Applications of the Cumulative Rate to Kidney Cancer Statistics in Australia

  • Janelle Brennan
  • K. C. Chan
  • Rebecca Kippen
  • C. T. Lenard
  • T. M. Mills
  • Ruth F. G. Williams
Chapter
Part of the The Springer Series on Demographic Methods and Population Analysis book series (PSDE, volume 46)

Abstract

Cancer incidence and mortality statistics in two populations are usually compared by using either the age-standardised rate or the cumulative risk by a certain age. We argue that the cumulative rate is a superior measure because it obviates the need for a standard population, and is not open to misinterpretation as is the case for cumulative risk. Then we illustrate the application of the cumulative rate by analysing incidence and mortality data for kidney cancer in Australia using the cumulative rate. Kidney cancer, which is also known as malignant neoplasm of kidney, is one of the less common cancers in Australia. In 2012, approximately 2.5% of all new cases of cancer were kidney cancer, and approximately 2.1% of all cancer related deaths in Australia were due to kidney cancer. There is variation in incidence and mortality by sex, age, and geographical location in Australia. We examine how the cumulative rate performs in measuring the variation of this disease across such sub-populations. This is part of our e ort to promote the use of the cumulative rate as an alternative to the age-standardised rates or cumulative risk. In addition we hope that this statistical investigation will contribute to the aetiology of the disease from an Australian perspective.

Keywords

Kidney cancer Renal cell carcinoma Incidence Mortality Cumulative rate Descriptive epidemiology 

9.1 Introduction

We define kidney cancer, which is also known as malignant neoplasm of kidney, as the set of diseases classified as C64 according to the International Statistical Classification of Diseases and Related Health Problems, 10th Revision (ICD10) by Australian Institute of Health and Welfare (2016).

The incidence of kidney cancer is the number of new cases diagnosed each year in a given region, in this case Australia. For each year, the mortality of kidney cancer is the number of deaths for which the primary cause of death is kidney cancer in Australia. Incidence and mortality are whole numbers. Sometimes we may use the terms “incidence” and “mortality” more broadly; we trust that this will not cause confusion.

The incidence of kidney cancer has been increasing in many parts of the world (De et al. 2014; Li et al. 2015). The reason for this is unknown, especially as there are marked geographic variations, both within the same country and between countries; see, for example, the papers by De et al. (2014), Li et al. (2015) and Znaor et al. (2015). Some of the increase in kidney cancer incidence has been attributed to the increased use of modern diagnostic imaging methods such as ultrasound, computerized tomography and magnetic resonance imaging, resulting in increased detection of renal cell carcinoma (a common type of kidney cancer), and possibly down-ward stage migration. However, over-detection does not entirely explain all of these variations, especially in Europe where there exist variations within a single country with a national health care system; see for example (Li et al. 2015). In addition, the heterogeneity of kidney cancer incidence rates, which is well-known in clinical circles, suggests the existence of modifiable risk factors and potentially unknown genetic, infective, dietary, environmental or behavioural factors that influence prevalence. Detection at an earlier stage of the disease has also been observed in the last two or three decades with more localised tumours being found more recently. According to Tan et al. (2015), “[d]espite the frequent use of aggressive therapy, mortality rates among elderly patients with kidney cancer have remained stagnant over the past quarter century”.

It is important for Australia to have an initial framework for understanding the current state of kidney cancer in our society. Examination of the trends in incidence, mortality and survival may allow the identification of modifiable risk factors and also guide future workforce planning. We know, for example, that there is considerable variation in clinical patterns of the disease in Australia (Satasivam et al. 2014). A starting point is to examine the historical Australian data in order to detect patterns that, if they are statistically significant, may help our understanding of the epidemiological differences of kidney cancer. This is particularly important given the increasing incidence rate of kidney cancer with the associated increase in health care costs.

The aim of this paper is to compare the impact of kidney cancer on various sub-populations in Australia through incidence and mortality statistics.

There are two standard methods for making such comparisons. The first is by using age-standardised rates, the second is to use cumulative risks. We have reservations about both these methods.

Calculating age-standardised rates involves introducing an arbitrary, standard population. This allows us to compare the incidence rates in two populations that have different age structures. For example, the Australian Institute of Health and Welfare (AIHW) (2016) provides age-standardised rates based on three, different, standard populations: the Australian 2001 population, the Sergi world standard population, and the WHO standard population and these three rates are quite different from each other. For example, in 2012, the three age-standardised incidence rates for kidney cancer were 12.4, 8.6, and 9.4 per 100,000 persons in Australia respectively. This is confusing for policy makers, the media, and general readers, and we should bear in mind that there is considerable interest in cancer statistics in the community.

