Has equity in relative survival improved over time in Finland – a methodological exercise

Abstract

Background. Population-based relative survival is widely used as a method of monitoring the success of cancer control. This success may not be relevant only for an entire country but also regional developments over time are of interest. It would not only be important that the relative survival improved but also that the differences between regions decreased over time. Methods. In this paper the authors show how relative survival methods can be used to study such differences. In addition to standard methods, some more recently introduced approaches are used, most notably a method for checking the goodness of fit of the relative survival model. This gives confidence in the obtained results and provides additional insight when assumptions are not met. Results. An analysis of cancers of the colon and ovary by cancer control region in Finland in 1953–2003 shows an overall improvement in relative survival, accompanied in colon cancer also by a decrease of differences in relative survival between the regions. Thus, the desired course was observed in colon cancer but not in cancer of the ovary. Conclusions. These results, applied to further sites, should lead to investigation of differences in cancer control policies between regions.

One of the important tasks of a population-based cancer registry is to monitor relative survival over time. The monitoring may be done for an entire country [1] , and the results may be compared between countries [2]. But even in the countries with high overall relative survival, there is a possibility that the high survival is not shared by all regions [3], or population subgroups [4], and there is no guarantee that the eventual differences have been disappearing with time.

An earlier study in the Nordic countries, lacking the dimension over calendar time, showed that around 5% of colon-cancer deaths could be eliminated in Finland or Sweden, should it be possible to eliminate the variation by health care district or county, respectively [3]. The corresponding absolute number of potentially avoidable deaths was largest for prostate cancer.

The study presented in this paper focuses on regional survival differences over time. In addition to cancer of the colon, also cancer of the ovary without any previously published analysis between regions was included as a comparison. This analysis for the two sites also provides a methodological example for other sites and countries. Even though we find the results of our analysis practically relevant, our focus here is on methodological issues, providing an example of how such questions can be answered.

Patients and methods

All patients eligible for survival analysis diagnosed in Finland in 1953–2002 with cancers of the colon and ovary were included in this analysis. All the patients were followed-up for death and emigration until December 31, 2003, through the vital statistics and population register files, with the help of the unique personal identification numbers available for each resident in Finland. Only 0.1% times of the patients were censored due to emigration so that the follow-up for death was virtually complete.

The previous study [3] employed cases diagnosed in 1977–1992 in Finland. There were 22 areal units, the health care districts, under consideration. Cancer control, however, is the responsibility of the five cancer-control regions in Finland [5], each lead by a university central hospital. Each of them has a population of roughly one million, and it is easier to monitor developments over time by using these larger geographical units. Codes 1–5 are used for these regions when reporting results.

To study the trends of survival in time, we split our follow-up period into five decades (1953–1962, 1963–1972, 1973–1982, 1983–1992, 1993–2002). Since the introduction of new treatment approaches happened gradually and did not take place simultaneously in all regions, this time-scale splitting is irrespective of the actual changes and is a matter of convenience.

The relative survival ratios between the observed and expected survival proportions were calculated as shown by Hakulinen [6]. The expected survival probabilities were obtained from the general population life tables for Finland stratified by sex, age and calendar period.

To further illustrate our results, the method of individual relative survival, as introduced by Stare et al. [7], was used. The method is based on a simple idea: for every person in our sample, we use his/her expected survival (mortality) distribution from appropriate (in our case Finnish) population mortality tables. Let us say, for simplicity, that we calculated the percentiles of this expected distribution. For example, for a person of a given age and sex, surviving one year might mean that he/she outlived 10% of the general population, two years 15%, and so on. The percentile (or percentage) that he/she actually outlives is the value of his/her individual survival. It is then these values, instead of the observed survival times, that are taken as outcomes, for example when calculating the Kaplan-Meier curve. These values, denoted by ASP for Achieved Survival Percentiles, are directly comparable, as the differences in the expected survival (or population risk) have already been accounted for by calculating the individual expected distributions.

