As an illustration, the sex-specific age-adjusted cancer incidence rates and trends, including the cAPC, sAPC, and AAPC, for the top 15 cancers, were calculated using 1975-2002 population-based cancer registry data (SEER-9) collected by the SEER Program at the NCI. Since 1973, the SEER Program has collected data on all primary cancers occurring in residents of defined geographic regions. The Program currently collects and publishes cancer incidence and survival data covering approximately 26 per cent of the U.S. population (see www.seer.cancer.gov for detailed information).
These yearly age-adjusted cancer incidence rates also are adjusted for reporting delays (see [9
] for more details) and standardized to the 2000 U.S. Standard Population (Census pp. 25–1130). The segmented regression model of equation (2) was fitted using the default setting of weighted least squares in Version 3.0 of the Joinpoint software developed by the NCI (see http://srab.cancer.gov/joinpoint and [11
] for details).
The cAPC was calculated assuming that there were no transition points in the given time interval of interest, and the AAPC was calculated based on equation (4), using the results from the segmented regressions over the time period 1975-2002. Both the cAPC and AAPC also were calculated for the last 10 years, 1993–2002. Note that the AAPC, μ(1993, 2002), was estimated based on equation (9), using the results from the same segmented regression analysis over the period 1975–2002, whereas the cAPC was re-estimated based only on the 1993–2002 data.
represents sex-specific results of estimated sAPCs for each of the line segments from the segmented regression analyses, the estimated cAPCs, and AAPCs for the entire time period (1975–2002) and for the last 10 years (1993–2002), and their 95 per cent CIs as well. The trends of these top 15 cancer sites cover from 0 to 3 transition points.
Table I Estimated annual per cent changes of cancer incidence rates from the segmented regression analyses (sAPC) and the conventional method (cAPC), and the proposed new method (AAPC) with 95 per cent confidence intervals for the top 15 cancer sites: 1975–2002. (more ...)
When there are no transition points in the entire data series (e.g. leukemia for males and for females), the incident trend is linear on the log scale. Thus, exactly the same estimates are obtained for the cAPC, sAPC, and AAPC from the entire data series. The estimated sAPCs and AAPCs for the last 10-year period are exactly the same as those for the entire 28-year period. The estimated cAPCs for the last 10-year period, however, generally differ from the estimated cAPCs for the entire 28-year period. Moreover, comparing the cAPCs for the 10-year sub-time period and for the entire time period may lead to different statistical conclusions at the significance level of 0.05, although there are no transition points in the entire data series. For example, for the entire 28 years from 1975 to 2002, the estimated cAPC (also the sAPC and the AAPC) of male leukemia incidence rates is not statistically significantly different from 0; nevertheless, the estimated cAPC for the last 10 years (i.e. 1993–2002) indicates a statistically significant annual increase rate of 0.6 per cent. The estimated cAPC for 1993–2002 is not statistically significantly different from 0 for female stomach cancer incidence rates, in contrast the statistically significantly decreasing annual rate of 1.7 per cent during the entire period of 1975–2002.
When there is at least one transition point between 1975 and 2002 (that is, the assumption of a linearity of log incidence rates over the entire time period is not supported by the data), the cAPC tends to have narrower 95 per cent CIs than that of the AAPC, which indicates that the variance of the estimated cAPC tends to be underestimated when the linearity assumption does not hold. Furthermore, the estimated cAPCs are more likely to show a statistically significant difference from the null value than the AAPC estimates. For example, the segmented regression analysis reveals three transition points over the entire time period of 1975–2002 for male urinary bladder cancer incidence rates, and both the estimated AAPC and the estimated cAPC indicate that the male urinary bladder cancer incidence rate increases at 0.3 per cent annually, but the cAPC estimate indicates that this upward trend is statistically significantly different from zero, while the AAPC estimate does not. The AAPC estimate also indicates that during the 1975–2002 time period, the overall incidence trend for male pancreas cancer is flat (estimated AAPC = —0.6 per cent with the 95 per cent CI (—1.3 per cent, 0.1 per cent)), but the cAPC estimate shows a statistically significant downward trend.
For the example of the U.S. age-adjusted mortality rates for prostate cancer cited in the Introduction, the 10-year estimated AAPC from 1992 to 2001 is —3.2 per cent for whites and —1.5 per cent for blacks and both are statistically significantly different from zero. Thus, they suggest the possible benefits of PSA screening and treatment for both whites and blacks. The estimated relative rate of annual mortality change for whites, that is
, is 0.98 times that of blacks and we are 95 per cent confident that the relative rate of annual mortality change for whites versus blacks, that is (μ1
+ 1) is somewhere between 0.975 and 0.990, where subscript 1 indicates white and subscript 2 indicates black. Therefore, the downward mortality trend in the 10 years is faster for whites than for blacks on average, which suggests that whites have derived a larger benefit from the recent cancer control advances than blacks.
Quite often in the literature, the trends were presented, rather than the data points (i.e. rates) themselves. This is a situation where the AAPC can still be applied. For instance, the trend of high school students who were current users of cigarettes from 1991 to 2005 was presented as two segmented annual per cent changes (sAPC): increasing 5.29 per cent from 1991 to 1997, and then decreasing