br We applied Poisson age period
We applied Poisson age-period-cohort (APC) models using max-imum likelihood method to estimate the relative risks (rate ratios) by age groups, calendar JNJ-42153605 and birth cohort, with 95% confidence intervals. Under the full age-period-cohort model, the mean is specified as follows:
Second-order changes of slopes instead of the absolute risk ratios were interpreted . Akaike Information Criterion (AIC) was used to compare the models, including age, age-drift, age-period, age-cohort and age-period-cohort models; a lower AIC indicates a better fitting model, and hence a significant change in eﬀect through time for the relevant component. All analyses were implemented using R software (R Development Core Team, Vienna, Austria).
3.1. Age-standardized incidence rates
Overall, the age-standardized incidence rates are higher for men than women across all countries (Fig. 1). All populations except Shanghai and India have similar CRC incidence towards the most cur-rent years – i.e., around 40 new cases per 100,000 person-years. Re-garding trends of CRC incidence, only the US shows a decline. Incidence rates are relatively stable for the UK, Australia and Hong Kong, throughout their respective observed periods. Singapore’s incidence rates have also increased to a comparable level as Hong Kong around the late 1980s and did not see much of an increase afterwards. Japan has seen its incidence rates arisen from 1978 to the zenith around the 1990s and plateaued thereafter. Shanghai, albeit having lower in-cidence rates than most other countries, still sees its CRC incidence
Akaike information criteria (AIC) of age, age-drift, age-period, age-cohort and age-period-cohort models for risk of colorectal incidence across all populations under study.
Populations Age Age-drift Age-period Age-cohort Age-period-cohort
increasing over its relatively short period (1988–2007). India has had the lowest incidence among all countries with no apparent increase over the years.
3.2. Age, period and cohort eﬀects
For all countries, age, period and cohort contribute to the observed changes in CRC incidence. Models including all three components fit best (Table 1). Age-drift models generally have lower AICs than age models, but higher AICs than age-period and age-cohort models. Age-cohort models generally have lower AICs than age-period models – i.e., cohort eﬀects tend to contribute more than period eﬀects to the ob-served changes, but with the exceptions of Japan and India.
In general, the CRC incidence increases across age with slight downturn toward older ages in all populations (Fig. 2). UK, US and Australia display more apparent downturn towards the older age groups as compared to Japan, HK, Shanghai, Singapore and India.
In general, the period eﬀects reflect the trend of the age-standar-dized incidence rates of each country (Fig. 3). Japan displays a sharp downturn at around 1993–1997, which then continue in its decline till the end of observation period. There is also a sharp increase in the period eﬀects of CRC incidence in India around 2003–2007; however, no apparent trend can be concluded from this single-period increase without a longer observation beyond 2007. These observations are consistent with the AICs, where period eﬀects cannot explain all the observed changes of CRC incidence in general, and also the exceptions of Japan and India having significant period eﬀects.
All the Western populations (i.e., UK, US and Australia) had upward inflections observed as their last inflection direction of cohort eﬀects and no downturns are observed for their younger cohorts (Fig. 3). The upward inflections happen in diﬀerent cohorts among these countries, with the US displaying the earliest upward inflection with its 1940s cohorts. The patterns of cohort eﬀects are quite similar for the UK and Australia, with the UK displaying upturn for cohorts born around the mid-1960s, and Australia displaying upturn for cohorts born around the late 1950s.