and survival to be detected. 3. Examining mortality alone can be misleading Trends in cancer mortality are the result of previous trends in both incidence and survival. To provide a fuller understanding of the impact of cancer in a population, cancer mortality trends should be examined alongside trends in incidence and survival. 4. Analysis of M/I ratios alone can be misleading M/I ratios can be used as a crude surrogate for survival, but only in combination with incidence and mortality measures. Where population-based cancer survival can be estimated, M/I ratios should not be used.
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the UK: a population-based study, 2004–2007. Thorax 2013;68:551–64. Walters S, Maringe C, Butler J, et al. Breast cancer survival and stage at diagnosis in Australia, Canada, Denmark, Norway, Sweden and the UK, 2000–2007: a population-based study. Br J Cancer 2013;108:1195–208. Ito Y, Ohno Y, Rachet B, et al. Cancer survival trends in Osaka, Japan: the influence of age and stage at diagnosis. Jpn J Clin Oncol 2007;37:452– 8. Vostakolaei FA, Karim-Kos HE, Janssen-Heijnen M, et al. The validity of the mortality to incidence ratio as a proxy for site-specific cancer survival. Eur J Public Health 2010;21:573–77. Curtis RE, Freedman DM, Ron E, et al., eds. New malignancies among cancer survivors: SEER cancer registries 1973–2000. NIH Publication No. 05–3302. Bethesda, MD: National Cancer Institute, 2006. Mariotto AB, Rowland JH, Ries LAG, et al. Multiple cancer prevalence: a growing challenge in long-term survivorship. Cancer Epidemiol Biomarkers Prev 2007;16:566–71. National Cancer Institute. Surveillance, epidemiology and end results program. Multiple primary and histology coding rules. Bethesda, MD: National Cancer Institute, 2007. International Association of Cancer Registries Working Group Report. International rules for multiple primary cancers (ICD-O third edition). Eur J Cancer Prev 2005;14:307–8. Rosso S, De Angelis R, Ciccolallo L, et al.; the EUROCARE Working Group. Multiple tumours in survival estimates. Eur J Cancer 2009;45:1080– 94. Ellison LF. Measuring the effect of including multiple cancers in survival analyses using data from the Canadian Cancer Registry. Cancer Epidemiol 2010;34:550–5.
Appendix The mathematical tool used to analyse these processes is the “event rate”. For the cancer incidence rate, the event is a new cancer diagnosis. The concept behind the event rate is sophisticated, and it requires calculus for a fully rigorous definition, but intuitively, it may be defined as the probability that the event occurs in a given person during the next interval of time (year, month or day ...) given that this person is still at risk of the event (i.e., alive, and still under observation) at the beginning of the interval. This probability clearly depends on how long the person is under observation: the longer the period of observation, the higher the probability that an event will occur. Therefore, we divide the probability by the length of the period of observation to get the average event rate over that unit of time e.g., the annual death rate. This estimation of the event rate applies to all three measures: incidence, survival and mortality. For incidence and mortality rates, however, the number of persons in the general population who are at risk of being
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diagnosed with or dying from cancer, respectively, can only be obtained from national statistics agencies or census offices. These agencies usually publish the number of living persons in the general population of a given age at a fixed date each year. It is not practicable to maintain continuous follow-up of an entire national population to determine whether each individual is still “at risk” (alive and still resident in the country, state, province, ...). The total person-time at risk of an event in a given year is therefore approximated by the mid-year population; in some countries, this is directly available from the national statistics agency. Things are different for survival. The population at risk of an event (usually, death) is no longer the general population, but the subset of the population who have already been diagnosed with cancer. In a cancer survival study, we do know the history of each subject—and therefore their precise time at risk of death—because the cancer registry routinely obtains data on the vital status of each patient.
