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Frank SA. Dynamics of Cancer: Incidence, Inheritance, and Evolution. Princeton (NJ): Princeton University Press; 2007.

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Dynamics of Cancer: Incidence, Inheritance, and Evolution.

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Chapter 2Age of Cancer Incidence

Perturbations of the genetic and environmental causes of cancer shift the age-specific curves of cancer incidence. We understand cancer to the extent that we can explain those shifts in incidence curves. In this chapter, I describe the observed age-specific incidence patterns. The following chapters discuss what we can learn about process from these patterns of cancer incidence.

The first section introduces the main quantitative measures of cancer incidence at different ages. The standard measure is the incidence of a cancer at each age, plotted as the logarithm of incidence versus the logarithm of age. Many cancers show an approximately linear relation between incidence and age on log-log scales. I also plot the derivative (slope) of the incidence curves, which gives the acceleration of cancer incidence at different ages. The patterns of acceleration provide particularly good visual displays of how cancer incidence changes with age, giving clues about the underlying processes of cancer progression in different tissues.

The second section presents the incidence and acceleration plots for 21 different adulthood cancers. I compare the patterns of incidence and acceleration for 1993–1997 in the USA, England, Sweden, and Japan, and for 1973–1977 in the USA. Comparisons between locations and time periods highlight those aspects of cancer incidence that tend to be stable over space and time and those aspects that tend to vary. For example, many of the common cancers show declining acceleration with age: cancer incidence rises with age, but the rise occurs more slowly in later years.

The third section describes the different patterns of incidence in the common childhood cancers. The incidence of several childhood cancers does not accelerate or decelerate during the ages of highest incidence. Zero acceleration may be associated with a genetically susceptible group of individuals, each requiring only a single additional key event to lead to cancer. That single event may happen anytime during early life when the developing tissues divide rapidly, causing incidence to be equally likely over the vulnerable period.

The fourth section turns to incidence patterns in individuals that carry a strong genetic predisposition to cancer. Individuals carrying a mutation in the APC gene have colon cancer at a rate about three to four orders of magnitude higher than normal individuals, causing most of the susceptible individuals to suffer cancer by midlife. Susceptible individuals have an acceleration curve similar in shape to normal individuals, but shifted about 25 years earlier and slightly lower in average acceleration. Individuals carrying an Rb mutation have retinoblastoma at a rate about five orders of magnitude greater than normal individuals. This difference is consistent with the theory that two Rb mutations are the rate-limiting steps in transformation for this particular cancer, the susceptible individuals already having one of the necessary two steps.

The fifth section discusses how carcinogens alter the incidence of cancer at different ages. The best data on human cancers come from studies of people who quit smoking at different ages. Longer duration of smoking strongly increases the incidence of lung cancer. Interestingly, among nonsmokers, the acceleration of cancer does not change as individuals grow older, whereas among smokers, the acceleration tends to rise in midlife and then fall later in life. I also discuss incidence data from laboratory studies that apply carcinogens to animals. These studies show remarkably clear relationships between incidence and dose. Dose-response patterns provide clues about how mechanistic perturbations to carcinogenesis shift quantitative patterns of incidence.

The sixth section examines the different patterns of incidence between the two sexes. Males have slightly more cancers early in life. From approximately age 20 to 60, females have more cancers, mainly because breast cancer rises in incidence earlier than the other major adulthood cancers. After age 60, during the period of greatest cancer incidence, males have more cancers than females, male incidence rising to about twice female incidence. The excess of male cancers late in life occurs mainly because of sharp rises in male incidence for prostate, lung, and colon cancers. Male cancers accelerate more rapidly with age than do female cancers for lung, colon, bladder, melanoma, leukemia, and thyroid. Female cancers accelerate more rapidly for the pancreas, esophagus, and liver, but the results for those tissues are mixed among samples taken from different countries.

2.1 Incidence and Acceleration

Age-specific incidence is the number of cancer cases per year in a particular age group divided by the number of people in that age group. Figure 2.1a,b shows age-specific incidence for USA males and females plotted on logarithmic scales. For many types of cancer, incidence tends to increase approximately logarithmically with age (Armitage and Doll 1954), which can be represented as I = ctn−1, where I is incidence, t is age, n − 1 is the rate of increase, and c is a constant. If we take the logarithm of this expression, we have log(I) = log(c) + (n − 1)log(t). Thus, a log-log plot of log(I) versus log(t) is a straight line with a slope of n − 1.

