Conditional relative survival of cancer patients and conditional probability of death

A French National Database analysis


  • Members of the Association of French of Cancer Registries: Bas-Rhin, M. Velten; Calvados, G. Launoy; Côte d'Or, J. Faivre; Doubs, A. Danzon; Haut-Rhin, A. Buémi; Hérault, B. Trétarre; Isère, P. Delafosse; Loire-Atlantique, F. Molinié; Manche, S. Bara; Somme, O. Ganry; Tarn, P. Grosclaude.



Little information is available on the conditional probabilities of death among patients who survive for >5 years after a diagnosis with cancer. The objective of this study was to estimate the conditional probabilities of death for breast cancer, prostate cancer, colorectal cancer, and lung cancer in France.


The study included data from the French Network of Cancer Registries from 205,562 patients aged <75 years who were diagnosed with cancer between 1989 and 1997. The conditional probabilities of death were calculated by using a relative survival regression model in which age was included as a covariate.


After the first year and until 10 years after diagnosis, the annual probability of death decreased dramatically for colorectal cancer: It was the same in all age groups after 3 years, and it was approximately 1% at 10 years. For prostate cancer, the decrease was not as great, and the conditional probability of death remained higher among younger patients at >4% at 10 years. During the 3 years after diagnosis, the probability of death was greater for older patients with breast cancer; then, it decreased less for younger patients compared with older patients, leading to a greater conditional probability of death among younger patients at 4 years and up to 10 years. The annual probability of death in patients with lung cancer decreased for both sexes but remained substantially higher for men than for women, reaching approximately 8% and 5%, respectively, at 10 years.


Further studies would facilitate a better understanding of the observed differences in relative survival within European countries. Cancer 2009. © 2009 American Cancer Society.

In Europe, the burden of cancers is still increasing. The rise in life expectancy inevitably will lead to a growing number of affected patients. Cancer incidence in France increased by 89% between 1980 and 2005.1 The total number of cases was about 320,000 in 2005. Population-based cancer survival is complementary information necessary for planning the healthcare response to the increasing cancer burden. For each cancer site, 5-year crude and relative survival probabilities after diagnosis have been published.2 Along with those estimates, there is a need for further information that could help to evaluate the changing risk of death in each successive year after the diagnosis of the disease. For patients who have survived for a specified time after diagnosis, the probability of surviving the following year provides information that is not available from overall survival. The calculation of conditional survival provides an accurate evaluation of the patient's changing risk over time. To describe this evolution, the annual probability of death from cancer, conditional on having survived until then, can be calculated. These probabilities are useful for comparison with other countries that have different environments and/or medical care systems. They also are helpful for clinicians in the planning of appropriate surveillance after initial management. It has been demonstrated that, in Europe, insurance companies are reluctant to provide life insurance and banks are reluctant to provide loans to patients who have a history of cancer. Evidence that groups of patients present no significant excess of death compared with individuals from the general population of the same age and sex may help improve this situation. The objective of the current study was to investigate how the annual probability of death from cancer changed over time after diagnosis for the most frequent cancers, ie, breast, prostate, colorectal, and lung cancers, using the French cancer registries database.



The Association of French Cancer Registries (FRANCIM) and the Department of Biostatistics of the Hospices Civils de Lyon gathered data from all of the validated French cancer registries to create a common database that included nearly 650,000 incident cases diagnosed between 1975 and 2003 in the areas covered by a registry. A national estimation of cancer incidence recently was published using data from the Network of the French Cancer Registries.1 Of all cancers, 4 sites were predominant and contributed to about 56% of all new cancer cases in France in 2005: prostate cancer (19.4%), breast cancer (15.6%), colorectal cancer (11.7%), and lung cancer (9.5%). Conditional survival was computed for these cancer sites from all cases diagnosed and followed in the French registries, as described above.

The study was based on 205,562 incident cancer cases diagnosed between 1989 and 1997 in patients aged >15 years in 12 French administrative areas (covering about 15% of the French population) and was focused on patients aged <75 years. The quality and exhaustiveness of these registries are certified every 4 years by an audit of the National Public Health Institute and the National Institute of Health and Medical Research. Cancer sites were defined according to codes from the International Classification of Diseases for Oncology, 2nd edition. Notification came from many sources: public and private pathology laboratories, the regional database of the National Health System, public and private hospital databases, and Comprehensive Cancer Centers. French registries do not record incident cases using death certificates only. Tools provided by the International Agency for Research on Cancer were used to ensure quality control. All participating teams carried out active and rigorous research for vital status information for each case using a standardized administrative procedure. The information was collected “at the first line” through birthplace public services or through an electronic request to the National Register for the Identification of Physical Persons. Both procedures require the knowledge of the birthplace. Because this information could not be obtained for all cases, other sources of information for vital status were used (medical records or public services of the place of residence). Nevertheless, priority was given to the first-line standardized strategy, and the reliability of second-line strategies had to be judged by the registries before their use. The general principle was to minimize the number of patients who were lost to follow-up without compromising the quality of the information or introducing bias. The RNIPP is able to provide vital status for individuals who are not born in France, but this information probably is less reliable in that situation (accounting for <9% of the censored patients). These patients are followed as far as possible by contacting general practitioners and specialists and by consulting hospital files. Finally, 4% of the 205,562 patients were lost to follow-up at January 1, 2002, including 6.1% of 35,627 patients with colorectal cancer, 2.4% of 19,507 patients with lung cancer, 3.9% of 19,448 patients with prostate cancer, and 3.9% of 30,923 patients with breast cancer.