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Given t, the time at start of the interval, and x, the age at ^ is: time t, the estimated event rate k
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^ k5
kxt nxt X Dxi i51
where kxt is the total number of events among nxt subjects under observation until t, and the denominator is the sum of observed duration times (person-years) for all nxi. As the entire population cannot be followed up individually from birth to death, we cannot estimate directly the transition rates between the various states, but Figure A1 shows the competing risks that we are trying to model. The possible trajectories for a given person between various “states” (boxes), from an initial state of Healthy and the eventual state of Death, with possible spells in Cancer and/ or Other diseases states. The arrows represent transitions between the various states, required to study survival: incidence of cancer or other diseases, and death from cancer or other diseases. Each arrow is labelled with the corresponding “event rate”: k for the incidence rates, l and m for the mortality rates at a given age, where x is the age at incidence and y is the age at death. The indices, we have used
to label each event of interest are as follows: c for “cancer,” o for “other diseases” and a for “all causes of death.” The index y 2 x is the time elapsed since the diagnosis of cancer (xc) or other diseases (xo). The cancer incidence rate (kc) can be obtained from cancer registries. The cancer mortality rate (lc) can be obtained from national mortality statistics. The cancer mortality rate can also be considered as the two-step transition between Healthy and Cancer followed by the transition from Cancer to Death (kcmc). The dashed lines in Figure A1 represent other transitions. Thus, the population mortality rate from causes other than the specific cancer under study (lo) is also the two-step transition from Healthy to Other diseases and then from Other diseases to Death (komo). The idea behind concepts such as net survival and relative survival is to obtain the mortality rate from cancer among the cancer patients by subtracting the population mortality rate from causes other than the specific cancer (lo) from the mortality rate for all causes of death (ma); lo is obtained from population life tables. Note that the transition rate from Cancer to Other diseases is not usually equal to the transition rate from Healthy to Other diseases. This raises the problem of the appropriateness of the population life table for the cancer patients.
Figure A1. The relationship between incidence, survival and mortality.
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Cancer incidence, survival and mortality: Explaining the concepts Special Section Paper
Libby Ellis1, Laura M. Woods1, Jacques Este`ve2, Sandra Eloranta3, Michel P. Coleman1 and Bernard Rachet1 1
Cancer Research UK Cancer Survival Group, London School of Hygiene and Tropical Medicine, London, United Kingdom Biostatistics Division, Hospices Civils de Lyon, Universite Claude Bernard, Lyon, France 3 Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden 2
Cancer incidence, survival and mortality are essential population-based indicators for public health and cancer control. Confusion and misunderstanding still surround the estimation and interpretation of these indicators. Recurring controversies over the use and misuse of population-based cancer statistics in health policy suggests the need for further clarification. In our article, we describe the concepts that underlie the measures of incidence, survival and mortality, and illustrate the synergy between these measures of the cancer burden. We demonstrate the relationships between trends in incidence, survival and mortality, using real data for cancers of the lung and breast from England and Sweden. Finally, we discuss the importance of using all three measures in combination when interpreting overall progress in cancer control, and we offer some recommendations for their use.
Measuring the burden of cancer in a population is essential for public health and cancer control. Reliable estimates of the cancer burden can provide a comprehensive picture of how the impact of cancer varies between geographic areas and between population strata. These estimates, in turn, inform the development of cancer control strategies. Increasingly, survival trends are also being used to assess the efficacy of cancer strategies in reducing the impact of cancer over time. Incidence, survival and mortality are commonplace terms in epidemiology. For many years, they have been the principal measures used in population-based research to explore the causes (incidence) and outcomes of cancer (survival and mortality), and to assess its management. In England, for example, population-based estimates of cancer mortality have been published in some form since the 1850s,1 and national population-based estimates of incidence and survival have been published since the 1950s.2 Nevertheless, confusion and misunderstanding still surround the estimation and interpretation of these indicators. One recent examination of the WHO mortality database showed that among 30 European countries, the UK had one of the largest reductions in breast cancer mortality over the period 1989–2006.3 As breast cancer survival in the late 1990s Key words: cancer, mortality, incidence, survival, methods DOI: 10.1002/ijc.28990 History: Received 26 Nov 2013; Accepted 4 Dec 2013; Online 19 June 2014 Correspondence to: Prof. Michel P. Coleman, Cancer Research UK Cancer Survival Group, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, United Kingdom, Tel.: 144-0-20–7927-2478, Fax: 144-0-20–7580-6897, E-mail: [email protected]
