Comparison between measures to summarize trend: annual absolute change in survival (AAC_S) and the annual percent change in the conditional probability of cancer death (APC_D).

Characteristics

AAC_S: Annual Absolute Change in Survival

APC_D: Annual Percent Change in the Conditional Probability of Death

Underlying measure

S(i,y): Cumulative survival, i.e., the probability of surviving cancer after i years from diagnosis, for patients diagnosed in year y

P(i,y): Conditional probability of dying of cancer in interval i given alive at the beginning of the interval, for patients diagnosed in year y

Formula (approximation)

Average of the survival difference {S(j,y+1)-S(j,y)} for calendar years y in the joinpoint segment

100*{P(i,y+1)-P(i,y)}/P(i,y) = 100*[exp(B)-1] where B is the coefficient in the joinpoint segment

Unit

Percentage points (pp): difference of two percentages

Percent: relative change of percentages. Similar to annual percent change (APC) for rates

Examples

Moving from 40% to 42% means a 2–percentage point increase in cumulative survival

Moving from 40% to 38% means a 5 percent decrease in the annual probability of cancer death

Interpretation

AAC_S(5) = 2%: The 5-year cancer survival is increasing on average 2 percentage points for each subsequent year of diagnosis.

APC_D = −5%: The annual probability of dying of cancer is decreasing by 5% for each subsequent year of diagnosis, similar to a 0.95 relative risk of dying of cancer in year compared with year y.

Does it vary by time since diagnosis?

Yes.

No.

AAC_S(1) ≠ AAC_S(5)

APC_D is the same for 0–1 year, 1- years, … from diagnosis.

Motivation/Summary

More clear prognosis interpretation versus more awkward mathematical derivation.

Clear mathematical interpretation versus challenging prognosis interpretation