The Hakulinen estimator calculates the ratio between the observed survivaing proportion of our patients and the expected proportion in the population. In this way, the method aims to estimate net survival, that is survival in the hypothetical world where one could not die of other reasons then cancer. On the other hand, individual survival method transforms the follow-up time of each patient to the percentile of the expected survival distribution. In this way, survival experience of a patient is directly expressed in terms of survival experience of population. For example, an expected survival of five years may be a very bad prognosis for a 45-year-old woman, since this is a period in which only 1% of her population counterparts would die (ASP = 0.01). On the other hand, the same prognosis might be received less negatively by a 75-year-old woman, since it would mean outliving more than 20% of her population counterparts (ASP = 0.2). The individual survival method thus gives information about the actual survival experience on a scale which enables direct comparison between the observed and population survival percentiles.

The dependency of the excess hazard on the covariates was further modelled using the additive regression model, also called the relative survival regression model, as described in detail in Dickman et al. [8]. The model has the form

observed hazard = population hazard + excess hazard

where values for the population hazard are obtained from the population life tables, and the excess hazard is modelled as

λ_E (t,x) = λ_E0 (t)e^βx.

Here x is a vector of covariates and β a vector of regression coefficients to be estimated. The baseline hazard λ_E0 (t) is assumed piecewise constant within prespecified intervals (0–3 months, 3–12 months, 1–2 years, 2–5 years).

Further, the goodness of fit of both models (for colon and ovarian cancer) was checked. Such checks are important, as the previous study [8] had shown that with population-based survival, non-proportionality in modelling the excess hazard is likely to be more a rule than an exception.

A standard way of checking the proportional hazards assumption has traditionally been to allow the coefficient to vary with respect to different follow-up intervals and then test whether this interaction with time is significant. This method depends strongly on the arbitrary choice of these intervals. Furthermore, a likelihood ratio test comparing the two models can only imply that the effect of age varies, nothing can be said about the fit of the more flexible model. The recently introduced method of Stare et al. [9] applied in this paper provides a more reliable and complete insight into the proportional hazards assumption. First, the trends are presented graphically with the coefficient for the effect of a certain covariate plotted in time. Second, the null hypothesis of a constant effect in time (proportional effects) is tested formally, using a test based on the Brownian bridge process distribution.

In case of a non-sufficient fit, an interaction between the non-proportional covariate and follow-up time was added to allow for the non-constant effect of the covariate. The goodness of fit of these final models was again tested using the described method.

The analysis presented was performed using the relsurv package [10,11] of the R statistical software [12].

Results

Five-year relative survival ratios increased in both colon and ovarian cancers over calendar time in all cancer control regions (Figure 1). The upward trend was more intense for colon than for ovarian cancer and there was a tendency for decreasing differences between regions in colon cancer (Figure 1a) but this phenomenon was not observed in cancer of the ovary (Figure 1b).

Figure 1. Trends in five-year relative survival ratios for (a) colon and (b) ovarian cancer, by cancer control region in Finland (50s = 1953–1962, 60s = 1963–1972, etc.).

Figure 2 presents the five-year relative survival ratio through decades for five different age groups. Differences between the five-year relative survival ratios tend to decrease between the age groups in colon cancer (Figure 2a), while the same cannot be said for ovarian cancer (Figure 2b).

Figure 2. Trends in five-year relative survival ratios for different age groups for (a) colon and (b) ovarian cancer (50s = 1953–1962, 60s = 1963–1972, etc.).

The youngest group (45 and less) seems to be an exception with both cancer sites – its five-year relative survival ratio is considerably higher than that of the other groups and seems to increase almost linearly through the decades.

Figure 3a and b present the survival experience through the decades as presented by the individual survival method. The time on the x-axis spans until 20^th percentile, which is the time by which 20% of the population counterparts of our patients have died. Since ASP = 0.2 means more than 20 years for a 45-year-old individual, not all curves can be estimated without bias until this percentile. The follow-up percentiles are the shortest in the case of ovarian cancer, where all patients are female and thus have a better population survival.

Figure 3. The observed survival in transformed time throught the decades (50s = 1953–1962, 60s = 1963–1972, etc.), for (a) colon and (b) ovarian cancer.