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was lower in the UK than elsewhere in Europe,4 the authors postulated that differences in screening intensity between countries had resulted in spurious survival estimates, and concluded that “mortality data are a more realistic measure of successful cancer control than cancer survival, as the latter is influenced by changes in cancer incidence.”3 This despite the fact that mortality is itself affected by incidence and survival. Again, in 2011, controversy followed publication of an international comparison of survival from four common cancers during the period 1995–2007 in Australia, Canada, Denmark, Norway, Sweden and the UK, based on population-based cancer registry data.5 The study found persistently lower survival in Denmark and the UK for all four cancers, particularly in the first year after diagnosis. The authors noted that the trends in incidence, survival and mortality were broadly consistent. They also pointed out that “mortality is a function of both incidence and survival,” a statement that summarises the obvious point that your chances of dying from a disease depend on your chances of getting it in the first place, and then on your chances of surviving it. An accompanying editorial6 nevertheless dismissed this statement on the basis that colorectal cancer mortality in the UK had declined substantially over time, whilst international differences in incidence and survival had remained fairly constant. Other commentators have joined the debate on the relative merits of mortality, incidence and survival, often arguing fervently for one measure over another.7,8 One group of epidemiologists wrote recently9 that 5-year survival from a given cancer can be obtained from the formula: S5ðC2dÞ=C; where S is the survival, C is the number of cancer patients and d is the number of those patients who died from any cause in the 5 years after diagnosis.9 This could be true only
if (i) all cancer patients die only from their cancer (i.e., there are no competing causes of death), (ii) all patients were followed up for 5 years and (iii) the risk of a cancer patient dying from cancer was constant for the 5 years after diagnosis. None of these conditions is ever fulfilled. The formula was nevertheless used to argue that the results of the EUROCARE study of trends and international differences in cancer survival in Europe10 could not be trusted. These recurring controversies over the use—and misuse— of population-based cancer statistics in health policy suggest the need for further clarification. In our article, we describe the concepts that underlie the measures of incidence, survival and mortality. We illustrate the synergy between these three key measures of the cancer burden, and show how their joint application can be more informative in assessing progress against cancer than the use of any one measure in isolation. This point has been known for decades,11,12 but it has often seemed lost from view in recent years. We also address some of the common misunderstandings. We will only briefly mention the concerns that are sometimes raised about the quality of the various data sources, because they have also been widely discussed.13–17
The Relationship between Incidence, Survival and Mortality The concepts of incidence, survival and mortality represent the probability of a single event occurring at a given point in time: the occurrence of a specific cancer (incidence), occurrence of death from any cause (survival) or occurrence of death from a specific cancer (mortality). The common concept underlying these three random processes is the event rate. The population that is at risk of the event of interest must be carefully defined at each point in time. For incidence and mortality, the population at risk is the general population. For survival, the population at risk is the persons who have been diagnosed with cancer. This distinction has implications for the measurement and interpretation of the three measures (see Appendix for a more detailed explanation). The relationship between the three measures can be described as a multistate model that includes the various possible trajectories of individuals between birth and death, including a possible sojourn in the “cancer” state (see Fig. A1). If we have a good estimate of net survival,18 i.e., survival of cancer patients after adjusting for other causes of death, the three measures of cancer incidence, mortality and survival have a simple mathematical relationship, because the age at death is obviously the sum of the age at diagnosis and the duration of survival.19 However, because of competing risks of death, and differences between the populations at risk of each event and in the timing of the processes, the relationship between the three measures is much more complex. Incidence, survival and mortality are summary measures that provide snapshots of a long-term process that is timedependent. When we interpret these statistics, it is crucial to C 2014 UICC Int. J. Cancer: 135, 1774–1782 (2014) V
account for the dynamic nature of this process. Thus, evaluating progress in cancer control with summary statistics on incidence, survival and mortality for the same chronological year may be misleading, because the cancer mortality rate for a given year depends on both incidence and survival in the past 5, 10, etc. years. These errors are illustrated in the second part of this article.
