# Parallel Pairwise Comparison and Number of Joinpoints

For a statistical test of parallelism between two groups, how is the assumed number of joinpoints (which is displayed on the comparison tab) determined?

When conducting the test of parallelism between two groups, the true number of joinpoints for each group under the null hypothesis (H0) of parallelism and alternative hypothesis (HA) lack of parallelism are unknown.  As described in Kim, et al. (Biometrics, 2004) the test of parallelism is conducted under Kmax joinpoints, where Kmax is greater than or equal to the number joinpoints for both groups under both H0 and HA.  Simulations presented in Kim et al. have shown that a reasonable choice for Kmax is the maximum of the estimated number of joinpoints for each group fit separately, and for the two groups fit together under the assumption of parallelism.  For example, if the Joinpoint software selects 2 joinpoints for males and 0 joinpoints for females fit separately, and 1 joinpoint for males and females fit under an assumption of parallelism, then the parallelism test is conducted under an assumption of Max(2,0,1) = 2 joinpoints.

Kim, H-J, Fay, M.P., Yu, Binbing, Barrett, M.J., and Feuer, E.J. (2004) "Comparability of segmented line regression models", Biometrics 60, 1005-1014

### Example:

The Comparison tab shows "2 Joinpoints", when the cohort was deemed "parallel" and the parallel best fit was 1 joinpoint.

For the Pairwise comparison, you have the following three best-fit models:

• Male – Joinpoint selects 2 Joinpoints.
• Female – Joinpoint selects 0 Joinpoints.
• Combined Male and Female – Joinpoint selects 1 Joinpoint.

In the Pairwise Comparison help, there is a section labeled “How is the Kmax chosen?” That section describes the process of how Joinpoint determines the “2 Joinpoints” on the Comparison tab. This selection is based on the 3 models above. The number shown on the comparison tab (“2 Joinpoints”) is the maximum number of Joinpoints in the above 3 models. So, it is the max of 2, 0, and 1.

The test for parallelism is performed AFTER the three models are fit. So, the number of joinpoints displayed on the comparison tab is not necessarily the number of joinpoints selected for the model fit for the combined data. Below are the screen shots of the three models and the test for parallelism.

### Male – Joinpoint selects 2 Joinpoints, Female – Joinpoint selects 0 Joinpoints: ### Combined Male and Female – Joinpoint selects 1 Joinpoint: ### Test for Parallelism: 