What is the difference between 1-year partial prevalence and annual incidence? In cancer research, like in this article, partial prevalence is sometimes used to assess the epidemiological state of a disease in a population.
The document I'm trying to understand (link, in french) gives total prevalence and partial prevalences at 1, 3, 5 and 10 years. It defines partial prevalence at 1 year as:

Partial prevalence at 1 year:

*

*The number of people 15 years of age and older diagnosed with cancer during the year and still alive in 2008 is estimated at nearly
280,500: 155,675 men and 124,860 women.

*This indicator makes it possible to quantify people with cancer in initial treatment


To me, this definition is very close to the one of annual incidence.
I've found very few documents explaining what was partial prevalence (example, example) but no one ever compare it to incidence.
What is the difference between these two notions?
 A: This page from one of your links puts it pretty clearly:

Partial prevalence is the number of all cancer patients, being alive at specific date  (usually the last day of calendar year) and being diagnosed with cancer within a defined period of time before the date of calculation. One year partial prevalence includes patients, diagnosed with cancer one year before the date of calculation, patients included in 1-4 years prevalence were diagnosed within one and five years before calculation, ... they reflect the number of cancer cases in different course of disease, e.g. the one-year prevalence includes patients during their primary treatment, 1-4 years prevalence those requiring regular clinical follow-up, while 5-9 and especially 10 and more years prevalence includes predominantly those considered cured from cancer.

Start with the difference between the 1-year partial prevalence and the 1-year incidence. The latter is easy and independent of cancer type, simply how many patients were diagnosed with the disease in question over the previous year. The former is the product of that incidence times an estimate of survival over the year.* The partial prevalence thus depends on survival, not just incidence.
So for a disease like estrogen-receptor-positive stage 0 or 1 breast cancer, with 100% 5-year survival, you are correct that incidence and partial prevalence will be essentially identical in any partial prevalence calculated for time periods that do not extend beyond 5 years.
For anaplastic thyroid cancer, where "Most patients ... do not live 1 year from the day they are diagnosed," even the 1-year partial prevalence will be much lower than the incidence: many of those diagnosed over the year will have died by the end of the year. The 1-4 year partial prevalence for anaplastic thyroid would be almost 0.
Summary data like those in your second link can combine data across different types of cancer. Many people diagnosed with cancers have high 1-year survival, so 1-year partial prevalence combined across cancer types will be close to 1-year incidence. Incidence and partial prevalence will become more distinct at later time intervals after initial diagnosis.

*With epidemiologic whole-year data, this survival estimate might be taken at 1/2 year to account for accrual of patients over a period of 0 to 12 months.