Application of the Concepts to Real Data We now illustrate the relationships between incidence, survival and mortality by analysing real data for cancers of the lung [10th revision of the International Classification of Diseases (ICD-10)20 C33-C34] and breast (C50; women only) from England and Sweden. For incidence and survival, the measures relate to patients aged 15–99 years who were diagnosed during 1981–2009. For mortality, trends are presented for people who died from one of these cancers aged 15–99 years during the same period. For each sex and broad age group, incidence and mortality rates in a given year are calculated by dividing the number of new (incident) cases or deaths by the mid-year population. The mid-year population is used to approximate the number of person-years lived by persons in that population during the index year. For England, individual data on incident cases and deaths from breast and lung cancer were obtained from the National Cancer Registry and the national registry of deaths at the Office for National Statistics (ONS). For Sweden, the incidence data were obtained from a publicly available database maintained by the National Board of Health and Welfare, whilst mortality rates were taken from the NORDCAN database. In both countries, survival was estimated from the individual records of incident cancers, which are routinely linked to death registrations. The vital status of all cancer patients was ascertained up to the end of 2010. Net survival18 up to 5 years after diagnosis was estimated for each sex and country using a flexible excess hazard regression model in which year of diagnosis and age were modelled as quantitative variables.21,22 Net survival can be interpreted as survival from the cancer of interest, in the absence of deaths from other competing causes.19 It accounts for the mortality from other causes (the expected or background mortality), which is estimated from general population life tables defined by sex, single calendar year and single year of age, for each country.23 Where fewer than 5 years of follow-up were available, the model was used to predict net survival up to 5 years after diagnosis.
Results Lung cancer in men and women aged 50–69 years
There was a substantial reduction in lung cancer mortality amongst men between 1981 and 2009 in both countries, with a greater absolute decrease in England than in Sweden (Fig. 1a). As a result, mortality rates in 2009 were closer, although still higher in England. Among women, mortality was
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Figure 1. Annual mortality (a) and incidence rates (b) per 100,000 population and 1-year net survival (%) (c): lung cancer, men diagnosed aged 50–69 years in England and Sweden during 1981–2009.
Figure 2. Annual mortality (a) and incidence rates (b) per 100,000 population and 1-year net survival (%) (c): lung cancer, women diagnosed aged 50–69 years in England and Sweden during 1981–2009.
initially low in Sweden and high in England. Because mortality rates increased during this time in Sweden, but decreased in England, mortality rates became similar in both countries by 2005 (Fig. 2a). Examining the trends in mortality alone (Figs. 1a and 2a), we might conclude that the burden of disease due to lung cancer had decreased for both sexes in England, whereas in Sweden it had decreased for men but increased for women. Such an interpretation of the secular trends would immediately prompt inappropriate questions such as “Why are women with lung cancer in Sweden now being treated worse than women in England” or “Why are men in Sweden now obtaining better treatment for lung cancer than women?” Even though the graphics provide an accurate description of the lung cancer mortality trends in England and Sweden, such an interpretation would be entirely misplaced. To interpret these data correctly, we must first understand precisely what the mortality rate in each of these calendar years represents. Let us incorporate the incidence trends into our interpretation of the mortality trends. Trends in incidence closely mirrored trends in mortality over this period (Figs. 1b and
2b). This is because the vast majority of lung cancer patients die shortly after diagnosis. The mortality trends in each population (Figs. 1a and 2a) can therefore be interpreted as mainly due to the changes in incidence over time. Figures 1c and 2c complete the picture with the addition of 1-year net survival. Survival increased slightly for both sexes in both countries during the period 1981–2009, but remained very low. It becomes clear now that the greatest increase in survival from lung cancer during this period was for women in Sweden, with a persisting, if not widening, survival gap between England and Sweden over the study period. These trends in the three indicators are consistent and they directly contradict the initial interpretation we provided on the basis of the mortality trends alone. Breast cancer in women aged 50–69 years
National breast cancer screening programmes were implemented in both England and Sweden during the late 1980s for women of similar age ranges. The purpose of mammographic screening is to detect breast cancers earlier, at a less advanced stage, so that treatment options are greater and the C 2014 UICC Int. J. Cancer: 135, 1774–1782 (2014) V
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management of breast cancer patients, or a more effective screening programme in England than in Sweden. Furthermore, the decline in mortality seen from 1990 is unlikely to be solely due to the introduction of screening: the women aged 50–69 who died in 1990 were in fact diagnosed on average 6 years earlier, and thus would not have had an opportunity to be screened before their diagnosis (data not shown). Screening can also lead to so-called overdiagnosis, i.e., the detection of tumours that would not have been diagnosed clinically or caused death. Incidence and survival are affected by overdiagnosis, whilst mortality is not. However, this is unlikely to be an explanation for the difference in survival between England and Sweden because of the parallel incidence trends in both countries. Mortality rates are a reflection of the survival of persons whose diagnosis dates are back-scattered through time: An example comparing breast cancer and lung cancer deaths among women in England (1981–2009)
Figure 3. Annual mortality (a) and incidence rates (b) per 100,000 population and 5-year net survival (%) (c): breast cancer, women diagnosed aged 50–69 years in England and Sweden during 1981–2009.