Relative Survival

Relative survival is defined as the ratio of the observed survival in the cancer patients under study to the expected survival of a general population with similar sex, age, and year of death. It reflects the excess mortality in the cancer patient group relative to the background mortality. Relative survival was estimated using an excess rate model: We assumed that the observed mortality rate was the sum of 2 mortality rates: the expected mortality rate (ie, the natural mortality rate) and the excess mortality rate (λc) (ie, the mortality rate from cancer),3 which is the parameter of interest that we sought to estimate. We considered that the expected mortality rate was known and was obtained from published vital statistics provided by the National Institute of Statistics and Economic Studies. For each site and for each sex, the excess mortality rate λc was obtained by using a model in which age was introduced as a covariate. More precisely, using t as the time after diagnosis, the following model was used4:

equation image(1)

which f, g, and h are cubic splines. The “mean” effect of age was tested by comparing the likelihood of a model with a linear (and proportional) age effect versus the likelihood of a model without an age effect (a likelihood ratio test [LRT]). Furthermore, because the effect of age is neither linear nor constant over the follow-up period,5 Model 1 allows nonlinearity and accounts for a time-dependent effect of age.4 Theses 2 features also were tested in an LRT. The estimation procedure for parameters of the model was detailed in a seminal article.4

Age is considered as a continuous factor in Model 1 to optimally model its effect on mortality. For specific age groups, estimates of the excess mortality rate were obtained using the predicted values calculated from the observed mean age of these age groups (ie, if the mean age of patients in the group ages 15-44 years is 43 years, then this age was used in the model to predict rates). Relative survival was estimated from the excess mortality rate through the classic relationship between the hazard rate and the survival probability (see Eq. 2, below).

Conditional Probability of Death

The probability of death between time t0 and time t1, conditional on having survived until t0, is related directly to the excess mortality rate:

equation image(2)

Values of λc obtained from Model 1 were used in Equation 2 to obtain the conditional probability of death. This probability, based on a relative survival model, is interpreted as the probability that an individual will die from cancer and the consequences or causes associated with the risk factors.

The conditional probability of death from cancer is called the “probability of death” for the sake of simplicity, with the understanding that it is death from cancer and related causes and that it is conditional on the patient remaining alive until then. Note that the annual probability of death (t0 − t1 = 1) and hazard rate values are nearly identical when the hazard rates are small (ie, <0.1) and constant between t0 and t1. The conditional relative survival at 10 years if the patient is alive at 5 years is calculated from the integral of the excess death rate over this 5-year interval.


For each studied cancer, relative and conditional survival are shown in Table 1, and the annual probability of death up to 10 years after diagnosis is shown in Figure 1 and in Table 2 by age group and sex (as suitable). The mean effect of age at diagnosis was highly significant (P < .001) for all studied cancers and for both sexes.

Figure 1.

These charts illustrate the annual probability of death (%) during the first 10 years after diagnosis according to sex, age at diagnosis, and site (relative survival model).

Table 1. Relative and Conditional Survival (%) According to Sex, Age, Disease Site, and Time Since Diagnosis
Years Since DiagnosisAge at Diagnosis, y
Males, %Females, %
  • *

    Ten-year relative survival (%) was conditional on surviving for ≥5 years after diagnosis.

  • For the group ages 15 years to 54 years.

 10 Conditional*8888888888899093
 10 Conditional*7370676281767163
 1 939696    
 5 708183    
 10 577172    
 10 Conditional* 828787    
 1    98989796
 5    85878683
 10    74797875
 10 Conditional*    87909190
Table 2. Conditional Probabilities (%) of Death During the First 10 Years After Diagnosis According to Sex, Age, and Disease Site: Relative Survival Model
Males, %Age at Diagnosis, y
Years since diagnosis
Females. %Age at Diagnosis, y
Years since diagnosis10.412.814.617.942.546.547.

