Methodology for Characterizing Trends

Methodology for Characterizing Trends

The Cancer Trends Progress Report features joinpoint statistical methodology to present a consistent characterization of population trends for factors related to the prevention, early detection, or treatment of cancer. Joinpoint methodology characterizes a trend using joined linear segments on a logarithmic scale; the point where two segments meet is called a "joinpoint." The methodology is useful for identifying trends in cancer incidence and mortality rates (e.g., in the SEER Cancer Statistics Review).

The Joinpoint software uses statistical criteria to determine:

  • the fewest number of segments necessary to characterize a trend
  • where the segments begin and end; and
  • the annual percent change (APC) for each segment (a linear trend on a log scale implies a constant APC).

In addition, we the report authors used a 95-percent confidence interval around the APC to determine if the APC for each segment differed significantly from zero. Whenever possible, we calculated weighted regression lines (utilizing standard errors) using the Joinpoint software. Using a log response variable, the weight (motivated by the delta method) equals the square of the response variable divided by the square of the standard error. If the standard errors were unavailable, we used an unweighted regression.

With the results of these analyses, we characterized trends in this report with respect to both their public health importance and statistical significance. If a trend was:

  • Changing less than or equal to 0.5% per year (-0.5 ≤ APC ≤ 0.5), and the APC was not statistically significant, we characterized it as STABLE
  • Changing more than 0.5% per year (APC < -0.5 or APC > 0.5), and the APC was not statistically significant, we characterized it as NON-SIGNIFICANT CHANGE
  • Changing with a statistically significant APC > 0, we characterized it as RISING
  • Changing with a statistically significant APC < 0, we characterized it as FALLING

While these categorizations are somewhat arbitrary, they do provide a consistent method to characterize trends across disparate measures. Additionally, the statistical significance and absolute value of change for incidence and mortality trends were used to ensure consistency with all major publications on national cancer trends.

To avoid statistical anomalies, a joinpoint segment must contain at least 3 observed data points, and no joinpoint segment can begin or end closer than 3 data points from the beginning or end of the data series. Due to these constraints on the joinpoint models, data series with a smaller set of data points are limited as to where a joinpoint can occur and how many joinpoints can be fit into the series. For example, if there are 4 data points or fewer, only 1 segment and no joinpoints can be fit to the series; for 5 to 7 data points, up to 2 segments and 1 joinpoint can be fit to the series; for 8 to 10 data points, up to 3 segments and 2 joinpoints can be fit. To avoid some of these limitations and allow a degree of flexibility as to where a joinpoint can be placed in a series, we established a set of guidelines on what method to use for calculating the APC of a data series based on the number of estimates that make up the data series:

  • 2-6 data points: because of the limited number of data points, we did not use Joinpoint. Instead, we calculated an APC between each consecutive data point, and we calculated the statistical significance of the APC using a two-sample test based on the standard errors derived from the survey/data source.
  • 7-11 data points:  a joinpoint analysis with a maximum of 1 joinpoint.
  • 12-16 data points: a joinpoint analysis with a maximum of 2 joinpoints.
  • 17-21 data points: a joinpoint analysis with a maximum of 3 joinpoints.
  • 22-26 data points: a joinpoint analysis with a maximum of 4 joinpoints.
  • 27 or more data points: a joinpoint analysis with a maximum of 5 joinpoints.

In addition to the annual percent change (APC) estimates, this report also presents the average annual percent change (AAPC), which is characterized in the same way as the APC. The AAPC is a measure which uses the underlying joinpoint model to compute a summary measure of the trend over a fixed pre-specified interval. The AAPC is useful for comparing the most recent trend across different groups (e.g., racial/ethnic groups or sex) when the final joinpoint segments are not directly comparable because they are of different lengths. Regardless of where the joinpoints occur for the different series, the AAPC can be computed over the same fixed interval for all the series (e.g., 2007–2011 to characterize the most recent trend). The AAPC is computed as a weighted average of the APC's from the joinpoint model, with the weights equal to the length of the APC intervals included. When there were seven or fewer data points, the AAPC was computed based on the connected data points, rather than an underlying joinpoint model. The derivation of the AAPC and its standard error based on a series of connected points is presented in a technical report from the Surveillance Research Program.

Measures were age-adjusted to the 2000 U.S. standard population using the direct method of standardization (see the tutorial on Calculating Age-adjusted Rates). Whenever possible, age-adjustment for measures was done using the age-adjustment groups specified for the Healthy People 2030 objective that corresponds to the data series.