Choice of relative or cause-specific approach to cancer survival analysis impacts estimates differentially by cancer type, population, and application: evidence from a Canadian population-based cohort study

Subjects are members of the 1991 Census Mortality Cohort, a population-based cohort of adult respondents to the mandatory 1991 Canadian Long Form Census who have been followed up for incident cancers using probabilistic linkage to the Canadian Cancer Registry. Date and cause of death were ascertained using two sources: the Canadian Cancer Registry and the Canadian Mortality Database. Date of death was also supplemented with information from non-financial tax summary files. The Canadian Mortality Database includes all deaths occurring in Canada and deaths of Canadians occurring in some US states. A more thorough description of the cohort has been published elsewhere [14, 15].

We estimated survival from the nine cancers that were most common among First Nations. We restricted the study population to first primary cancers diagnosed in persons aged 45 to 90 between January 1, 2001, and December 31, 2009, excluding the province of Quebec. Quebec accounts for just under 25% of the Canadian population and about 10% of the First Nations population [16]. Cases from Quebec were excluded because of differences in registration procedures that make survival estimates non-comparable with those from other provinces/territories. We excluded cases identified based on death certificate or autopsy only or who had negative survival time (in total 1.1% of non-Aboriginal cases and 1.6% of First Nation cases). Cancers were grouped according to the Surveillance Epidemiology and End Results (SEER) site recodes based on the International Classification of Diseases for Oncology (ICD-O) 2nd and 3rd Editions conventions.

We estimated 5-year age-standardized survival and excess mortality rate ratios/hazard ratios using four methods: relative survival with ethnicity-specific life tables (RS-ELT), relative survival with general population life tables (RS-GLT), cause-specific survival with a broad definition of cancer death (CS-Broad), and cause-specific survival with a narrow definition of cancer death (CS-Narrow). For all four methods, we used flexible parametric survival models, which employ restricted cubic splines and were implemented with the stpm2 command in Stata [8, 17]. Five-year survival was age-standardized to International Cancer Survival Standards, which vary by cancer type [18]. Age-standardized survival models were adjusted for sex if applicable. Excess mortality rate ratios and hazard ratios were stratified by sex and adjusted for age. All models used the complete approach, meaning that the conditional survival probabilities of all calendar years are used for all survival estimates [19]. More information about the models can be found in the Additional file 1.

Under both relative and cause-specific frameworks, survival time was the interval between the date of diagnosis and the date of death, 5 years post diagnosis, or December 31, 2009, whichever came first. For RS-ELT, expected survival was estimated using life tables produced based on the mortality experience of members of the cohort at large of the same age (single-year integers), sex (male, female), and ethnicity (First Nations or non-Aboriginal) during the same time period (1992–2000 and 2001–2009 rates were applied to each individual year within the time period) [20]. For RS-GLT, expected survival was estimated using life tables produced for the CONCORD-2 study [21]. These life tables were specific to age (single-year integers), sex (male, female), calendar year (single-year integers), and province/territory (nine provinces and three territories) but did not take ethnicity into account.

Under the narrow definition of cancer death (CS-Narrow) only deaths that were recorded as due to the first primary cancer were counted as events and all others were censored. The ICD-O codes used to produce this definition are available publicly from SEER [22]. The broad definition of cancer death (CS-Broad) was introduced by Howlader in 2010 and includes not only deaths attributed to the incident cancer directly, but also deaths attributable to other cancers, AIDS, and/or site-related diseases. What gets counted as a “cancer death” under the broad definition depends on whether the cancer was the only malignancy within an individual’s lifetime or the first of two or more malignancies and on the site of the of the original cancer diagnosis [9]. For both CS-Narrow and CS-Broad, if cause of death was missing (1.3% of non-Aboriginal cases and 2.3% of FN cases), patients were censored at their date of death.

Two major sources of bias will drive the differences in cancer survival between methods: (i) the extent to which the life tables represent the mortality of the cancer patients had they been cancer-free; and (ii) the proportion of cancer-consequent deaths that are attributed to cancer according to the death certificate and/or its interpretation [4]. For each cancer, the relative impact of these biases will vary.

In the case of prostate cancer, cause-specific survival was consistently lower than relative survival. This is consistent with other comparisons of relative and cause-specific survival for prostate cancer [9, 10, 12]. Cases were diagnosed in 2001 or later, by which time evidence had accumulated that prostate-specific antigen (PSA) testing should not be routinely used as a screening test [23, 24], but the PSA test may still have contributed to this difference. Higher uptake of the PSA test by people who are more socially advantaged and therefore healthier can result in underestimation of expected mortality in life tables and inflated estimates of relative survival from prostate cancer [25, 26].

Among non-Aboriginal women, estimates of RS from breast cancer were higher than estimates of CS survival. In contrast, among First Nation women, estimates of CS from breast cancer were higher than estimates of RS. American women with early-stage breast cancer have been shown to be less likely to die of non-cancer causes than other women of their same age without cancer [27]. Accordingly, if women with early-stage disease make up a large proportion of cases in the non-Aboriginal population, their expected mortality will be overestimated using general population life tables and the relative survival ratio will be inflated. First Nation women in Canada are less likely to be diagnosed with early stage disease, reducing the mismatch between life tables and true survival, and accordingly reducing the difference between survival measured by relative and cause-specific approaches [28].

