Introduction
Ionizing radiation is known to cause biological damage over a broad range of doses (BRER 2006). Virtually all of the work in this field, however, has evaluated cancer risks from radiation exposure occurring during an individual's life. In a previous report we used time-series analysis on population data to implicate a relationship between ground-level galactic cosmic ray exposure and increased cancer mortality deriving from exposure during the time of germ cell formation and migration in the foetus (Juckett & Rosenberg Reference Juckett and Rosenberg1997). This is a grandmother effect, with exposure occurring at the time of germ cell formation of the affected cohorts within the foetal growth stage of the parents. The importance of this type of exposure is that a defect could propagate through all cells of an ensuing organism derived from an altered germ cell. The earlier study examined only US female breast cancer and total female cancer deaths between 1940 and 1990. Data are now available to extend the study to both earlier and later times in the US and to explore similar time frames in other developed countries on other continents.
Cancer does not affect all populations equally nor are cancer rates uniform in time within given populations. Industrialized countries tend to have greater per capita incidence and mortality (Parkin et al. Reference Parkin, Whelan, Ferlay, Teppo and Thomas2002), and varying time trends have been noted in both cohort and period dynamics (Bergstrom et al. Reference Bergstrom, Adami, Mohner, Zatonski, Storm, Ekbom, Tretli, Teppo, Akre and Hakulinen1996; Petrauskaite & Gurevicius Reference Petrauskaite and Gurevicius1996; Llorca et al. Reference Llorca, Prieto and Delgado-Rodriguez1999; Chirpaz et al. Reference Chirpaz, Colonna, Menegoz, Grosclaude, Schaffer, Arveux, Lesech, Exbrayat and Schaerer2002; Janssen & Kunst Reference Janssen and Kunst2005; Liaw et al. Reference Liaw, Huang and Lien2005) spanning several decades of the modern era. Contributions from environmental factors are anticipated to be the major determinants of these variations, but identifying the factors and deciphering their relative strengths is a significant hurdle in epidemiology. In this study, an effect attributable to galactic cosmic rays may be detectable in all populations as a global environmental risk.
In general, identifying and quantifying global effects is problematic because there are no control groups when the whole population is exposed. However, if the risk varies with time then it can impart a time signature to the population. If it varies with latitude or longitude, it can impart a spatial signature. The former introduces the possibility of oscillatory variations, which can be examined for their frequency components and phase shifts by time-series analysis. The latter may be addressed with cluster analysis or regional comparisons.
Time-series analysis is a vast discipline containing powerful analytical tools to describe the behaviour of a temporal sequence of measurements and, by inference, the behaviour of the system generating the sequence. Time-series analysis is routinely found in physics, electronics, geophysics, astrophysics, climatology, computer science and biometric applications. The tools of time and frequency analysis address questions of harmonic order, deterministic properties, chaos versus stochastic variability, etc. A less-often utilized, yet nonetheless powerful methodology that can be applied to epidemiology is to use a population time series as a signature for comparison with risk factors that contain intrinsic, measurable and reproducible time signatures. Comparisons are often accomplished with cross-correlations and phase alignment analyses (Kuo et al. Reference Kuo, Lindberg and Thomson1990; Duncan et al. Reference Duncan, Scott and Duncan1993; Juckett & Rosenberg Reference Juckett and Rosenberg1997; Upshur et al. Reference Upshur, Knight and Goel1999).
To obtain a time series from disease incidence or mortality data, the intertwined age, period and cohort effects must be sorted out satisfactorily. A pure age effect is only modulated by intrinsic failure mechanisms; therefore, the period and cohort variations are of interest for environmental considerations. The available data (two-dimensional in age and period), however, present an identifiability problem because, as single cohorts age, they pass through progressively changing periods, whereas each time period encompasses multiple cohorts moving through it. Several methods have been presented to sort out the individual effects (Clayton & Schifflers Reference Clayton and Schifflers1987a,Reference Clayton and Schifflersb; Weinkam & Sterling Reference Weinkam and Sterling1991; Holford et al. Reference Holford, Zhang and Mckay1994; Chie et al. Reference Chie, Chen, Lee, Chen and Lin1995; Lee & Lin Reference Lee and Lin1996; Roberston & Boyle Reference Robertson and Boyle1998a,Reference Robertson and Boyleb; Robertson et al. Reference Robertson, Gandini and Boyle1999; Holford Reference Holford1999), but the consensus is that linear trends can never be uniquely determined, whereas oscillatory trends can be reliably detected, although their amplitudes may only be approximate. To confound matters further, age–period interactions due only to factors external to the natural disease process must be recognized. This would include such perturbations as incomplete reporting or newly developed treatment modalities differentially affecting certain age groups or periods.
