The age–period–cohort (APC) forecasting method that we used here has been applied in previous studies14,15. In brief, we used an ensemble APC model to estimate bladder cancer incidence rates and to forecast the rates to 2025. The ensemble of the APC models comprises a total of 53 model types: the cubic spline APC models16, the polynomial APC models (the quadratic, cubic, and other types of polynomial models)17 and Tzeng and Lee's APC model18 (Table S1), each coupled with 5 different link functions (log, power 2, power 3, power 4, and power 5). The cubic spline model can smooth the changes over time and has been used to model noncommunicable disease projections in previous studies16,19. For the polynomial model, the quadratic, cubic, or higher degree components were used for smoothing the period and cohort effects. For Tzeng and Lee's APC model, the linear period and quadratic cohort effects were used. With the assumption that the historical trends may not continue indefinitely, the projection of each APC model was subject to 21 different levels of attenuation (0%, 5%, 10%, 15%, …, or 100%). Finally, 5,565 sets of projection models (53 model types × 5 link functions × 21 levels of attenuation) were estimated. Considering the perfect collinearity between the three temporal factors: period = age + cohort (the nonidentifiability problem), we deliberately left out the linear component of the cohort effect for all APC models in this study. Note that the nonidentifiability problem does not affect the incidence rate projections because the fitted values are consistent with all possible sets of parameter estimates.

Note: The content above has been extracted from a research article, so it may not display correctly.

Please log in to submit your questions online.
Your question will be posted on the Bio-101 website. We will send your questions to the authors of this protocol and Bio-protocol community members who are experienced with this method. you will be informed using the email address associated with your Bio-protocol account.

We use cookies on this site to enhance your user experience. By using our website, you are agreeing to allow the storage of cookies on your computer.