Figure 2.1. Age-specific cancer incidence and acceleration.

Figure 2.1

Age-specific cancer incidence and acceleration. (a,b) Age-specific incidence, the number of cancer cases for each age per 100,000 population on a log-log scale, aggregated over all types of cancer. For example, a value of 3 on the y axis corresponds to (more...)

The plots of actual cancer data rarely give perfectly straight lines on log-log scales. The ways in which cancer incidence departs from log-log linearity provide interesting information (Armitage and Doll 1954; Cook et al. 1969; Moolgavkar 2004). For example, Figure 2.1a shows the number of new cases among males per year. This is a rate, just as the number of meters traveled per hour is a rate of motion. If we take the slope of a rate, we get a measure of acceleration. Figure 2.1c plots the slope taken at each point of Figure 2.1a, giving the age-specific acceleration of cancer (Frank 2004b). If cancer accelerated at the same pace with age, causing Figure 2.1a to be a straight line with slope n −1, then acceleration would be constant over all ages, and the plot in Figure 2.1c would be a flat line with zero slope and a value of n − 1 for all ages.

Figure 2.1e takes the age-specific acceleration in Figure 2.1c and re-scales the age axis to be linear instead of logarithmic. I do this to spread the ages more evenly, which makes it easier to look at patterns in the data.

The age-specific acceleration for males in Figure 2.1e shows that cancer incidence accelerates at an increasing rate up to about age 50; after 50, when most cancers occur, the acceleration declines nearly linearly. The acceleration plot for females in Figure 2.1f also shows a linear decline, starting at an earlier age and declining more slowly than for males. The acceleration plots provide very useful complements to the incidence plots, because changes in acceleration suggest how cancer may be progressing within individuals at different ages (Frank 2004b).

2.2 Different Cancers

There is a vast literature on descriptive epidemiology (Adami et al. 2002; Parkin et al. 2002). Those studies examine cancer incidence at different times, under different environmental exposures, and in different ethnic groups. Here, I intend only to introduce the kinds of data that occur, and to show some of the broad patterns that will be useful in discussing the underlying molecular and cellular processes.

Figure 2.2 plots age-specific incidence for different cancers in the USA. Solid lines show male incidences, and dashed lines show female incidences. Figure 2.3 plots the age-specific accelerations. I find it useful to look at both incidence and acceleration: incidence describes the frequency of cancer at different ages; acceleration describes how rapidly incidence changes with age at different times of life.

Figure 2.2. Age-specific incidence for different cancers.

Figure 2.2

Age-specific incidence for different cancers. The curves were calculated with the same database and methods as the top row of plots in Figure 2.1. Male cases are shown by solid lines, female cases by dashed lines. Abbreviations: Oral.phr for oral-pharyngeal (more...)

Figure 2.3. Age-specific acceleration for different cancers.

Figure 2.3

Age-specific acceleration for different cancers. The curves were calculated with the same database and methods as the bottom row of plots in Figure 2.1. Male cases are shown by solid lines, female cases by dashed lines. Abbreviations: Oral.phr for oral-pharyngeal (more...)

The acceleration plots in Figure 2.3 show nearly universal positive acceleration for these adult cancers, which means that incidence increases with age. Interestingly, the accelerations, although positive, often decline late in life (Frank 2004b). I discuss possible explanations for the late-life decline in acceleration in the following chapters.

Cancer incidence changes over time for people born in different years, perhaps because they have different lifestyles or environmental exposures (Greenlee et al. 2000). Cancer incidence also varies in different geographic locations (Parkin et al. 2002). To illustrate patterns in different times and locations, The Appendix compares incidence and acceleration of the common cancers in the USA in two time periods, 1973–1977 and 1993–1997, and in England, Sweden, and Japan in 1993–1997 (Figures A.1–A.12).

2.3 Childhood Cancers

Inherited genetic defects sometimes cause tumors in very young children (Ries et al. 1999). For example, bilateral retinoblastoma is inherited in an autosomal dominant manner (Knudson 1971). Nearly all carriers develop cancer. The early incidence and the decline in incidence with age (Figure 2.4) occur because most cell divisions in the developing retina happen in the first few years of life, and because incidence declines as the onset of disease depletes the number of susceptible but previously unaffected carriers. Unilateral retinoblastoma arises mainly in genetically normal individuals. The decline in incidence with age happens in accord with the decline in cell division in the susceptible tissue.