In this study, the nonlinear birth cohort effects are extracted from age-specific, total cancer mortality data of several populations around the Earth. The United States (US), United Kingdom (UK) and Australian (AU) data span approximately 100 years and generate birth cohort series approximately 140 years in length. The risk of cancer oscillates by 10–15% over the course of this span. Shorter time series from Canadian (CA) and New Zealand (NZ) mortality, as well as Connecticut cancer incidence, are examined for corroboration of the observed birth cohort oscillatory patterns.
The birth cohort oscillations are compared with those of incident cosmic radiation at the time of birth and the time of germ cell formation (grandparent effect) to evaluate the possible role of this global risk factor in cancer predisposition. To further examine the possible role of background radiation in cancer, the age-standardized cancer incidence rates are plotted as a function of geomagnetic latitude for 199 populations in 42 countries and are found to correlate to the latitude dependence of cosmic ray flux. The results indicate that both spatial patterns and time patterns of cancer occurrence correlate strongly to cosmic ray patterns. The issues of plausibility presented by these correlations are discussed as well as the implications of radiation exposure if these correlations represent a true cause and effect.
Methods
Data sources
Total cancer mortality was obtained from vital statistics sources in the USA, UK, AU, NZ and CA. In the US, mortality rates were available in five-year age groups from 1939 to 2002 (vital statistics of the United States 1939–2002 obtained from the US Department of Health and Human Services, National Center for Health Statistics (NCHS)) and deaths were available by 10-year age groups from 1900 to 1933 (mortality statistics 1900–1938 obtained from the US Department of Commerce, Bureau of the Census). Mortality rates were calculated for the latter set using US census data (US Department of Commerce, Bureau of the Census, Census of the Population 1900, 1910, 1920, 1930 and 1940) and were interpolated to five-year age groups using a cubic spline along the age dimension. Each five-year age bracket was assigned to the middle year of the bracket. UK mortality from 1901 to 1992 was obtained from the historic data files of the National Digital Archive of Datasets (NDAD; National Archive of the UK, historic mortality data files (RG 69, CRDA/20), 1901–1992). AU historical mortality (1907–1949) was obtained from the 2005 General Record of Incidence of Mortality (GRIM) published by the Australian Institute of Health and Welfare (AIHW). Early CA mortality rates, for the years 1926 to 1947, were calculated from deaths and population estimates from Canadian vital statistics and census publications (Dominion Bureau of Statistics, Vital Statistics Canada annual reports 3–27, 1923–1947 and Statistics Canada, Census Branch, Revised annual estimates of population by sex and age group, Canada and the provinces, 1921–1971).
Modern mortality (~1950–2000) for all five countries was obtained from World Health Organization databank compiled by the International Agency for Research on Cancer available online from the CANCERMondial Statistical Information System at http://www-dep.iarc.fr. In cases of overlap with other data sources it was used to validate the data accuracy. A short gap in the CA data, between 1947 and 1950, was interpolated along the age dimension.
Connecticut cancer incidence was obtained from data published by the Connecticut Tumor Registry (Heston et al. Reference Heston, Kelly and Meigs1986) spanning 1937–1979 and from the Surveillance, Epidemiology, and End Results (SEER) Program of the NCI (DCCPS Surveillance Research Program, Cancer Statistics Branch), incidence data for 1973–2002 (April 2005 release based on the November 2004 submission; see http://www.seer.cancer.gov/data).
Total cancer incidence for various countries was obtained from volume VIII of the Cancer Incidence on Five Continents series (Parkin et al. Reference Parkin, Whelan, Ferlay, Teppo and Thomas2002), generally covering the period 1993–1997. The latitude and longitude of each site was converted to geomagnetic latitude and longitude using a rotation of coordinates to the 1995 locations of the geomagnetic poles (as calculated from the International Geomagnetic Reference Field (IAGA 1995); see also http://swdcwww.kugi.kyoto-u.ac.jp/poles/polesexp.html).