Colorectal Cancer

In men with colorectal cancers, the 5-year and 10-year relative survival rates decreased from 62% to 56% and from 55% to 49%, respectively, with increasing age at diagnosis (Table 1). In women with colorectal cancers, the impact of age on relative survival was less important (although highly significant because of the large sample size): The 5-year relative survival rate varied between 61% and 63% according to age group, and the 10-year relative survival rate varied between 55% and 57%. The effect of age at diagnosis on the probability of death varied with the time elapsed since diagnosis (P for nonproportionality <.001 for both sexes). Consequently, the 10-year relative survival rate conditional on survival 5 years after diagnosis was 88% in men of all age groups and increased with age at diagnosis from 88% to 93% in women.

In both men and women with colorectal cancers, the probability of dying was high during the first year. It rose with the increasing age from 12.5% to 20.6% in men and from 10.4% to 17.9% in women (Table 2, Fig. 1). After the first year and until the 10th year after diagnosis, the probability of dying dropped dramatically over time in both sexes. During the first 3 years, older patients were at a higher risk than younger patients; however, after 3 years, the risk in all age groups was similar. During the 10th year, the probability of dying for both sexes ranged from 0.4% to 1.2% and was greater in the younger age groups than in the older age groups.

Lung Cancer

In men with lung cancer, the relative survival rate decreased with increasing age at diagnosis, varying from 17% to 13% at 5 years and from 12% to 8% at 10 years (Table 1). In women with lung cancer, the rate was higher for the group ages 15 to 44 years than for older patients and varied from 26% to 18% at 5 years and from 21% to 11% at 10 years. Patients who survived for 5 years after diagnosis had a better chance of surviving for an additional 5 years if they were aged <55 years at diagnosis (>70%) than if they were older (<70%). Risk patterns were quite similar in men and women (Table 2, Fig. 1). The probability of dying was very high during the first 4 years after diagnosis and was higher in men than in women. After the first 4 years, the probability of dying decreased, varying between 5% and 10% every year, except in the youngest age group of women, in which it was stable at <5%. In men, the probability of dying during the 10th year for those who remained alive after 9 years still was 7% and 7.8% for the 2 youngest age groups, and it was slightly lower than that in the 2 oldest age groups (8.5% and 9.9%). In women, the probability of dying during the 10th year did not vary much according to age group (range, 5.3%-5.7%).

Prostate Cancer

Because of the distribution of patients according to age at diagnosis, the groups ages 15 years to 44 years and ages 45 years to 54 years were pooled for prostate cancer. The 5-year relative survival rate differed according to age at diagnosis, increasing from 70% in men aged <55 years at diagnosis to 83% in men aged >65 years (Table 1). The gap increased 10 years after diagnosis, when there was a difference of 15 points between the 2 age groups (57% vs 72%). The prognostic impact of age at diagnosis was not linear (P < .001). The 10-year relative survival rate conditional on patients surviving 5 years after diagnosis was the lowest for the youngest patients but did not vary with age at diagnosis after age 55 years.

The probability of dying during the first year after diagnosis was relatively low and was somewhat higher for men aged <55 years at diagnosis (6.9%) compared with older men (approximately 4%) (Table 2, Fig. 1). It increased in the second year and progressively decreased after the second year until the seventh year for all age groups. From the eighth year until the 10th year, the probability of dying increased again in all age groups. The difference according to age at diagnosis remained throughout follow-up; the probability of dying during the 10th year was 4.4% for patients who were ages 15 years to 54 years at diagnosis, 3% for patients who were ages 55 years to 64 years at diagnosis, and 3.1% for patients who were aged >65 years at diagnosis.

Breast Cancer

The effect of age at diagnosis on the probability of death from breast cancer was not linear (P < .001): The youngest and oldest women were at greater risk than middle-aged women. Therefore, the 5-year relative survival rate was lowest in the groups ages 15 years to 44 years and ages 65 years to 74 years (85% and 83%, respectively) and was highest in the group ages 45 years to 54 years (87%) (Table 1). This pattern was similar 10 years after diagnosis. However, the effect of age at diagnosis on the conditional probability of death varied with the time elapsed since diagnosis (P for nonproportionality <.001). The 10-year relative survival rate conditional on surviving 5 years after diagnosis still was the lowest in the youngest women (87%) but was stable after age 45 years (90%).

Overall, the probability of dying each year was low in patients with breast cancer compared with other sites; the highest probability of dying was 4.2% and occurred among women in the group ages 64 years to 74 years during the first year after diagnosis (Table 2, Fig. 1). However, this probability did not decrease substantially over time. The probability increased between the first year and the third year in all age groups. From the fourth year to the 10th year after diagnosis, the probability of death decreased progressively in all age groups. However, it was slightly higher in the group ages 15 years to 44 years than in the other age groups. Among the women who remained alive after 9 years, the probability of dying during the 10th year after diagnosis was 2.3% among women who were aged <45 years at diagnosis and varied from 1.7% among women who were between ages 45 years and 64 years at diagnosis to 1.9% among women who were aged >65 years at diagnosis.