treatment itself is more effective. However, there is debate regarding the best measure to evaluate the effectiveness of a screening programme. Screening had a short-term effect on the incidence rate of breast cancer because it led to the detection of small prevalent cancers, many of which would have been diagnosed symptomatically within the next few years. This effect is known as the “prevalent wave” and it can be clearly seen during the period 1988–1994 in both countries (Fig. 3b). Breast cancer mortality rates (Fig. 3a) decreased rapidly in England for women aged 50–69, by about 40% during the period 1981–2009 while in Sweden, the reduction was much smaller (around 25%). Nevertheless, in 2009, breast cancer mortality was still higher in England (57 per 100,000 person-years compared to just below 50 in Sweden), whilst the incidence rates remained very similar in the two countries (Fig. 3b). The only viable explanation for the persistently lower mortality rates in Sweden, matched with similar incidence to that seen in England, is that survival in Sweden is persistently higher than in England (Fig. 3c). Such trends cannot be interpreted as better C 2014 UICC Int. J. Cancer: 135, 1774–1782 (2014) V
The dates of diagnosis associated with the cancer deaths observed in any given year are back-scattered through time. The degree of this back-scattering is dependent on prognosis, i.e., survival: the higher the survival, the further back in time the dates of diagnosis will be scattered. Figure 4 shows, for women who died in 2009, the year in which they were diagnosed with lung cancer (a) or breast cancer (b). It is clear that the back-scattering is far greater for breast cancer (good prognosis) than for lung cancer (poor prognosis). For example, 55% (N 5 7,000) of the women diagnosed with a lung cancer in 2009 died in the same calendar year as their diagnosis: for breast cancer, the figure was only 10% (N 5 1,500). This back-scattering highlights the fact that mortality rates are a confusing indicator when it comes to evaluating how changes in cancer diagnosis and management have influenced prognosis. This is crucial when comparisons are being made between groups of patients with very different prognoses. This confusion arises because the deaths occurring in a given year are not deaths among patients who were diagnosed around the same time (and would thus have received similar medical treatment). For breast cancer, these deaths consist of a mixture of women diagnosed quite recently, combined with those who were diagnosed a number of years earlier. Lung cancer deaths in the same year, however, occur among patients diagnosed much more recently, with the majority in the previous 2 years (Fig. 4). This back-scatter also changes over time. Figure 5 displays the percentage of patients who were diagnosed within the 5year period preceding their death for those who died between 1986 and 2009. Because the prognosis of lung cancer remained poor in England throughout this period, the percentage is high and has remained fairly constant: nearly 100% of women with lung cancer who died in 1986 were diagnosed within the preceding 5 years, and this figure remained as high as 95% for those who died in 2009. By contrast, survival from breast cancer has improved rapidly, so
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Figure 4. Women with lung cancer (a) or breast cancer (b) who died in 2009: back-scatter of the year of diagnosis. The bars represent the number of women diagnosed in a given year, while the curves represent the percentage of the total number of women diagnosed in a given year.
interpreting overall progress in cancer control by the use of all three measures in combination. Trends and contrasts in any one of these three measures cannot be appropriately interpreted alone. We have demonstrated the mathematical derivation of each of these measures and proved their interdependence. We have illustrated the concepts with data on lung and breast cancer. We chose these malignancies because the prognosis of lung cancer has remained very poor over the past three decades, whereas the prognosis of breast cancer has improved substantially. We now summarise the merits and limitations of each measure. Mortality Figure 5. Women who died of lung cancer or breast cancer in England, 1986–2009: percentage of patients who were diagnosed within the 5 years preceding their death.
that a progressively larger proportion of women who died in a given year were diagnosed more than 5 years earlier. The progressive increase in the time between diagnosis and death has therefore led to a slow decline in breast cancer mortality rates: as a result, the mortality rate from breast cancer increasingly reflects the experience of a group of women who were diagnosed progressively further in the past.
