The baseline survivor function in is estimated by solving where is the Breslow (1972) estimator: The survival function of censoring can be also approximated by the Breslow (1972) estimator by considering events as "censored" observations and censored observations as "events" (Satten and Datta, 2001).
For a group of patients with covariates (x1, x2, … x p), the model is written mathematically as S (t )= S 0 ϕt ) where S0 t) is the baseline survivor function and ϕ is an 'acceleration factor' that depends on the covariates according to the formula ϕ =exp{(b 1 x 1+ b 2 x 2+⋯+ b p x p )}.
The 95% confidence limits of the survivor function are shown.
Cox survivor plots were used for graphical depiction; the Cox survivor function was used for quantitative estimates of survival.
The Weibull frailty model given in 2 can be equivalently expressed in terms of the survivor function of the Weibull distribution as: (3) (4) where S0 t) is the baseline survivor function of the conditional Weibull distribution, that is, S0 t) = exp(- α0 t γ ), where α0 = exp β0).
For clustered survival data, the general AFT model with normal random frailty effect can be written as: (5) where ξ i ~Normal (0, σ), S0 is the baseline survivor function of a parametric survival distribution, such as Weibull distribution, log-normal distribution, generalized gamma distribution, log-logistic distribution, generalized F distribution [ 13], and inverse Gaussian distribution [ 4].
Ŝ 0 (t ) is the baseline survivor function from a Cox proportional hazards model estimated according to one of the available methods [ 23, 24].
The coefficients were used as weights, which were combined with the baseline survivor function to derive risk equations at age 50 years.
Deaths from other causes were estimated from the baseline survivor function for competing mortality after adjusting for age.
The Cox models were used to derive the baseline survivor function and the hazard ratio associated with each prognostic factor.
