Survival Formulas

Mixture Cure Model

\(S(x-t,t) = \{(1-C) + C\times \exp\{-[\mu(x-t)]^{\gamma}\}\}^{\exp[\beta_{1}(t-t_{0})+ \beta_{2}(t+y-y_{0})+\beta_{3}\delta]}\)

where

• C is the portion of individuals who will die of cancer (while 1-C will have the same mortality as the general population),
• \(\mu\) is the scale parameter of the Weibull distribution,
• \(\gamma\) is the shape parameter of the Weibull distribution,
• \(t_0\) is the reference age (normalizing constant),
• \(\exp[\beta_{1}(t-t_{0})]\) is the relative risk of being diagnosed one year older than the references age \(t_0\),
• \(y_{0}\) is the reference period (normalizing constant),
• \(\exp[\beta_{2}(t+y-y_{0})]\) is the relative risk of being diagnosed one year later than the reference period \(y_0\) (notice that t+y is the year of diagnosis for the y-th birth cohort),
• \(\exp[\beta_{3}\delta]\)  is the relative risk of belonging to a population (for example a race/ethnicity group or a geographic area) different from the reference once, \(\delta\) is a reference variable.