As we can see in Figure 3a, the improvement over the years is substantial, implying that colon cancer survival has improved at a much faster rate than that in the population. In the 1950s, cancer mortality was huge and only 25% of the patients would survive the period in which 10% of their population counterparts die. These numbers have improved substantially and more than 50% of the patients can expect to survive this long in the 1980s. Nevertheless, this is still rather far from the population. Comparing Figure 3a and b, we can see that the survival experience of the patients as compared to the population in the 1950s was slightly better for ovarian cancer, but the trends over time are very different. While improvement at the early percentiles is substantial for both cancer sites, the longer term ovarian cancer survival has not improved much over the decades. In other words, while the treatment advances have enabled more patients to outlive at least a few of of their population counterparts, this gain is lost when considering a longer term survival. In the 1970s, less than 25% of ovarian cancer patients are estimated to live up to the time by which 20% of their population counterparts have died (or 80% survived) and this percentage is only slightly higher than in the 1950s.

The survival experience is further explored by region, Figures 4 and 5 present the survival at two fixed population survival quantiles. Figures 4a and 5a present the percentage of patients in each region surviving until the time by which 1% of the respective general population group has died (ASP = 0.01), while Figures 4b and 5b give the percentages at ASP = 0.2. Note that, since the follow-up of the youngest patients is too short in the last too decades to reach ASP = 0.2, Figures 4b and 5b should only be regarded as a comparison between regions but not also as a good estimator of the actual percentage.

Figure 4. Colon cancer: survival probabilities for transformed time at two population quantiles (ASP = 0.01 (a), ASP = 0.2 (b)50s = 1953–1962, 60s = 1963–1972, etc.).

Figure 5. Ovarian cancer: survival probabilities for transformed time at two population quantiles (ASP = 0.01 (a), ASP = 0.2 (b) 50s = 1953–1962, 60s = 1963–1972, etc.).

We can see that all regions are rather similar at the 1^st percentile, but the survival experience diverges considerably at ASP = 0.2 for ovarian cancer. This information is similar as the one gained with relative survival ratio and the reason for this fact is that the population life tables are not split by region. On the contrary, when comparing the survival experience by age (Figure 6), the interpretation of the individual method results is considerably different. While we were interested in excess mortality in Figure 2, we here compare the observed survival with that of the population. We can see that at ASP = 0.01 older patients do better than younger. This means that even though the older patients might be having a higher excess hazard, this increase is not that important when comparing it to their population hazard. Therefore, in this initial phase, a young person having cancer loses much more compared to his population counterparts than an old one. On the other hand, at ASP = 0.2, this is no longer true. All age-groups seem to be quite similar relative to their population counterparts. The only exception is again the youngest group – their excess hazard seems to be so much lower than that of the other groups that it is low even compared to their population hazard and thus this group loses the least with both cancer sites.

Figure 6. Survival probabilities in transformed time with respect to age at two population quantiles (ASP = 0.01 (a and c), ASP = 0.2 (b and d) for colon (a and b) and ovarian (c and d) cancer (50s = 1953–1962, 60s = 1963–1972, etc.).

The effects of age and region in calendar time for each of the cancer sites were further explored using a multiple additive regression model, thus ensuring that the observed trends of one variable are independent of the other variables. Both age and year were used as continuous variables and their effects assumed linear. To allow the effects to change through the decades, interactions between the decade and all other variables were included in both models and turned out to be highly significant. Similarly, a different baseline hazard in each decade was needed to provide a sensible model.

With both cancer sites, the model giving a reasonable fit included also an interaction between the age at diagnosis and the follow-up period (categorical, cut points at three months, one year and two years), thus allowing the age effect to change with the follow-up time (non-proportional hazards).

For ovarian cancer patients, an additional interaction between the calendar year and follow-up period (allowing a different effect in the first three months and in the period three months to five years) was needed to provide a good overall fit. Nevertheless, to ensure a more direct comparison with colon cancer, an average effect of year through time was used in Figure 7a. Note that sex was not needed as a prognostic variable for colon-cancer survival.

Figure 7. (a) Excess hazard ratio for calendar year (per year) in calendar time. The significant values are denoted with filled dots; (b) excess hazard ratio (reference = Region 1) for region in calendar time for colon cancer; (c) for ovarian cancer (50s = 1953–1962, 1963–1972, etc.).