Furthermore, if we want to compare the Australian incidence rate with the incidence rate of another country, then we may have to re-calculate the rates for at least one of the countries using a suitable common, standard population.

Finally, it is unlikely that, 100 years from now, we will still be using the Australian 2001 population as a standard, and to make comparisons between then and now will involve re-calculation.

The second standard method for making comparisons is based on the cumulative risk by a certain age. For example, AIHW (2016) reports that the risk of being diagnosed with kidney cancer by age 75 in Australia is 1 in 101. This measure is open to misunderstanding. The model, on which the calculation of this risk or probability is based, contains the assumption that the only cause of death is kidney cancer. This issue has been pointed this out in (Day 1976, p. 443; Lenard et al. 2013) and the underlying mathematical model has been explained in Lenard et al. (2014).

The age-standardised rate and the cumulative risk serve the same purpose: namely, to enable comparing incidence (or mortality) rates in populations with different age-structures. Both methods involve introducing assumptions that may be misleading. The age-standardised rate is based on assuming that the populations have an age-structure that they do not have. The cumulative risk is based on assuming that the disease in question is the only cause of death.

The cumulative rate does not have these deficiencies, as will be explained below. In this paper we compare the incidence and mortality of kidney cancer for various sub-populations in Australia using the cumulative rate.

9.2 Methods

Historical data on the incidence and mortality of kidney cancer were obtained from Australian Institute of Health and Welfare (2016). These data sets contain the incidence of kidney cancer for 1982–2012, the mortality for kidney cancer for 1968–2013, and the population counts for those years. Data are strati ed. by age group and sex. As a note of explanation, incidence data for cancer in Australia have been collected since 1982 whereas mortality data for cancer is available for a much longer period of time. Thus, the two time intervals for incidence and mortality are different. This has no effect on the analysis below. The (estimated) cumulative incidence rate by age 75 is calculated as follows.
$$ a(75)=5\ast \sum \limits_{k=1}^{k=15}\frac{x(k)}{n(k)} $$
(9.1)
The cumulative incidence rate by age 75 is, essentially, the sum of the age-specific incidence rates for each age from 0 to 75 (if we assume that the age-specific incidence rate is constant throughout any particular 5-year age group). Hence the name “cumulative incidence rate”. Notice that this calculation does not involve introducing an arbitrary standardised population, and it requires no special assumptions as does the cumulative risk. Note that the cumulative rate and the cumulative risk are approximately equal in value; if y is the cumulative rate by age t, then 1 exp(y) is the cumulative risk by age t and these are approximately equal if y > 0 is small (Lenard et al. 2014) (Table 9.1).
Table 9.1

Data for calculating cumulative rate by age 75

Group

Age group

Population

Incidence

1

[0;4]

n(1)

x(1)

2

[5;9]

n(2)

x(2)

k

[5k 5; 5k 1]

n(k)

x(k)

15

[70;74]

n(15)

x(15)

The 95% confidence interval for the cumulative rate by age 75 is given by a(75) ± 1:96 s(75) where
$$ s(75)=5\sqrt{\sum \limits_{k=1}^{k=15}\frac{x(k)}{n{(k)}^2}} $$
(9.2)

See (Chan et al. 2015; Lenard et al. 2014, 2015) for mathematical details.

9.3 Results

9.3.1 Incidence and Mortality

Figure 9.1 shows that the incidence of kidney cancer has been steadily increasing since 1982. In 1982, there were 793 new cases of kidney cancer reported in Australia; by 2012, there were 3082 new cases reported. This increasing incidence leads to increased costs and increased demands on a highly specialised workforce.
Fig. 9.1

Incidence of kidney cancer in Australia, 1982–2012

Figure 9.2 shows that the mortality associated with kidney cancer has been steadily increasing since 1968: note that the mortality does not necessarily increase from 1 year to the next, but the trend is unmistakable. In 1968, there were 300 deaths from kidney cancer in Australia; by 2013, there were 962 deaths reported.
Fig. 9.2

Mortality from kidney cancer in Australia, 1968–2013

It is not surprising that incidence and mortality are increasing: after all, the population is increasing, and ageing. So, in the next sub-section, we consider the cumulative rates to age 75. We have chosen the age 75 for several reasons. This upper age limit was proposed by Day (1976) in his original paper. We are trying to isolate the effects of kidney cancer on the population, and health issues become complex for people aged over 75. However, in other sections below, we will also consider the cumulative rates for other ages as well, as part of our investigation of the usefulness of cumulative rates.