Figure 2.4. Age-specific incidence of childhood cancers on log-log scales.

Figure 2.4

Age-specific incidence of childhood cancers on log-log scales. Incidence is given as log10 of the number of cases per one million population per year. Data from Ries et al. (1999) for both sexes and all races from the USA. Circles show the actual data; (more...)

In testicular cancer, the early cases up to age four appear similar in pattern to the inherited early syndromes, whereas after puberty the number of cases accelerates at ages during which cell division greatly increases (Figure 2.4). Osteosarcomas increase in incidence during the ages of rapid bone elongation; these cancers decline in frequency after the teen years, with the decline in cellular division that accompanies cessation of growth. Carcinomas mostly increase in incidence throughout life, because the epithelial cells continue to divide and renew those tissues at all ages.

The acceleration patterns for these cancers provide an interesting view of changes in incidence with age (Figure 2.5). The inherited syndromes have accelerations near zero or below, with a tendency to decline with age. Teen onset testicular cancer and osteosarcoma have declining accelerations, whereas carcinomas have increasing acceleration in the teen years.

Figure 2.5. Age-specific acceleration of childhood cancers.

Figure 2.5

Age-specific acceleration of childhood cancers. Calculated as the slopes of the fitted splines in Figure 2.4.

2.4 Inheritance

Genetically predisposed individuals develop cancer earlier in life than do normal individuals. Ideally, we would compare age-specific incidences for different genotypes to measure how genes affect the onset of cancer.

Three problems arise in analyzing age-specific incidence curves for particular genotypes. First, currently available sample sizes tend to be small, so that we get only a rough idea of the age distribution of cases for particular kinds of genetic predisposition. Second, individuals with genetic predisposition are often identified by their cancers or the cancers of family members, causing the sample of genetically predisposed individuals to be biased and incomplete. Third, because we often do not know the base population for individuals with particular genetic tendencies, we usually cannot directly calculate incidence—the ratio of cases relative to the total number of individuals with a particular genetic predisposition over a particular time interval.

Studies vary in the extent to which they suffer from one or more of these sampling problems. Measurements will improve as better genomic techniques allow screening larger samples of individuals in an unbiased way. For now, we can look at the existing studies to get a sense of what patterns may arise.

The plots in Figures 2.4 and 2.5 use all individuals of a particular age as the base population, measuring incidence as the number of cases divided by the number of individuals in the base population. But many of those cases arose among a small subpopulation of individuals who carried particular genetic defects. It would be better to measure incidence and acceleration against the correct base population of carriers at risk for the disease. The following two examples show that, for high penetrance inherited genetic defects that lead to particular cancers, one can approximate the base population by assuming that a fixed fraction of carriers eventually develops the disease (Frank 2005).

Familial adenomatous polyposis (FAP) occurs in individuals who carry one mutated copy of the APC gene (Kinzler and Vogelstein 2002). This form of colon cancer can be identified during examination and distinguished from sporadic colon cancers. Figure 2.6a,b compares the incidence and acceleration for inherited and sporadic (nonfamilial) cases.

Figure 2.6. Comparison of incidence and acceleration between inherited and sporadic cancers.

Figure 2.6

Comparison of incidence and acceleration between inherited and sporadic cancers. Incidence is given as log10 of the number of cases per one million population per year. Solid lines show inherited forms; dashed lines show sporadic forms. (a,b) I calculated (more...)

Retinoblastoma occurs as an inherited cancer in children who carry one mutated copy of the Rb gene (Newsham et al. 2002). Inherited cases often develop multiple tumors, usually at least one in each eye (bilateral). Retinoblastoma also occurs as a sporadic cancer, usually with only a single tumor in one eye (unilateral). Figure 2.6c,d compares the incidence and acceleration for inherited and sporadic cases.

The comparison between inherited and sporadic forms illustrates the role of genetics; the comparison between colon cancer and retinoblastoma illustrates the role of tissue development and the timing of cell division. I will return to these data in later chapters, where I consider various hypotheses to explain these incidence and acceleration patterns. The retinoblastoma data have been particularly important in understanding how inherited and somatic mutations influence cancer progression (Knudson 1993).

Many recent laboratory studies compare the age-onset patterns of cancer between mice with different genotypes. These controlled experiments provide a clearer picture of the role of inherited genetic differences than do the uncontrolled comparisons between humans with different inherited mutations. However, most of the mouse studies have small sample sizes, making it difficult to obtain good estimates for age-onset patterns.

