Empirical Quantile CI for APC and AAPC

Answer:

APC and AAPC estimates are calculated directly from the data. On the other hand, the empirical quantile CI for the APC and AAPC are calculated using a Monte Carlo resampling method based on the data. Without loss of generality, assume 5001 resamples are used. For each resample of the data, a new Joinpoint model is fit using the same number of joinpoints as the fit using the original data, but the location of the joinpoints could differ. To calculate the 95% CI for the APC (or AAPC), the empirical quantile method finds the 2.5^th percentile and the 97.5^th percentile among the 5001 APCs (or AAPCs) calculated from the resampled data.

Suppose the final joinpoint segment runs from 2013-2019 and a user is requesting a 5-year AAPC (2015-2019). In this case the final segment APC and AAPC are identical because of the overlapping period. However, the CIs for the AAPC and APC could differ if at least one Monte Carlo resample of the data finds a final joinpoint segment shorter than 5 years, for example, 2016-2019. In this resample, the AAPC is calculated by transforming a weighted average of the slope from the final segment and the slope from the prior segment to an annual percent change. Thus the last segment APC and 5-year AAPC estimates for this resample will be different. The AAPC and APC estimates from such resamples are included in the 5001 resampled estimates to derive the 2.5^th and 97.5^th percentiles for the AAPC and APC 95% CIs. This could result in a difference between the 5-year AAPC (2015-2019) and last segment APC CIs.