Estimating average annual per cent change in trend analysis

Abstract

Trends in incidence or mortality rates over a specified time interval are usually described by the conventional annual per cent change (cAPC), under the assumption of a constant rate of change. When this assumption does not hold over the entire time interval, the trend may be characterized using the annual per cent changes from segmented analysis (sAPCs). This approach assumes that the change in rates is constant over each time partition defined by the transition points, but varies among different time partitions. Different groups (e.g. racial subgroups), however, may have different transition points and thus different time partitions over which they have constant rates of change, making comparison of sAPCs problematic across groups over a common time interval of interest (e.g. the past 10 years). We propose a new measure, the average annual per cent change (AAPC), which uses sAPCs to summarize and compare trends for a specific time period. The advantage of the proposed AAPC is that it takes into account the trend transitions, whereas cAPC does not and can lead to erroneous conclusions. In addition, when the trend is constant over the entire time interval of interest, the AAPC has the advantage of reducing to both cAPC and sAPC. Moreover, because the estimated AAPC is based on the segmented analysis over the entire data series, any selected subinterval within a single time partition will yield the same AAPC estimate--that is it will be equal to the estimated sAPC for that time partition. The cAPC, however, is re-estimated using data only from that selected subinterval; thus, its estimate may be sensitive to the subinterval selected. The AAPC estimation has been incorporated into the segmented regression (free) software Joinpoint, which is used by many registries throughout the world for characterizing trends in cancer rates.

Figure 1

U.S. Mortality Rates, Prostate, 1975.2001, By Race. Source: National Center for Health Statistics public use data file for the total US. Rates are age-adjusted to the 2000 US standard million population by 5-year age groups. *The sAPC (annual per cent change from segmented analysis) is significantly different from zero (p<0.05).