Age-period-cohort analysis of lung cancer mortality in Japan, 1960-1995.

The mortality data on lung cancer in Japan from 1960 to 1995 was analysed based on an age-period-cohort (APC) model. Though the APC model has an 'identifiable problem' caused by the relationship of age, period and cohort parameters, non-linear components of them revealed their original (separated) effects. They were: (1) non-linear age effects had a peak in 55-59 and 60-64 years old in males and 50-54 in females, (2) non-linear period effects were very small in both genders, (3) non-linear age and period effects were small enough to neglect compared with their linear effects, and (4) there were five parts of trends in Japanese lung cancer mortality in both genders in the non-linear birth cohort effects. The 1961-65 birth cohort effect seemed to increase differently from previous birth years. This trend should be monitored carefully.


INTRODUCTION
In Japan, deaths caused by cancer have been increasing, and cancer has been the leading cause of death since 1981 1). Lung cancer especially is the leading cause of death in males and has the third highest mortality rate in females among all forms of cancer at the present. To reveal the temporal trends of age, period and birth cohort effects is of importance for providing clues or hypotheses for its aetiology. Components of age, period and birth cohort of death are three separate temporal factors related to the mortality of the cancer.
Each component bears a different biological meaning in the process of carcinogens with the multi-stage model 2,3}. For example, exposure to early stage carcinogens (initiators) will often introduce a birth cohort effect, whereas late-stage carcinogens (promoters) or diagnostic and therapeutic improvements will produce a period effect. Standard cross-sectional analysis of the trend, however, cannot separate age and period effects. In general, conventional birth cohort analysis is a mainly graphical approach and only can provide combined effects of the three time factors mentioned above. To differentiate them, a log linear model has been developed in the past two decades and applied to the analysis of various forms of cancer. The earliest use of this form of modelling was Kermack et al 'I and Frost 5), and early works of development of this model were briefly summarized in Osmond and Gardner 6). Though Kupper 7,8) gave critiques of this model in the point of interpretation, this model has been developed by many authors. At present, the APC model is used for many studies 9-12) for its instructive usefulness.
In the APC model, the three time variables are not identifiable due to the exact linear relation: birth year + age at death = calendar year at death (1) Many methods have been developed to solve the problem , which are classified into roughly five groups at the present: (1) penalty function approach 6.14), (2) individual records approach 15) (3) autoregressive models 16), (4) Bayesian approach [17][18][19] and (5)  In this study, mortality data of lung cancer in Japan over the period of 1960 to 1995 was analysed. Separated age, period and birth cohort effects were analysed and are presented using the APC model based on non-linear *deviation from linearity' by Holford 13,33) .
If linear period effects were assumed to be zero, the corresponding cohort effect was obtained. These effects were also peculiar in pattern even in the full effects ( Figure 2). The pattern also changed five times : 1903,1928,1938,1948 and in males and 1908,1918,1933,1943 and 1958 in females.
In both genders, the trends of non-linear and full birth cohort effect means: (1) The latent risk in the birth cohort has increased since 1883, (2) The birth cohort effect has five points of change, (3) The change in the 1963 birth cohort effect seemed to increase differently from previous birth years. DISCUSSION It is unfortunate that Japan has not started a cancer registry system at the national level. As a result, for a longer trend analysis, mortality seems to be the only indicator. The most prominent weakness of mortality data is the impossibility of separating factors of incidence and improvement of medical technology (length of case-fatality). In the case of lung cancer, incidence rate and mortality rate are considered to be almost parallel because of the little improvement in medicine for survival.  In the APC model, the interpretation of changes of pattern of birth cohort effects is difficult. One way to interpret is to observe the pattern of change of non-linear effects.
Full effects of age and period were shown to change linearly because of small influence of their non-linear effects compared with linear ones. Averaged change rate of full effects of age and period by moving five years were 0.544 and 0.107, respectively. Increasing risk by aging was almost five times larger than that by changing period. In contrast, non-linear birth cohort effects had enough values not to be neglected. The birth cohort effects had unique patterns, differently from age and period effects.
Non-linear birth cohorts between the periods with minimal values and maximal values (1938-1948 in males and 1933-1943 in females) had peculiar patterns. Persons who were born in those periods had their main growth period in the middle of World War 11 (1940War 11 ( -1945. There may be some characteristics for these changing patterns. The first pattern, before 1903 in males and before 1908 in females, might be considered rapid modernization in Japan in the Meiji era. The second pattern of change to decrease in 1903-1938 in males and in 1908-1933 in females, were considered as the first success of activities of promoting hygiene and public health in Japan. The third pattern of change to increase in 1938-1948 in males and in 1933-1943 in females, might be due to wars in the early Showa era. The peculiarity in this period was also reported for diabetes mellitus, ischemic heart disease, cirrhosis of the liver and suicide 34). The fourth pattern of decrease in 1948-1958 in males and in 1943-1958 in females might be improvement of hygiene and public