Cosmic ray rigidity values were obtained from the listing of neutron monitor sites provided by Space Physics Data System, University of New Hampshire, and posted at http://ulysses.sr.unh.edu/NeutronMonitor/Stations.txt. Latitude and longitude values of the monitor sites were converted to geomagnetic values, as above. Cosmogenic nuclide (10Be) data from the North and South Poles were obtained from the National Geophysical Data Center, as deposited by Beer et al. (Reference Beer1990, Reference Beer, Baumgartner, Dittrich-Hannen, Hauenstein, Kubik, Lukasczyk, Mende, Stellmacher, Suter, Pap, Frohlich, Hudson and Solanki1994) and Bard et al. (Reference Bard, Raisbeck and Yiou1997, Reference Bard, Raisbeck, Yiou and Jouzel2000), respectively.
Age–period–cohort method
The standard approach to age–period–cohort modelling is to assume that the mortality rate is the product of age, period and cohort effects, and thus the log transformation can be used to create a linear sum of factors
where r, μ, α, β, and γ represent mortality rate, mean rate, age effect, period effect and cohort effect, respectively. In this formulation, the mean rate is modulated by the age, period and cohort effects. In practical applications, a noise term can also be added to absorb random fluctuations. Several approaches have been used to fit this type of model to the data (Clayton & Schifflers Reference Clayton and Schifflers1987a,Reference Clayton and Schifflersb; Weinkam & Sterling Reference Weinkam and Sterling1991; Holford et al. Reference Holford, Zhang and Mckay1994; Chie et al. Reference Chie, Chen, Lee, Chen and Lin1995; Lee & Lin Reference Lee and Lin1996; Roberston & Boyle Reference Robertson and Boyle1998a,Reference Robertson and Boyleb; Robertson et al. Reference Robertson, Gandini and Boyle1999; Holford Reference Holford1999) with differing strategies to cope with the identifiability problem inherent in the non-orthogonality of the age, period and cohort variables.
Alternatively, the age, period and cohort effects can be modelled without transformation under the assumption that the age effect is dominant, with period and cohort effects acting as perturbations (Juckett & Rosenberg Reference Juckett and Rosenberg1997). This is given by
where M, A, ΔP and ΔC are two-dimensional arrays defined over age and period. (The multiplication indicated in (1) is scalar and not matrix multiplication.) Each array is a function of one or more of the three variables age (a), period (p) and cohort (c).
Both mathematical models represent the ideal conditions devoid of external factors that can skew the actual data with interacting age-related and period-related confounders. For example, reliable diagnosis of cancer in the oldest age populations increases with time causing incomplete disease ascertainment in the oldest cohorts. In addition, early cancer detection and treatment create a period effect, but these treatments are more successful in the younger age groups causing this period effect to be distorted by age. Thus, a more realistic description of the mortality rate matrix is given by
where Єa·Єp represents the intertwined age and period external effect. For simplicity of presentation, the array indices a and p are dropped on most terms and the functional dependences on age, period and cohort variables a, p and c are suppressed. We can define Єa and Єp by the Taylor expansions
where On represents higher-order terms beyond the linear trend. Therefore, Єa·Єp is given by the equation
Without the higher-order terms, this represents the equation of a twisted plane in the a, p dimensions (Robertson & Boyle Reference Robertson and Boyle1998b). It can be used to remove the linear portion of the age–period interactions, as well as the linear portion of the period effect, enhancing the ability to identify the nonlinear variations in the period and cohort effects.
Analysis procedure
Equation (2) can be simplified by subtracting and dividing through by the age effect array:
which simplifies to
The left-hand side represents the fractional change in mortality with respect to the age effect while the right-hand side equates this to the sum of separate period, cohort and external perturbations, plus higher-order cross-product terms that can be ignored in most cases. For simplicity the left-hand side will be referred to as M−A.
The calculation of M−A begins by averaging the mortality array over the period dimension at each age level. This generates an age-effect vector that is used to calculate (Ma,p − Aa)/Aa. The extraction of the individual perturbing effects is performed in the following order: Єa Єp, ΔP and then ΔC. The equation of the twisted plane is fit to the M−A array and then subtracted generating the M−A−TP array. This array is averaged over age at each period time point, generating an estimate of the nonlinear ΔP, which is then subtracted yielding M−A−TP−ΔP. The final array predominantly represents the cohort effect, ΔC, as mapped into the rectangular grid of age and period dimensions. The final array also includes random noise, the cross-product effects and nonlinear Єa·Єp components. By shifting each age row to the age at birth and averaging, a single cohort-effect vector can be extracted. The variation around this average gives a crude estimate of the noise and higher-order effects.