Discussion We have discussed the differences between measures of cancer mortality, incidence and survival in an attempt to clarify their individual features, but especially the importance of
Cancer mortality rates are vital to inform public health and health-care priorities. The numerator of a mortality rate is the number of deaths for which the underlying cause of death has been coded to a particular cancer in a particular year. This information is often widely available from statutory death registration in high-income countries. Cancer mortality is useful to identify potential bias in measures of cancer incidence and survival, such as overdiagnosis. When a cancer is rapidly lethal, mortality can serve as a rough proxy for incidence, and is closely allied to survival. As shown in the example above, trends in lung cancer mortality closely track trends in incidence. In combination with cancer survival, cancer mortality rates can help evaluate the effectiveness of treatment over time. However, trends in cancer mortality are affected by trends in incidence and survival. We have shown that mortality trends provide a delayed reflection of progress in cancer C 2014 UICC Int. J. Cancer: 135, 1774–1782 (2014) V
control. Trends in cancer mortality rates are also subject to changes and international differences in the accuracy of death certification, and in the selection and coding of the underlying cause of death, especially in older patients, who represent about one-third of all cancers. Incidence
Measures of incidence are most commonly used in the study of cancer aetiology. Population-based measures of cancer incidence are often derived from regional or national cancer registry data, which are subject to strict quality control procedures. The numerator of a cancer incidence rate is the number of newly diagnosed cases in a given year, and is therefore unaffected by events occurring after the cancer diagnosis, such as changes in treatment or trends in survival. The cancer incidence rate is, however, affected by events that occur before diagnosis, such as screening. As shown by the example above, there was a clear increase in the incidence of breast cancer in both England and Sweden following the introduction of a national breast cancer screening programme. Improvements in diagnostic techniques, such as the increased use of endoscopy in the diagnosis of gastrointestinal tumours, or of computed tomography and magnetic resonance imaging in the diagnosis of brain tumours, will lead to increased estimates of cancer incidence. Trends in cancer incidence can also be affected by the way in which the underlying data are collected, such as improvements in the completeness of cancer registration, or any change to the definition of a particular malignancy. For example, major changes in the coding of benign and in situ bladder tumours between the first and second editions of the International Classification of Disease for Oncology in 1998 led to their removal from estimates of incidence of invasive, malignant disease. This artificially altered the pattern of bladder cancer incidence, both between regions and over time.24 Survival
Survival completes the triangle of cancer measures, summarising, on an individual basis, the elapsed time between diagnosis and death for particular groups of patients diagnosed with a particular cancer. It is crucial to understand that survival is a dynamic measure, aiming to reflect the course of the disease from its diagnosis. Survival is the most accurate measure of disease prognosis at a given time, because it is derived from data on all the individuals diagnosed in the same period of time and followed up until death. Survival estimates derived from cancer registration data are population-based, and the records of cancer cases derive from a number of different sources of information, such as pathology reports, GP notes and hospital records. Cancer registrations also undergo a number of quality control checks before a cancer is registered and the date of diagnosis determined, such as whether the cancer was morphologically verified. That is not the case for mortality data, which are derived from a single source, the death certificate. Death cerC 2014 UICC Int. J. Cancer: 135, 1774–1782 (2014) V
tificates are very rarely validated against any pathological or clinical information. Survival is susceptible to misinterpretation when patterns in incidence are forgotten or ignored, particularly when those incidence patterns have changed over time. For example, the rapid increase in the incidence of breast cancer detailed above was associated with a rapid increase in survival: but part of this increase will have been due to the diagnosis of small, localised breast cancers (including the so-called overdiagnosed tumours) via the screening programme. Earlier diagnosis of tumours without an ultimate improvement in prognosis will also affect measures of short-term survival because of the lead-time effect.25 However, long-term survival and estimates of population “cure” (the point at which cancer patients have the same overall mortality as the general population26) will remain unchanged. Therefore, because of substantial changes in diagnostic investigation, is important to estimate cancer survival by tumour stage for better interpretation, in particular in international studies27,28 or when temporal changes in survival are investigated.29 Mortality/Incidence ratio
Mortality/Incidence (M/I) ratios are occasionally presented as a crude surrogate for survival.30 Used in combination with incidence and mortality measures, these ratios can help to understand how the impact of a particular cancer has changed over time. However, with the exception of cancers with a very poor prognosis, the interpretation of the M/I ratio alone is problematic. This is because in any given year, the mortality rate relates to a different group of patients than the incidence rate (Fig. 5). Examining the M/I ratio alone makes no allowance for this “back-scattering” through time. Rapid improvements in prognosis are not observable in the M/I ratio before the time between diagnosis and death has elapsed. In the case of a nonlethal cancer, this period is lengthy, whilst for a lethal cancer the change would be detectable more immediately. Comparison of M/I ratios alone can therefore be very misleading. Second and multiple cancers