health after World War H. The fifth pattern after 1958 should be interpreted cautiously. After 1960, Japan faced a so-called `high speed economic growth period'. Because of the high industrial growth in this period, the environmental pollution by chrome, nickel, asbestos and nitrosamines were H . Takahashi, et al. higher level than at present, (but the nitrosoxide level has remained almost a constant level) 35) . Many everyday foods containing chemical substances with high fat and high cholesterol 36) have also emerged in this period . Based on these points, monitoring may be necessary for 1958 birth cohort and later . In this analysis, however, the effect of 1958 birth cohort is the last time frame that was analysed. The possibility that the result was caused by a random fluctuation cannot be denied , because the effect of the 1958 birth cohort was only estimated from the one cell, that was 30-34 years old in 1995.
To analyse temporal trends of mortality and incidence rates , APC analysis is one of the more popular tools. However conventional APC analysis has suffered from the identifiable problem, which causes difficulties with interpretation of the results , because of an unreasonable additional assumption. The method to separate common linear effects and original non-linear effects is reasonable in the technical sense. To interpret the results is still not easy, however, meaningful reasonable results can be obtained. Conventional univariate analysis based on standardised mortality ratio (SMR) or comparative mortality figure (CMF) in period effects (differences of both indices were examined 37) and standardised cohort mortality ratio (SCMR) or comparative cohort mortality figure (CCMF) in birth cohort effects is the other tools. These methods clarify the trend of only one of the effects by using the above annual indices. So these results have been believed to easiliy interpreted. However these methods could not separate the three linear effects of age period and cohort.
Hamajima et al 38) developed another model based on a Weibull hazard function with each birth cohort effect as a constant to analyse the single birth cohort effect and to predict the future risks. According to the Hamajima model, the birth cohort effect of 1896-1900 and 1931-35 were 0.0805 and 0.2181, respectively. The corresponding logarithms of the full birth cohort effects in males in the APC model were 1.0854 and 1.9209, respectively. The increasing birth cohort effect is 2.57 times in the Hamajima model, and 2.31 times in our model, which are almost equivalent. The advantages in using the APC model compared to his model are: (1)The assumption in our model is less strict meaning not to have common mortality distribution on each year,(2) The birth cohort effects in our model are estimated by considering the other two effects simultaneously.
As is well known, lung cancer is related to cigarette smoking. Recently the quantitative relationship between cumulative cigarette consumption and lung cancer mortality was recognized by linear regression analysis between the estimated adjusted cumulative cigarette consumption and the lung cancer death rate in each age group (20-24,...,70-74) 39). Consideration between cigarette smoking and lung cancer based on our model is interesting. With the exception of the period during World War H, cigarette sales in Japan have steadily increased and smoking prevalence has been decreasing in males and almost constant in females since the 1960's when statistics started to be gathered( Figure. 3). To simplify this situation, annual smoking amounts can be estimated by the product of national cigarette sales and smoking prevalence. The respective vales were 107.4 billion, 75.9% in males, 12.4% in females in 1960, and 328.9 billion, 60.4% in males and 13.3% in females in 1992. These logarithms of changes are 0.89 in males and 1.19 in females. Our period effect in 1995 is 0.859 in males and 0.666 in females. In males the APC model was considered to support the relation. The factors that cause this difference in females might be the daily smoking amounts per day or the method of inhaling. Another interesting problem is that of area difference. In our model we consider Japan as a unit, though there is considered to be area variation. According to Kano et al 40), Saitama males and Fukushima females had the highest lung cancer death rate in 1960 and Okinawa males and Oita females in 1980. The major change of age-adjusted death rates from 1960-1980 were observed in Kagoshima, Tokushima and Wakayama, in males; and Shimane, Oita and Kagawa in females.
APC analysis based on estimable function could separate linear effects and non-linear effects. Linear effects are recognized as common effects (impossible to separate). Non-linear effects are original effects of time factors. The best way to interpret the APC model at the present is to reveal changing patterns with estimable parameters, and if necessary, to add linear effects obtained by one of three effects extinguished to zero. This method shows that the APC analysis produces more precise and reasonable results than conventional analyses (summarised indices or two parameters AP, AC model). Estimators from conventional analyses have non-negligible problems: (1) The pattern depends on the ways of taking a standard population, (2) Incomplete cells based on missing values in the birth cohort gave less precise SCMRs (CCMFs), (3) Two way model (age-period, or age-cohort) gave no information for the other component. The APC model overcomes these ambiguities. So, this model is considered effective although there have been many criticisms.

CONCLUSION
The mortality of lung cancer in Japan based on the APC model revealed that there are five changing patterns in the birth cohort effects in Japanese lung cancer mortality. The 1938The , 1943The and 1948The birth cohort in males and 1933The , 1938The and 1943 birth cohort in females were peculiar patterns. Successive birth cohorts need to be monitored for increased risk. Future prevention activities will be based on need, if risk increases in these birth cohorts.