Figure 2.7 compares the age-onset patterns of tumors between mice with different DNA mismatch repair (MMR) genes knocked out. The figure presents Kaplan-Meier survival plots, the traditional way in which such data are reported. These plots show an association between the increase in mutation rate for defective MMR genes and a shift to earlier ages of tumor onset, in which the ordering of mutation rate is: Mlh3 < Pms2 < Mlh1Mlh3Pms2 (Frank et al. 2005).

Figure 2.7. Age of lymphoma onset in mice with different mismatch repair genotypes: Mlh3, dashed line; Pms2, dot-dashed line; Mlh1, solid line; and Mlh3Pms2, dotted line.

Figure 2.7

Age of lymphoma onset in mice with different mismatch repair genotypes: Mlh3, dashed line; Pms2, dot-dashed line; Mlh1, solid line; and Mlh3Pms2, dotted line. For each genotype, both alleles at each locus were knocked out. Data presented as traditional (more...)

Analyses of laboratory experiments usually do not extract the quantitative information about age-specific incidence and acceleration from survival plots. Thus, such experiments leave unanalyzed much of the information about how particular genotypes affect the dynamics of progression. In later chapters, I show how to extract quantitative information from the traditional survival plots and use that information to test hypotheses about how genetic variants affect the dynamics of cancer progression (Frank et al. 2005).

2.5 Carcinogens

Carcinogens alter age-specific incidence patterns. The extent to which incidence patterns change depends on the dosage and the duration of exposure, and also on the age at which an individual is exposed (Druckrey 1967; Peto et al. 1991). The ways in which carcinogens change age-specific incidence may provide clues about the processes that cause cancer.

Most of the data on carcinogens come from studies of lab animals because, of course, one cannot apply carcinogens to humans in a controlled way. In later chapters, I will provide a more extensive discussion of the experimental data on carcinogens in relation to various hypotheses about the processes that lead to cancer. Here, I continue my emphasis on the patterns of incidence.

Figure 2.8 shows the best data available for carcinogen exposure in humans: the effect on lung cancer of different durations of smoking. As expected, the later the age at which individuals quit, the higher their mortality (Figure 2.8a). Interestingly, the acceleration of lung cancer is fairly constant for nonsmokers, with a slope of the log-log incidence plot for nonsmokers of about four (Figure 2.8b). For those who smoke until an age of at least 40 years, acceleration declines later in life; the late-life decline in acceleration becomes steeper with a decrease in the age at which individuals quit smoking.

Figure 2.8. Fatal lung cancer in males for groups that quit smoking at different ages.

Figure 2.8

Fatal lung cancer in males for groups that quit smoking at different ages. The six curves defined in the legend show individuals who never smoked (quit at age 0), individuals who quit at ages 30, 40, 50, and 60, and individuals who never quit (shown as (more...)

Carcinogens applied to lab animals allow controlled measurement of dosage and incidence. In the largest study, Peto et al. (1991) measured the age-specific incidence of esophageal tumors in response to chronic exposure to N-nitrosodiethylamine (NDEA). Exposure of inbred rats began at about six weeks of age and continued throughout life. The data fit well to

Image ch2e1.jpg
where I is the standard measure of age-specific incidence, b is a constant depending on dosage, t measures in years the duration of carcinogen exposure until tumor onset, and n determines the scaling of incidence with time. Peto et al. (1991) showed mathematically that the constant b is related to m, the median duration of carcinogen exposure to tumor onset, as
Image ch2e2.jpg
Later I will show how to derive this result. From the laboratory observations, Peto et al. (1991) estimated n = 7, so we can describe age-specific incidence for this experiment as
Image ch2e3.jpg
and, on a log-log scale,
Image ch2e4.jpg
This equation and Figure 2.9 show that the median, m, sets the pattern of incidence.

Figure 2.9. Age-specific incidence of tumor onset as a function of duration of exposure to a carcinogen.

Figure 2.9

Age-specific incidence of tumor onset as a function of duration of exposure to a carcinogen. The circles show the observed median duration, the time until one-half of the experimental rats has esophageal tumors in response to chronic exposure to N-nitrosodiethylamine (more...)

