Converts a cumulative rate to a cumulative risk using the standard exponential formula. This is commonly used in cancer epidemiology to estimate the probability of developing or dying from cancer up to a certain age, under the assumption of constant rates.
cumrisk(cumrate, mp = 100, decimal = 2)Numeric. The cumulative incidence or mortality rate,
typically calculated using cumrate.
Numeric. The rate multiplier used in cumrate.
This is used for labeling purposes only. Default is 100.
Integer. Number of decimal places to round the result.
Default is 2.
A named numeric value representing the cumulative risk (as a percentage).
The cumulative risk is calculated as: $$1 - \exp(-\text{cumrate})$$ This converts the cumulative rate to a probability, assuming the event rate is constant over each age interval and the competing risks are ignored.
px <- c(
20005, 86920, 102502, 151494, 182932, 203107, 240289, 247076, 199665,
163820, 145382, 86789, 69368, 51207, 39112, 20509, 12301, 6586, 1909
)
dx <- c(
156, 58, 47, 49, 48, 68, 120, 162, 160, 294, 417, 522, 546, 628,
891, 831, 926, 731, 269
)
mx <- dx / px
cumrate(mx, eage = 70)
#> Cumulative Rate(1/1)
#> 0.497705
cumrisk(cumrate(mx, eage = 70))
#> Cumulative Risk (1/100)
#> 39.21