The extraction procedure does not obviate the identifiability problem for the linear age, period and cohort effects, but the oscillatory variations are recovered in frequency and phase, even though amplitude may vary with approach. The main difficulty in extracting the correct amplitude is the ‘bleeding’ of the oscillatory cohort effect into the nonlinear period effect estimate due to the natural truncation of the age dimension by birth and maximal lifespan limits of humans. As a cohort ‘hump’ moves diagonally through the age–period dimensions, there is a time when it is located in the middle age groups and tends to dominate the whole age range. This can cause an apparently elevated period effect in that time range. This can, subsequently, reduce the amplitude of the cohort effect when analysed by the above method.
The 95% confidence range around the cohort effects can be minimized by an iterative variational methodology, where the whole extraction procedure is repeated until a minimum dispersion among the cohort lines is achieved. At each iteration, correction terms must be employed for each member of the age-effect and period-effect vectors creating a large number of degrees of freedom and consequently many local minima in the solution space. Owing to the uncertainty of the final solution, it was not implemented in this analysis.
Results
Age–period–cohort analysis
The US female total cancer mortality rate data are used as an example of the age–period–cohort analysis described in the methods section (see Fig. 1). The rates are shown in the upper left panel of Fig. 1, denoted by M. After subtraction of, and division by, the average age effect, the M−A array is generated (upper right). This is fitted with the equation for a twisted plane, generating TP (middle left), which is subtracted from M−A, yielding M−A−TP (middle right). After calculation and subtraction of the nonlinear period effect, the M−A−TP−ΔP array is generated (lower left). When this array is plotted as lines of constant age and assigned to their birth cohort time era, a cohort effect plot is generated (lower right).
Fig. 1. Graphical example of the age–period–cohort analysis of US female total cancer mortality. Three-dimensional representations of various data arrays (see the materials and methods section). In each three-dimensional plot, the right axis is the calendar year, the left axis is the age at death and the vertical axis is mortality rate per 100 000 (upper left panel) or fractional change in mortality rate.
The average cohort effect can by obtained from the shifted M−A−TP−ΔP array by averaging at each birth year. The average cohort effect series for male and female US, UK and AU are shown in Fig. 2, with 95% confidence intervals. The average cohort effects for the shorter data sets of NZ, CA and Connecticut cancer incidence are shown in Fig. 3. Consistent peaks occur near 1840–1860 in the longer data sets and near 1920–1930 in all but UK males. The 95% confidence intervals for male cancer incidence in Connecticut includes zero throughout most of the series; therefore, no conclusions can be made for this data set.
Fig. 2. Cohort effects for male and female total cancer mortality in US, UK and AU populations. Averages of the shifted cohort lines are shown by bold curves, 95% confidence intervals are shown by light curves.
Fig. 3. Cohort effects for male and female total cancer mortality in CA and NZ populations plus male and female total cancer incidence in Connecticut, USA. Averages of the shifted cohort lines are shown by bold curves, 95% confidence intervals are shown by light curves.
The nonlinear period effect vectors, ΔP, for each of the data sets is plotted in Fig. 4(a), with the average and confidence intervals shown in Fig. 4(b). The only consistencies among the vectors are in the earliest and latest time regions. The confidence interval along the central region includes zero, whereas the ends deviate from zero significantly. This probably represents that portion of the under-reporting problem at the earliest times and the effect of treatment advances in the later times, which affects all age groups equally.
Fig. 4. Nonlinear period effects, ΔP, for total cancer mortality for each population and the average and 95% confidence interval. (a) Individual ΔP vectors for US female (open square), US male (closed square), AU female (open triangle), AU male (closed triangle), UK female (open circle), CA female (grey diamond), CA male (black diamond), NZ female (asterisk) and NZ male (plus). (b) Average of the vectors in (a) (bold curve) with 95% confidence intervals (light line).
