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Exact(7)

where j denotes a failure time.

For left censoring, a failure time is only known to be before a certain time.

The two-parameter Birnbaum-Saunders (for short, BS) distribution was originally proposed by Birnbaum and Saunders (1969a) as a failure time distribution to describe the total time until the damage caused by the development and growth of a dominant crack grows to a critical level that would cause fracture of failure.

The stick survival curves have the characteristic shape expected for a failure time process [28], [29].

At time t, we observe for each individual either a failure time or a censoring time and an indicator specifying which.

The hazard function of a failure time T given a p-vector of possibly time-dependent covariates Z based on Lin and Ying additive hazards model is as follows: (1) λ (t ; Z ) = λ 0 (t ) + β 0 T Z, where λ0 is an unknown baseline hazard function which is common to all subjects and β0 is a p-vector of regression coefficients [ 4, 15].

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Similar(53)

We simulated two possible outcome scenarios (A and B) for this trial using a latent failure time approach.

A mediational analysis that considered gender as the initial variable, time to death as the outcome, initial CD4 count as the mediator, and age as a covariate was performed using an accelerated failure time model with a Weibull distribution.

In a latent failure time perspective, there is a random variable T i for the time to each possible event, but only the time to the first event can be recorded.

To accomplish this, we use an accelerated failure time model, a method particularly suited for time to event outcomes.

The "product method" of estimating the indirect effect requires the construction of a linear regression model for baseline CD4 cell count and an accelerated failure time model with a Weibull distribution using gender, baseline CD4 cell count and age.

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