The interest of conditional survival has come to light over the last 10 years, in that it provides useful information for practitioners and patients. This information should quantify the changes in a patient's profile over time with regard to the risk of dying from cancer. It will allow the practitioner to determine an appropriate surveillance strategy and will help patients return to a normal social life after cancer. Most available information comes from the Surveillance, Epidemiology, and End Results Program of the National Cancer Institute in the United States.6-12 Few European studies have been published on conditional survival among patients with cancers,13-15 and none have dealt with data from Latin regions, although all European survival studies have underlined differences between European countries with regard to cancer prognosis.16 One of focus of this report, which was based on the French national cancer database, was to allow comparisons with previous publications.

The French network dataset has the advantage of including large-scale, population-based data with standardized registration procedures and a high level of completeness. Nonetheless, some important explicative factors, such as stage at diagnosis or treatment modalities, could not be considered in this study because of unavailable information in some geographic areas. For colorectal, breast, and prostate cancers, the conditional probability of death decreased to low values by 5 years and even before then in some cases. For lung cancers, the excess probability decreased regularly but leveled off at non-null values. For breast and prostate cancers, the initial annual excess probability was lower, but the difference was small and varied according to age group.

In our statistical approach, estimations for both sexes were obtained separately using a single model in which the effect of age at diagnosis was modeled (rather than by adjusting a separate model for each age). It enabled us to pool all of the available data to optimize the use of this information. This approach was possible because our model allows for flexible modeling of the age at diagnosis effects (nonlinear and time-dependent effects).4 One of the main interests of this study was to underline the finding that age at diagnosis did not influence the long-term annual conditional probability of death in the same way for all cancer sites. After the fifth year and until the 10th year, the annual probability of death was higher in younger age groups for prostate and breast cancers, whereas it did not vary in age groups for colorectal or lung cancers. Previous publications did analyze the effect of age at diagnosis on short-term conditional relative survival (between 1 year and 5 years after diagnosis), but few reports have covered a period of 10 years. In those studies, younger patients generally had a better prognosis than older patients.8, 9, 14 In a Danish study on crude conditional survival, patients who were diagnosed with lung cancer before age 50 years and who survived for 5 years after diagnosis had a greater chance of surviving an additional 5 years (81%) than older patients (37% after 70 years).14 We used relative conditional survival to improve assessment of the age at diagnosis effect and calculated equivalent rates of >70% and approximately 62%, respectively. This discrepancy is explained in part by the use of different methodologies. Other studies did not take into account the effect of age at diagnosis on short-term conditional relative survival.16 For breast cancer, it is well known that younger patients have a worse 5-year prognosis17, 18 and that this is related to aggressive tumor characteristics, such as tumor grade or proliferation index. The effects of the natural history of breast cancer may persist over time and affect the long-term conditional probability of death for young women.

The difference between men and women with regard to the probability of dying from colorectal cancer between the fifth year and the 10th year was small. Six years after diagnosis, the probability of death for survivors was low. About 80% of recurrences occurred during the first 3 years after resection of colorectal cancer, and >90% occurred within the first 5 years.19 This may explain in part the marked decrease in the annual probability of death after the fifth and sixth years as a result of the selection of patients who no longer were exposed. Although relative survival was higher for women than for men in all age groups,2 only the 10th year conditional probability of death for the oldest women appeared to be a little more favorable than that for men. It is possible to hypothesize that, because sex does not influence the recurrence of colorectal cancer, the risk of death does not differ between sexes within the first years after diagnosis.19 Then, because other competing causes of mortality (for example, life-long exposure to tobacco and alcohol) are less frequent among women, women may benefit from longer conditional survival after the first 3 to 5 years. Previous studies among patients with colon cancer who remained alive 5 years after diagnosis indicated that the difference in survival between groups according to disease stage remained significant 10 years after diagnosis, although it decreased with time since diagnosis.10 Additional French studies that take into account disease stage and morphology would be useful for further analysis of colorectal cancers and other cancer sites.

Overall, the annual probability of death from lung cancer was slightly lower in women than in men. Previous publications were in accordance with this finding.14 To our knowledge, no studies have dealt with the effects of both sex and age at diagnosis, whereas we demonstrated that there was no greater relative benefit for younger age groups compared with older age groups. For some cancer sites, the finding that the diagnosis was recent may have reduced the excess probability of death during the first year compared with those who were diagnosed earlier. However, these survivors may experience greater morbidity and mortality, because they remain exposed to recurrences and to treatment effects. Thus, some future analysis taking into account the year of diagnosis will be needed to explore the evolution of the annual probability of death according to such factors. It is now important to determine the nature of the differences within countries with regard to relative 5-year survival when analyzed in terms of conditional survival.

Conflict of Interest Disclosures

Supported in part by a grant from the Ligue Nationale Contre le Cancer.