The average birth cohort effect for US (male and female), UK (female) and AU (male and female) is shown in Fig. 5 (top), while the average cohort effect of CA and NZ, male and female, is shown in the middle plot. The 95% confidence intervals are indicated with dashed lines. The width of the confidence interval indicates that the oscillation is significant and has the same shape in most of the populations. The UK male cohort effect is not included in the average, although its inclusion does not obviate the significance of the oscillation (not shown). The cosmic ray surrogate, ice core 10Be, is shown in the lower plot. The yearly ice core values were an average from cores of Greenland and Antarctica. The series was smoothed by convolution with a 36-year window (order five) Savitzky–Golay filter (Savitzky & Golay Reference Savitzky and Golay1964) to extract the low-frequency component and was shifted by 28 years to show its possible alignment with the birth cohort series. Cross correlation of the unshifted 10Be series with the average US, UK and AU birth cohort oscillation (Fig. 6) yields a lag of 28 years and a correlation peak of 0.8. This level of correlation indicates a strong oscillatory similarity between the two series and a possible role of cosmic radiation 28 years before birth. This is the time of germ cell formation as is shown in Fig. 7.
Fig. 5. Average cohort effects for total cancer mortality in US (male and female), UK (female), AU (male and female) in the upper panel; CA (male and female), and NZ (male and female) in the middle panel; and the smoothed and shifted 10Be cosmogenic nuclide series in the lower panel.
Fig. 6. Cross correlation of the average birth cohort and smoothed 10Be time series. Lag indicates the time delay between the 10Be time series and the average mortality birth cohort series.
Fig. 7. Demonstration of birth cohort and germ cell cohort timelines using AU male cohort effect data array (M−A−TP−ΔP). The data array is shown as a contour plot with shades black to white representing values low to high. The cone between the time of germ cell formation and the year of birth indicates that each birth year cohort is composed of a spectrum of maternal ages and, thus, germ cell ages.
Worldwide cancer incidence rates versus latitude
A possible correlation between cosmic ray flux and human cancer was examined as early as 1948 by Morris & Nickerson (Reference Morris and Nickerson1948). Subsequently, similar patterns were noted for multiple sclerosis (Barlow Reference Barlow, Haley and Snider1962), foetal mortality (Wesley Reference Wesley1960) and anencephalus (Archer Reference Archer1979). In each case, a variation in mortality versus latitude was similar to cosmic ray distribution. A half-century later, this can be examined more reliably using cancer incidence from around the globe, as organized and reported by the International Agency for Research on Cancer in their Cancer Incidence in Five Continents reports (Parkin et al. Reference Parkin, Whelan, Ferlay, Teppo and Thomas2002). The age-standardized incidence (world population) rates for both males and females from 199 reporting sites in 42 countries are plotted in Fig. 8 versus geomagnetic latitude. The cosmic ray rigidity for neutron monitor sites around the globe is plotted inversely. As the rigidity increases, more of the cosmic ray spectrum is blocked from penetrating the geomagnetic field surrounding Earth. The rigidity has a characteristic maximum at about 10°N, due to the non-uniform shape of the dipole magnetic field, thus this region receives the lowest radiation dose.
Fig. 8. Comparison of male and female total cancer age-standardized incidence rates to the cosmic ray rigidity as function of geomagnetic latitude. Total cancer incidence from Cancer Incidence in Five Continents, vol. VIII, for 199 reporting sites in 42 countries representing most regions of the globe shown in the left panels for females and males as closed circles. Cosmic ray rigidities for 41 neutron monitor sites around the globe are shown by open squares (left panels) and by a sixth-order polynomial best fitting curve (solid curve). All values are plotted against geomagnetic latitude (see the materials and methods section). In the right panels, cancer incidence is averaged in bins of 5° widths and fitted with a fourth-order polynomial (dashed curve). Polynomial fits are used only to aid in visual comparison.
The individual cancer incidence values are plotted in the left panels, while the averages and standard errors of 5° bins are shown in the right panels. The incidence data are fitted with fourth-order polynomial functions and the rigidity data are fitted with a sixth-order polynomial function, as represented by dashed and solid curves, respectively. The incidence data share the same skewed shape, with a minimum near 10°N. The qualitative similarity between incidence and rigidity further suggests that a global environmental radiation effect may be operating in cancer.
Discussion
A sequential age–period–cohort analysis was used to extract the nonlinear total cancer mortality cohort effect for 10 separate populations in five countries, as well as the total cancer incidence cohort effect of males and females in the Connecticut Tumor Registry. The available data allowed the extraction of cohort effects of significant length (100 to 140 years) to facilitate comparisons across continents, centuries and politico–social conditions. The large percentage of European descendants in all of these populations helped to reduce ethnic variability, thereby increasing the sensitivity to external factors.
