Simple parametric survival analysis with anonymized register data: A cohort study with truncated and interval censored event and censoring times

Table 2 Parameterization of distributions

Model	S(y)	Parameter restrictions	Mean
Weibull:	exp (-λy^γ)	λ > 0, γ > 0	$\frac{Γ (1 + \frac{1}{γ})}{λ^{1 ∕ γ}}$
Gamma:	$I {(α, \frac{y}{β})}^{†}$	α > 0, β > 0	αβ
Gompertz:	$exp (- \frac{λ}{γ} (e^{y γ} - 1))$	γ > 0	No closed formula
Log-Logistic:	$\frac{1}{1 + {(y ∕ α)}^{β}}$	α > 0, β > 0	$\frac{α π}{β s i n (π ∕ β)}$
Log-Normal:	$Φ {(- \frac{l o g (y) - μ}{σ})}^{‡}$	σ > 0	$exp (μ + \frac{1}{2} σ^{2})$

^† I(a, x) is the incomplete gamma function given by $I (a, x) = \frac{1}{Γ (a)} \int_{0}^{x} e^{- t} t^{a - 1} d t$
^‡ Φ(x) is the standard normal cdf given by $Φ (x) = \frac{1}{\sqrt{2 π}} \int_{- \infty}^{x} e^{- \frac{1}{2} t^{2}} d t$
For each distribution the survivor function S(y) is given accompanied by parameter restrictions, if applicable, and the formula for the mean survival as a function of parameters.

ISSN: 1756-0500