Relative versus cancer-specific survival: assumptions and potential bias

Diana Sarfati1, Matt Soeberg1, Kristie Carter1, Neil Pearce2, Tony Blakely1. 1University of Otago Wellington, New Zealand 2Centre for Public Health Research, Massey University

Cancer-specific and relative survival analyses are the two main methods of estimating net cancer survival.

Bias through misclassification of cause of death is well recognised for cancer-specific survival.

To date there has been no systematic examination of the potential bias where lifetable mortality rates are used as the external comparison group for relative survival.

This latter bias may be particularly important for smoking-related cancers where the expected survival is lower than the general population because of the high incidence of non-cancer smoking-related mortality.

Background

Study Objectives1. To assess the impact on relative survival

ratios (RSRs) for lung and bladder cancers using crude compared with ethnicity and smoking adjusted life table data.

2. To compare these results with simulations to estimate the effect of misclassification bias on cancer-specific estimates.

The1996 Census population for the New Zealand (NZ) population was probabilistically linked to cancer records from the NZ Cancer Registry.

The 1996 census included two questions to elicit smoking status.

Four sets of life tables were generated: 1) official period New Zealand life-table for 1995-97 stratified by year of age and sex, 2) ethnic- specific life-tables, 3) smoking-specific (current, ex, never smoker) life-tables and 4) ethnicity by smoking life-tables.

We generated five-year RSRs for each of bladder and lung cancers using each of the four sets of life-tables. Only results for life-tables 1) and 4) are presented here.

We also simulated the effect on cancer-specific survival rates of misclassification of cause of death of up to 20% for cancers with good (79%), moderate (48%) and poor (16%) five-year survival.

Methods

Results Discussion

Conclusions

• Both cancer-specific and relative survival methods are potentially valid for population-based cancer survival studies.

• A comprehensive understanding of the likely biases arising from each of the two methods is necessary for appropriate study design and interpretation of study findings.

Both cause-specific survival and relative survival are valid epidemiological methods in population-based cancer studies.

The choice will depend on study objectives, type of data available and the appropriateness of the assumptions underlying the two methods.

The main concern in relative survival analyses is the potential lack of comparability between the cancer group and the external population comparison group.

This error will be more marked where there are risk factors of the specified cancer strongly associated with other causes of death.

RSR estimates are reasonably robust to this type of error for many cancers.

When excess mortality models are run using mis-specified life-tables, the bias can be more substantial but depends on both background mortality and excess mortality rates.1

The main concern in cancer-specific analyses is the potential for bias due to misclassification of cause of death

The magnitude of this error will vary depending on quality of mortality data, but cannot be avoided altogether.

This bias has greater impact on cancers with moderate or poor survival.

Because Cox proportional regression models hazards (usually mortality) rather than survival, the impact of this bias is relatively small in etiological studies. 1

For cause-specific survival, misclassification of cause of death had little impact on estimates of survival for cancers with good survival.

The effect of misclassification was greater for cancers with moderate or poor survival.

When sex-specific life tables were used relative survival estimates tended to be underestimated for smokers and slightly over-estimated for non-smokers compared with sex, ethnicity and smoking specific life tables.

1. Sarfati D, Blakely T, Pearce N. Measuring cancer survival in populations: relative survival versus cancer-specific survival. International Journal of Epidemiology 2010; 39: 598-610. and

2. Blakely T, Soeberg M, Sarfati D, Carter K, Atkinson J. What is the difference in lung and bladder cancer relative survival between ethnic and smoking groups? What is the impact of using incorrect life table data? Manuscript in preparation.

Relative Survival Cancer-Specific

Study type

Interested in:

Endpoint

Analysis

Data required

• Cohort • Cohort

• Survival from cancer

• Survival from cancer

• All deaths • Cancer deaths

• Cancer-specific survival

• Observed survival

Expected survival

• All deaths

• Expected deaths /

expected survival (comparison group)

• Cancer-specific deaths

• Loss to follow-up

(including non-cancer deaths)

  Sensitivity* Specificity*

         

5-year cancer-specific survival

    100% 90% 80%

Good survival 100% 0.79 0.78 0.77

  90% 0.81 0.80 0.79

  80% 0.83 0.82 0.81

         

Moderate 100% 0.48 0.48 0.47

 survival 90% 0.52 0.51 0.51

80% 0.56 0.55 0.55

         

Poor survival 100% 0.16 0.15 0.15

  90% 0.19 0.19 0.19

  80% 0.23 0.23 0.22

Estimated 5-year cancer-specific survival rates for varying levels of misclassification of cancer, and non-cancer deaths for cancers with good, moderate and poor survival, assuming a fixed annual mortality rate from non-cancer causes (2.3%).

*Sensitivity and specificity refer to the proportion of cancer and non-cancer deaths respectively that are recorded as such.

Current Smoker Never Smoker Current Smoker Never SmokerMale Female

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Bladder Cancer 5 year cumulative relative survival

Sex-specific life tablesSex-, ethnic-, smoking-specific life tables

Current Smoker Never Smoker Current Smoker Never SmokerMale Female

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Lung Cancer 5 year cumulative relative survival

Sex-specific life tablesSex-, ethnic-, smoking-specific life tables