The main finding of this comparison is the elevated risk of all cancer mortality in cohorts born within broad times around the years of 1850 and 1925. The elevation in risk near 1925 has been noted in previous reports on cohort effects in breast cancer (Juckett & Rosenberg Reference Juckett and Rosenberg1997; Jemal et al. Reference Jemal, Chu and Tarone2001), lung cancer (Tarone & Chu Reference Tarone and Chu1992) and various cancer-specific rates for many European countries (LaVecchia et al. Reference LaVecchia, Lucchini, Negri, Boyle, Maisonneuve and Levi1992), as well as countries in the Americas (LaVecchia et al. Reference LaVecchia, Lucchini, Negri, Boyle and Levi1993). The results of this study corroborate the earlier findings for the 1925 era and suggest another peak exists 75 years earlier. The consistency of this finding across various continents is consistent with a global environmental risk factor that varies with time synchronously over the planet.
The data in this study spans all of the revisions (1–10) of the International Classification of Diseases (ICD), which is the primary reason for using total cancer deaths. While there may be under-reporting in the early years, this choice reduces the errors resulting from diagnosis and death certificate inaccuracies for particular cancer types. Details of ICD implementation and the accuracies of the population denominators for each country (census data) can be found in the references provided in the methods section.
Owing to the large time span covered by this analysis, the question of competing risks must be addressed. In the early part of the 1900s, infectious diseases resulted in many early deaths, therefore a large part of the population did not live long enough to develop cancer or severe cardiovascular disease. Could the competing risks of infectious diseases influence the analysis presented here? The removal of an early acting, independent risk factor will lead to more deaths from other causes in older age groups because people live longer; however, the age-specific mortality rate does not change significantly (e.g. Llorca et al. Reference Llorca and Delgado-Rodriguez2006). The stability of the age-specific rate is strengthened, in this analysis, by using the large numbers of total cancer and total country populations. Furthermore, the deployment of antibiotics and improved sanitation would tend to introduce a period effect rather than a cohort effect.
Two of the populations, Connecticut male incidence and UK male mortality, deviate from the oscillatory pattern to some degree. The Connecticut male birth cohort series is only marginally significant in some years, suggesting the population at risk is too small to raise this effect above random fluctuations. The additional risk factors in males during this era, such as smoking, may contribute to the fluctuations. The UK males agree with other populations up until the early 20th century and then the second peak deviates to earlier times. During this era, two broad male cohorts were severely depleted due to the two world wars, therefore it was deemed reasonable to censor this population from the average.
The smoking histories of these populations probably do not play a role in the observed oscillations because smoking prevalence varied significantly between the sexes, with female smoking rising several decades after males. While smoking is a potent risk factor for cancer, Barendregt et al. (Reference Barendregt, Looman and Bronnum-Hansen2002) concluded that smoking effects on cancer have very high variability between males and females as well as between various countries. In the analysis of US lung cancer in white and black, males and females, Jemal et al. (Reference Jemal, Chu and Tarone2001) showed each population exhibited a cohort effect peak near 1925, yet all four groups had different smoking histories. These studies appear to preclude smoking as the source of the common cohort oscillation around the globe. In addition, it would be difficult to expect a smoking effect causing the early peak near 1850, since smoking in women was virtually non-existent and cigarettes were rare.
A comparison of the average birth cohort effect to the smoothed 10Be series yielded a 28-year lag between radiation levels and birth cohort changes in risk. This indicates that if cosmic radiation is involved in this effect, it must be acting before birth. The only reasonable hypothesis for a risk to act before birth is if it acts during germ cell formation in one of the parents of the affected members of the birth cohort. The germ cells are formed during the parents' foetal growth in the grandmother of the affected cohort member, making the expression of a germ cell defect delayed by the time between the birth of the parents and the birth of the affected individual. The maternal age distribution (MAD) can represent that delay for population-based analyses. The MAD has changed somewhat over the last 150 years, becoming narrower with time as family sizes have diminished (Lutz Reference Lutz1989), but the global and temporal variations are small compared with the overall width of the distributions, which spans 35 years from age 15 to age 50. A typical example of a MAD would be the US fertility distribution from 1910 (US Bureau of the Census 1945; Juckett & Rosenberg Reference Juckett and Rosenberg1997), which is near the midpoint of the birth cohort series presented in this analysis. It peaks around age 26, but is skewed to higher ages with a distribution mean of approximately 28 years. Therefore, this average span between generations, as represented by the MAD, is consistent with the lag detected in Fig. 6. This conclusion is similar to a previous analysis of the birth cohort time series in US breast cancer (Juckett & Rosenberg Reference Juckett and Rosenberg1997).