For an increasing proportion of patients registered with a cancer in a given organ or tissue, the malignancy is not that person’s first primary cancer.31 The availability of sensitive new diagnostic tests and improved treatments increases the prevalent pool of long-term survivors who remain at risk of developing a new malignancy.32 The introduction of prostatespecific antigen (PSA) testing, for example, has led to a rapid increase in the incidence of prostate cancer in some countries. Many of these cancers have a benign clinical picture, and their diagnosis has resulted in a large number of elderly male survivors who remain at high risk of developing a different cancer. The proportion of cancer patients with a known prior cancer depends largely on the length of operation of the cancer registry. This is simply because cancer
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registries that have been in existence for many years are likely to hold more information on a given patient’s previous cancer diagnoses than a more recently established registry. The presence of multiple primary cancers in cancer registry data can affect the measurement of incidence, survival and mortality. For cancer incidence, it is usual to include first-, second- and higher order primary cancers in the numerator of the rate. Measures of incidence can therefore be affected by the definition of a multiple primary cancers. The Surveillance, Epidemiology and End Results (SEER) programme in the United States and the International Association of Cancer Registries (IACR) have both developed rules to standardise the definition and coding of multiple primary cancers in an individual patient, including cancers that were diagnosed concurrent with or subsequent to a first primary cancer.33,34 The two sets of coding rules are different (the IACR criteria are more conservative), and this needs to be considered when making international comparisons of cancer incidence. Inclusion of all primary cancers, regardless of rank order in a given patient, will reduce the impact of such differences on incidence comparisons. Survival can also be affected, depending on the nature of the study. When survival is analysed separately for each type of malignancy, usually defined by the ICD-O topography code at the three-character level (e.g., colon, rectum and anus), it is reasonable to permit the inclusion of a person with two malignancies at different anatomic sites in the separate analysis of survival from each of those cancers. Survival from a second malignancy is typically shorter than survival from a cancer at the same site when it presents as the first malignancy, so restricting survival analyses only to first primary malignancies may introduce bias in comparisons of survival if the definitions of multiple primary cancer differ between populations.35,36 As the proportion of multiple primary cancers increases, with new diagnostic tests and improved long-term survival, the effect of this bias will also increase. However, multiple primary cancers that arise at the same anatomic site must be excluded from survival analyses because a given individual can only die once. To do anything else would permit inclusion of two deaths (events) for a single person in the same survival analysis; whilst statistically feasible, this is inherently illogical. Similarly, if data are pooled from more than one anatomic site to analyses survival
from all cancers combined, it would again be inappropriate to include a single person more than once in the analyses, which should thus be confined to first primary malignancies that were registered in the period covered by the study. The effect of multiple primary cancers on measures of cancer mortality is perhaps more straightforward. Although a person can have more than one independent cancer in their lifetime, they can die only once, and only one cancer can be selected as the underlying cause of death, i.e., the cause of death for which the death will be counted in the numerator of the death rate. A mortality rate for the “other” cancer, not selected as the underlying cause of death, will not be calculated and is therefore disconnected from the corresponding incidence and survival estimates. In conclusion, incidence, survival and mortality capture different aspects of a dynamic, time-dependent process. Examination of trends in all three metrics is crucial to obtain a fuller understanding of progress in cancer control. Recommendations
1. Examining incidence and survival together provides a more accurate picture of the impact of cancer in a population Cancer incidence can be used to identify the population(s) at highest risk, whilst survival provides a measure of prognosis. Used in combination, these two measures illustrate how the impact of cancer varies between groups and over time. 2. Cancer mortality is essential to inform public health and health-care priorities Examining mortality rates enables bias in cancer incidence and survival to be detected. 3. Examining mortality alone can be misleading Trends in cancer mortality are the result of previous trends in both incidence and survival. To provide a fuller understanding of the impact of cancer in a population, cancer mortality trends should be examined alongside trends in incidence and survival. 4. Analysis of M/I ratios alone can be misleading M/I ratios can be used as a crude surrogate for survival, but only in combination with incidence and mortality measures. Where population-based cancer survival can be estimated, M/I ratios should not be used.