In the study by Peto et al. (1991), the observed relation between median duration and dosage followed the classical dose-response formula given by Druckrey (1967),

Image ch2e5.jpg
where k is a constant measured in each data set; d is dosage given in this experiment as mg/kg/day; r determines the rate of increase in incidence with dosage at a fixed duration; m is the median duration; and n − 1 is the exponent on duration in Eq. (2.1) that fits the observed age-specific incidences. The Druckrey formula is often given as k = dms, which is equivalent to Eq. (2.3) with s = n/r and a different constant value, k.

Because median time to onset captures the patterns in the data, dose-response experiments are usually summarized by plotting the medians in response to varying dosage levels. We get the expected dose-response relation by rearranging the Druckrey formula in Eq. (2.3) as

Image ch2e6.jpg
Figure 2.10 shows the close experimental fit to this dose-response equation obtained by Peto et al. (1991). Figure 2.11 summarizes eight earlier experiments that also showed a close fit to the Druckrey formula.

Figure 2.10. Esophageal tumor dose-response line.

Figure 2.10

Esophageal tumor dose-response line. The circles show the same observed median durations as in Figure 2.9. Here, each median duration is matched to the dosage level for that experimental group of rats. The line shows the excellent fit to the Druckrey (more...)

Figure 2.11. Dose-response lines from a variety of animal experiments.

Figure 2.11

Dose-response lines from a variety of animal experiments. For each experiment, I list the slope of the line, −r/n = −1/s, from Eq. (2.4): (×) methylcholanthrene applied to mouse skin three times per week, skin tumors with slope (more...)

2.6 Sex Differences

Males and females have different patterns of cancer incidence. The most obvious differences occur in the reproductive tissues. For example, the breast and prostate account for a significant fraction of all cancers, as shown in Figure 2.2.

Apart from the reproductive tissues, other distinctive patterns occur in the incidence of cancer in males and females. The left column of Figure 2.12 shows that, over all cancers, the relative age-specific incidences follow the same curve in different time periods and in different geographic areas. The curves show the ratio of male to female incidence rate at each age. Early in life, males have a slight excess of cancers. From roughly age 20 to 60, females have an excess of cancers, with a distinctive valley in the male:female ratio at about 40 years of age. After age 60, during which most cancers occur, males have a significant excess of cancers, rising to about twice the rate of female cancers.

Figure 2.12. Ratio of male to female age-specific incidence.

Figure 2.12

Ratio of male to female age-specific incidence. The y axis shows male incidence rate divided by female incidence rate for each age, given on a log2 scale. This scaling maps an equal male:female incidence ratio to a value of zero; each unit on the scale (more...)

Part of the aggregate pattern over all cancers can be explained by breast cancer, which occurs at a relatively high rate earlier in life than the other common cancers. The relatively high rate of breast cancer in midlife causes a female excess in the middle years, which appears as a depression in the male:female incidence ratio in the left column of Figure 2.12. Prostate and lung cancers also influence the aggregate male:female ratio—these cancers rise strongly in later years and occur only (prostate) or mostly (lung) in males.

Figures A.13A.18 in the Appendix show the male:female ratios for the major adult cancers. The plots highlight two kinds of information. First, the values on the y axis measure the male:female ratio. Second, the trend in each plot shows the relative acceleration of male and female incidence with age. For example, in Figure 2.12, the positive trend for lung cancer shows that male incidence accelerates with age more rapidly than does female incidence, probably because males have smoked more than females, at least in the past.

Figures A.13A.18 show that positive trends in the male:female incidence ratio also occur consistently for colon, bladder, melanoma, leukemia, and thyroid cancers. Negative trends may occur for the pancreas, esophagus, and liver, but the results for those tissues are mixed among samples taken from different countries. Simple nonlinear curves seem to explain the patterns for the stomach and Hodgkin's cancers, and maybe also for oral-pharyngeal cancers.

The patterns of relative male:female incidence probably arise from differences between males and females in exposure to carcinogens, in hormone profiles, or in patterns of tissue growth, damage, or repair. At present, the observed patterns serve mainly to guide the development of hypotheses along these lines.

2.7 Summary

This chapter summarized patterns of cancer incidence. The best theoretical framework to explain those patterns arises from the assumption that cancer progresses through multiple stages. Before turning to multistage theory and its connections to the data on incidence, it is useful to consider the observations on how cancer develops within individuals with regard to stages of progression. The next chapter summarizes observations of multistage progression.

Copyright © 2007, Steven A Frank.

This book, except where otherwise noted, is licensed under a Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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