Figure 7a presents the estimated effect of year (hazard ratio for two patients diagnosed in two consequent years) through decades, the horizontal line at 1 indicating no difference. All the hazard ratios in both cancers are below one, implying that there had been a continuous improvement. The interaction between the calendar year and decade was highly significant in both cancer sites (p < 0.001), suggesting that the effect changed through the decades. The results indicated that during 1963–1992 the improvement in relative survival by calendar year had been faster in colon cancer than in ovarian cancer. Within each decade, the region variable did not have an interaction with any of the other prognostic variables. By calendar period, the regional effects had very different patterns for the two sites: In colon cancer there was a convergence of the effects whereas in ovarian cancer a divergence took place (Figure 7b and c), the interactions between the region and decade allowing these effects to take a different course were highly significant (p < 0.001). Note that Figure 7b and c are presenting the hazard ratios with region 1 as the reference – a hazard ratio above one implies that that region had a higher hazard than region 1 in that period of time.

The age at diagnosis was by far the most problematic variable in terms of non-proportionality – except for colon cancer in the 1950s, the assumption of a constant age effect is significantly violated in all the decades. The effect of age was the largest in the first year of follow-up and declined in follow-up time in both cancers (Figure 8), this trend became more pronounced in later calendar periods in the case of ovarian cancer (Figure 8b). For modelling purposes, the non-proportionality was controlled by allowing the age coefficient to change in each follow-up time interval (0–3 months, 3–12 months, 1–2 years and 2–5 years). After this correction, the goodness-of-fit tests no longer returned significant results, implying that allowing a piecewise constant effect of age in the four prespecified follow-up intervals provides a good enough fit to the data.

Figure 8. The log excess hazard ratios of age in follow-up time for (a) colon and (b) ovarian cancer.

Discussion

The study presents an example how the recently developed methods can enrich the standard cancer data analysis. The first step of the analysis was to describe the overall mortality due to cancer. As the cancer studies last long and the cause of death is unknown, the observed survival is not a good measure of cancer treatment success. The standard option is to describe it using the quotient between the observed and population survival, named the relative survival ratio. In this paper, we additionally report the proportion surviving a certain population percentile. We learn from this how the expected survival of patients was affected, a piece of information not obtainable from the standard methods.

The second step of the analysis attempted to explain the association of the net survival with various covariates, in particular the interest lied in differences between regions and age. The standard choice in modelling relative survival is the additive model, its assumptions however, are only rarely tested, a fact that can lead to questionable interpretation of the results. The goodness of fit methods presented in this paper were used to confirm that the effect of all variables but age (and calendar year in the ovarian cancer case) was modelled correctly and to illustrate how the age effect changes with the follow-up time. In this paper, we assumed both age and year to have a linear effect (piecewise linear in case of year) and used a step-wise function for the baseline hazard and the interactions with time. These are obvious simplifications and more flexible approaches to modelling are possible [13,14], and they should be considered if fit of the model is not satisfactory.

In Finland, the differences in relative survival between regions have decreased in colon cancer but an opposite development has taken place in ovarian cancer. The former should be the result to be wished when there is a uniform success in cancer control. In ovarian cancer the survival has, nevertheless, improved as well.

The relative survival is highest for the younger ages where it is likely that the treatment measures are more radical and the patient is able to better tolerate radical treatment. Nevertheless, despite the much lower absolute value of the excess hazard in the early phase after the diagnosis, the younger patients lose most when comparing their survival experience to the expected survival of their population counterparts.

Although equity between ages in cancer survival may be equally desirable as that between regions, it may not be possible to achieve it easily. However, the relative survival differences by age seem to be particularly characteristic to European patients compared with American patients [15] and at least partly in colon cancer related to diagnostic and treatment practices and the definition of cancer [16] .

The Finnish Cancer Registry has been shown to be very complete in terms of diagnoses [17] and follow-up [18]. Unfortunately, the Finnish population tables available did not allow for calculation of different expected survival proportions by region and we therefore attributed any observed differences to cancer. Nevertheless, we believe not much would be gained from having more complex population tables since these differences are likely to be rather small in Finland [19].

It is important to study that the health care system works well also in population subgroups and if there is an improvement in the performance, it will be observed also in the subgroups. The models presented here are helpful in making a more complete picture of what has happened and may contribute to planning of future measures where they are needed. Particular attention has to be, however, paid to the updatedness of the data. Changes in clinical practice, early detection by, e.g. screening and centralization of treatment may well have happened even after the most recent data available for monitoring.

Declaration of interest: The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.