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2007 (the International Cancer Benchmarking Partnership): an analysis of populationbased cancer registry data. Lancet 2011;377: 127–38. Autier P, Boniol M. Caution needed for countryspecific cancer survival. Lancet 2011;377: 99–101. Woods LM, Coleman MP, Lawrence G, et al. Evidence against the proposition that "UK cancer survival statistics are misleading": simulation study with national cancer registry data. Br Med J 2011;342:d3399.
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Appendix The mathematical tool used to analyse these processes is the “event rate”. For the cancer incidence rate, the event is a new cancer diagnosis. The concept behind the event rate is sophisticated, and it requires calculus for a fully rigorous definition, but intuitively, it may be defined as the probability that the event occurs in a given person during the next interval of time (year, month or day ...) given that this person is still at risk of the event (i.e., alive, and still under observation) at the beginning of the interval. This probability clearly depends on how long the person is under observation: the longer the period of observation, the higher the probability that an event will occur. Therefore, we divide the probability by the length of the period of observation to get the average event rate over that unit of time e.g., the annual death rate. This estimation of the event rate applies to all three measures: incidence, survival and mortality. For incidence and mortality rates, however, the number of persons in the general population who are at risk of being
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diagnosed with or dying from cancer, respectively, can only be obtained from national statistics agencies or census offices. These agencies usually publish the number of living persons in the general population of a given age at a fixed date each year. It is not practicable to maintain continuous follow-up of an entire national population to determine whether each individual is still “at risk” (alive and still resident in the country, state, province, ...). The total person-time at risk of an event in a given year is therefore approximated by the mid-year population; in some countries, this is directly available from the national statistics agency. Things are different for survival. The population at risk of an event (usually, death) is no longer the general population, but the subset of the population who have already been diagnosed with cancer. In a cancer survival study, we do know the history of each subject—and therefore their precise time at risk of death—because the cancer registry routinely obtains data on the vital status of each patient.
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Given t, the time at start of the interval, and x, the age at ^ is: time t, the estimated event rate k
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^ k5
kxt nxt X Dxi i51
where kxt is the total number of events among nxt subjects under observation until t, and the denominator is the sum of observed duration times (person-years) for all nxi. As the entire population cannot be followed up individually from birth to death, we cannot estimate directly the transition rates between the various states, but Figure A1 shows the competing risks that we are trying to model. The possible trajectories for a given person between various “states” (boxes), from an initial state of Healthy and the eventual state of Death, with possible spells in Cancer and/ or Other diseases states. The arrows represent transitions between the various states, required to study survival: incidence of cancer or other diseases, and death from cancer or other diseases. Each arrow is labelled with the corresponding “event rate”: k for the incidence rates, l and m for the mortality rates at a given age, where x is the age at incidence and y is the age at death. The indices, we have used
to label each event of interest are as follows: c for “cancer,” o for “other diseases” and a for “all causes of death.” The index y 2 x is the time elapsed since the diagnosis of cancer (xc) or other diseases (xo). The cancer incidence rate (kc) can be obtained from cancer registries. The cancer mortality rate (lc) can be obtained from national mortality statistics. The cancer mortality rate can also be considered as the two-step transition between Healthy and Cancer followed by the transition from Cancer to Death (kcmc). The dashed lines in Figure A1 represent other transitions. Thus, the population mortality rate from causes other than the specific cancer under study (lo) is also the two-step transition from Healthy to Other diseases and then from Other diseases to Death (komo). The idea behind concepts such as net survival and relative survival is to obtain the mortality rate from cancer among the cancer patients by subtracting the population mortality rate from causes other than the specific cancer (lo) from the mortality rate for all causes of death (ma); lo is obtained from population life tables. Note that the transition rate from Cancer to Other diseases is not usually equal to the transition rate from Healthy to Other diseases. This raises the problem of the appropriateness of the population life table for the cancer patients.
Figure A1. The relationship between incidence, survival and mortality.
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