Combining the observed temporal and spatial correlations between cancer rates and cosmic rays with the possible explanation for the delay between cosmic ray flux and affected cohorts leads to the speculation that a linkage between cosmic rays and cancer is worth considering. Such a linkage presents a major plausibility issue, however, because sea-level cosmic rays constitute only a modest portion (~20–30%) of the already low background radiation (NCRP 1987). On the other hand, the plausibility threshold may be reduced if one considers that an amplification process occurs in ontogeny resulting from germ cells transmitting their genetic information to the entire organism. A disease predisposing defect in the germ cell would ultimately be present in every cell of the adult, increasing the likelihood of the multi-hit processes of cancer reaching completion. Furthermore, during an early phase of foetal development, the migrating germ cell is highly sensitive to radiation (Mandl & Beaumont Reference Mandl, Beaumont, Carlson and Gassner1964) and, as calculated previously (Juckett & Rosenberg Reference Juckett and Rosenberg1997), there is a real probability that each germ cell could receive more than one ionizing radiation event during this sensitive migration period. Finally, if one postulates that an epigenetic defect occurs during this migration period, then the energetic threshold may be reduced and the non-permanence of this cancer modulation might also be explainable.
The overall stability of total cancer incidence spanning several generations plus the oscillations in birth cohort incidence are both evidence that fixed genetic defects are not rapidly accumulating on a population-wide scale. Therefore, the seventy-five year oscillation is likely due to transient effects that are globally invariant but variable in time. This would be the hallmark of a global epigenetic effect that has the opportunity to reset at each generation.
During germ cell migration the genome is highly methylated, only to be mostly erased once the cell reaches the genital ridges, prior to gonad formation (Hajkova et al. Reference Hajkova, Erhardt, Lane, Haaf, El-Maarri, Reik, Walter and Surani2002). The methylation sites that survive are part of the imprinting process, passing maternal and paternal information to the final germ cell populations. If a radiation-induced chemical modification creates an unremovable methylation site, then an unintended imprint could be carried into a future organism. Recent work has demonstrated that radiation can induce DNA and histone methylation changes that persist unrepaired (Koturbash et al. Reference Koturbash, Pogribny and Kovalchuk2005; Pogribny et al. Reference Pogribny, Koturbash, Tryndyak, Hudson, Stevenson, Sedelnikova, Bonner and Kovalchuk2005). Such damage could affect the organism's life trajectory, but would be erased at the next generation's germ cell formation.
This hypothetical link between cosmic radiation and epigenetic changes may only be the tip of the iceberg regarding background radiation effects. This particular radiation is detectable because of its time signature. The remainder of background radiation is time invariant by comparison. It too, however, may be generating a background level of random epigenetic mutations in each germ cell generation. This could be a significant driver of intra-species variation that drives adaptation and ultimately evolution.
It must be noted that the latitude effect on cancer incidence (Fig. 8) is also invoked in the argument for the protective effect of vitamin D (Garland et al. Reference Garland, Garland, Gorham, Lipkin, Newmark, Mohr and Holick2006). Those sites closer to the equator receive more UV radiation and therefore the population has a higher production rate of vitamin D. While the relationship between vitamin D levels within individuals has been shown to correlate to UV exposure (Ruston Reference Ruston, Hoare, Henderson, Gregory, Bates, Prentice, Birch, Swan and Farron2004) there is conflicting evidence that these levels have any meaningful effect on cancer incidence (Williamson Reference Williamson2006). Until the significance of vitamin D and cancer is resolved, the cosmic radiation hypothesis offers an alternate explanation for this latitude effect, which is strengthened by the correlation of the two time-series components.
Finally, while the results of this analysis suggest a global cohort effect that may be linked to environmental cosmic radiation, knowledge of this effect does not lend itself to simple strategies that can prevent the damage from occurring in Earth populations. However, it may provide insight into the exploration of genetic or epigenetic sources of cancer predisposition that could be used to identify individuals carrying the damage. Appropriate intervention could then be initiated to prevent cancer development. Validation of this effect, however, has significant implications for populations that travel through high-radiation environments or who intend on settling in space stations and on under-protected planets.
Acknowledgements
This work was supported by the Barros Research Institute and by a joint operating agreement grant from the Michigan State University Foundation.