For all cancers except prostate and breast, CS-Narrow produced higher survival estimates than the other three methods. This was expected – if cancer death is more narrowly defined, it will be rarer and cancer survival will appear higher. The differences in survival estimated by CS-Narrow compared to RS-ELT were greatest for stomach cancer, lung cancer, and cancers of the oral cavity and pharynx. The differences between the CS-Broad and CS-Narrow estimates for stomach cancer and cancers of the oral cavity and pharynx in particular suggest that the driving force behind these differences is a misclassification of cancer-consequent deaths as non-cancer under the narrow definition.

This was confirmed when we investigated the deaths counted as due to cancer under the broad definition but not under the narrow. For oral cavity and pharyngeal cancers, the discrepancy was mostly attributable to laryngeal cancer deaths that had not been counted as cancer deaths under the narrow definition because they were not of the same site. For stomach cancer, the discrepancy was a result of deaths attributed to esophageal cancer that had not been counted as cancer deaths under the narrow definition. These cancers stand out because cancers of the oral cavity, digestive tract, and respiratory tract are internal and contiguous, leading to a greater likelihood of attributing death to a neighboring organ.

Misattribution of cause of death along the continuous respiratory tract likely also explains, to some extent, the higher age-standardized survival from lung cancer calculated with CS-Narrow compared to the other methods. Unlike stomach and oral cavity and pharyngeal cancers, however, the CS-Broad estimate was also inflated compared to the RS-approaches. This suggests that the relative survival approach may be underestimating survival. Since lung cancer is highly associated with smoking, and smoking is associated with poorer health and more comorbidities, general population life tables overestimate expected survival among lung cancer patients [27].

Differences across methods in the relative risk measures will only arise if the assumptions underlying each method are violated to different extents in the subgroups being compared. For example, the use of general population life tables rather than ethnicity-specific ones introduces a differential bias. General population life tables underestimate the background mortality of First Nations to a greater extent than they overestimate the background mortality of non-Aboriginals. In this study, for all but breast and prostate cancers, this bias had a minimal effect on the EMRRs, which were comparable under RS-ELT and RS-GLT frameworks.

For prostate cancer, cause-specific approaches produced HRs that indicated a significant difference in survival that was not found with relative survival. The cause-specific HRs for prostate cancer were lower than the EMRRs estimated by RS-GLT but higher than the EMRRs estimated by RS-ELT. The biases we have previously described do not clearly explain this pattern; however there is substantial uncertainty around these estimates because of the small proportion of cases that died during the 5-year follow-up, so the pattern we see may be due to chance.

For breast cancer, CS estimates of disparity were lower than RS estimates. As described above, this is likely attributable at least in part to a differential bias introduced by life tables (even ethnicity-specific ones) for First Nations and non-Aboriginal Canadians. In the general population, where breast cancers may more often be screen-detected, life tables would underestimate expected survival due to the “healthy screener” effect [29, 30]. First Nation women, in contrast, may be more likely to be diagnosed incidentally while in contact with the health system for other illnesses/comorbidities, in which case life tables would overestimate expected survival. More research to explore methods of detection and how they vary in Indigenous and non-Indigenous persons would be worthwhile to further explore this hypothesis.

For many cancers, there were small numbers of cases and deaths among First Nations. The resulting uncertainty around survival estimates for First Nations could have led to an under-ascertainment of what, with more power, may be statistically significant differences between the estimates using different methods. We therefore considered the differences in interpretation of effect estimates produced by each of the approaches rather than the statistical relationship between them. A second consequence of the small numbers was an inability to consider differences between the methods with longer follow-up or by age. Based on existing literature, we would expect the differences between the methods to be greater with increasing time since diagnosis and among older patients [11‐13].

While the small numbers may not have permitted such analyses, stage-specific comparisons, particularly for breast and prostate cancers, would provide insight into the factors driving differences between estimates. Stage has not been historically collected in Canadian cancer registries and so was not available for analysis in this study.

The analyses presented in this paper were limited to first primary cancers because the broad definition of cancer death is only applicable to first cancers [9]. Given that the incidence of second cancers is rising, and that second cancers are accounting for a growing proportion of all cancers, we believe that including higher-order malignancies in survival estimates is generally good practice. The development of a broad classification of cancer-specific death for higher-order cancers would be valuable.

We used a model-based approach to estimate net survival in a relative survival framework. The relatively new Pohar Perme estimator of net survival is an alternative approach that has been recently introduced and promoted. The Pohar Perme estimator is theoretically unbiased because it is not subject to the influence of informative censoring mechanisms whereby the people who are least likely to die overall (and therefore would presumably have the highest cancer survival) contribute more time into the expected mortality denominator [31]. The disadvantages to the Pohar Perme estimator are that it is non-parametric and has high variability. The high variability is exaggerated if relative survival ratios are age-standardized [31]. Given the small numbers of cancers and deaths among First Nations in this study, and the similarities in estimates produced by model-based methods and the Pohar Perme estimator for short follow-up times, such as the 5-year time horizon in this study, we think the model-based approach was justified.

With respect to generalizability, the magnitude of the differences in results generated by each method will be affected by the differences between the populations being compared. If, for example, uptake of breast cancer screening was similar in both populations, we might expect to see smaller differences in the measures of disparity. Furthermore, the dataset used for this study had a high level of completeness of cause of death data. In general, the exclusion of persons with missing cause of death from cause-specific analyses, while they are included in the relative survival estimates, could introduce further differences between the estimates generated by each method.