Sentence examples for marginal survival function from inspiring English sources

One knot, placed at the median of the failure time distribution, seems to be sufficient to model the marginal survival function, see Figure 3.

Only one of the above methods is proposed to estimate the marginal survival function and can adjust for dependent censoring through using the information from auxiliary variables [ 5].

Although we can estimate S k (t; z ) from the cause- k specific cumulative hazard, exp{- Λ k (t; z )} is not interpretable as the marginal survival function for cause- k specific alone [ 12].

In general, such constraints between marginal survival functions are not easily verified.

The key feature of our bivariate survival function is that the marginal survival functions correspond exactly to the Kaplan-Meier product limit estimators.

for all x 1,x 2,t≥0, where (phantom {dot {i}!}S_{mathbf {X}_{t}}(x_{1}, x_{2})) is the joint survival function of residual lifetime vector X t and (phantom {dot {i}!}S_{X_{it}} (x_{i})) are its marginal survival functions, i=1,2.

The marginal or observable survival function for the shared gamma frailty model (4) is S (t | Z hk ij ) = E u [ S (t | Z hk ij, u hk i ) ] = 1 (1 + γ hk Λ hk ij (t ) ) 1 / γ hk with Λ hk ij (t ) the cumulative transition intensity function specific to the transition hk.

In this note we provide the only method for estimating a bivariate survival function such that the marginal estimators correspond exactly to the Kaplan-Meier product limit estimators such that there is a relative consistency between the marginal estimates derived via univariate or bivariate methods.

In this population focus, each conditional survival function is replaced by its marginal version.

In other words, the corresponding joint survival function is valid only for certain marginal distributions of X 1 and X 2.

To the best of our knowledge one of the key limitations of all of the completely nonparametric bivariate survival function estimators developed to-date is that they yield marginal estimators that may not be equivalent to the product-limit estimator corresponding to each dimension.