9.3.2 Cumulative Rates to Age 75

Figure 9.3 shows the cumulative incidence rate of kidney cancer for males and females up to age 75 since 1982 and the corresponding 95% confidence intervals. The rates are increasing, and the rates for males are consistently higher than the rates for females. Thus the increasing incidence of kidney cancer shown in Fig. 9.1 is not simply due to an increasing, ageing population: there are also other forces at work.
Fig. 9.3

Cumulative incidence by age 75 of kidney cancer in Australia

By contrast, Fig. 9.4 shows the cumulative mortality rate of kidney cancer for males and females up to age 75 since 1968 and the corresponding 95% confidence intervals. Again, the rates for males are consistently higher than the rates for females; however both rates have been decreasing during the last 20 years or so.
Fig. 9.4

Cumulative mortality by age 75 of kidney cancer in Australia

9.3.3 Cumulative Rates to Age 40

Kidney cancer affects younger people as well as older people but not to the same extent. We now consider cumulative rates to age 40.

Figure 9.5 shows the cumulative incidence rate of kidney cancer for males and females up to age 40 since 1982 and the corresponding 95% confidence intervals.
Fig. 9.5

Cumulative incidence by age 40 of kidney cancer in Australia

It is noticeable that, historically, there is no apparent difference between males and females in the cumulative incidence rates to age 40 although Fig. 9.5 suggests that such a difference may be emerging. Only time will tell.

By contrast, Fig. 9.6 shows the cumulative mortality rate of kidney cancer for males and females since 1968 and the corresponding 95% confidence intervals. Again we see that, historically, there is no apparent difference between males and females in the cumulative mortality rates to age 40.
Fig. 9.6

Cumulative mortality by age 40 of kidney cancer in Australia

9.3.4 Cumulative Rates to Various Ages

Figure 9.7 shows the cumulative incidence rate of kidney cancer up to various ages for four selected years 1982, 1992, 2002, 2012. The graphs are monotonic with respect to the year. In other words, for just about all ages x, the cumulative incidence rate to age x is monotonic increasing over time. Thus the incidence of kidney cancer is increasing among all age groups. Furthermore, the cumulative incidence rate is considerably higher for higher age limits.
Fig. 9.7

Cumulative incidence rate for various ages of kidney cancer in Australia over several years

Figure 9.8 shows the cumulative mortality rate of kidney cancer up to various ages for five selected years 1973, 1983, 1993, 2003, 2013. It is surprising that the graphs are not monotonic with respect to the year. In other words, for many ages x, the cumulative mortality rate to age x is not monotonic over time; however, the rate is consistently considerably higher for higher age limits.
Fig. 9.8

Cumulative mortality rate for various ages of kidney cancer in Australia over several years

9.4 Conclusions

In this paper, we have illustrated the application of the cumulative rate to kidney cancer statistics in Australia. The cumulative rate does not share the disadvantages of the age-standardised rate or the cumulative risk. Furthermore, we have illustrated how the analysis of cancer statistics can raise interesting questions about the disease itself. For example, why is the incidence of kidney cancer higher among men than women? Why are the cumulative mortality rate curves for all ages not monotonic with respect to the year?

The recent clinical literature indicates that there is much to learn about kid-ney cancers. We hope that our work contributes, in a small way, to improving our understanding of kidney cancers, and promotes the use of the cumulative rate in cancer epidemiology.

Notes

Acknowledgements

We thank the organisers of 4th SMTDA2016 Valletta, Malta, 1–4 June 2016, University of Malta for the opportunity to present our work. Bendigo Health is supported by the government of the state of Victoria in Australia.

References

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Janelle Brennan
    • 1
    • 2
  • K. C. Chan
    • 3
  • Rebecca Kippen
    • 4
  • C. T. Lenard
    • 5
  • T. M. Mills
    • 5
  • Ruth F. G. Williams
    • 5
  1. 1.Department of UrologyBendigo HealthBendigoAustralia
  2. 2.St. Vincent’s Hospital MelbourneFitzroyAustralia
  3. 3.School of Management and EnterpriseUniversity of Southern QueenslandSpringfieldAustralia
  4. 4.School of Rural HealthMonash UniversityBendigoAustralia
  5. 5.Mathematics and StatisticsLa Trobe UniversityBendigoAustralia

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