On the collapsibility of lifetime regression models

In this paper we derive conditions on the internal wear process under which the resulting time to failure model will be of the simple collapsible form when the usage accumulation history is available. We suppose that failure occurs when internal wear crosses a certain threshold or a traumatic event causes the item to fail. We model the infinitesimal increment in internal wear as a function of time, accumulated internal wear, and usage history, and we derive conditions on this function to get a collapsible model for the distribution of time to failure given the usage history. We reach the conclusion that collapsible models form the subset of accelerated failure time models with time-varying covariates for which the time transformation function satisfies certain simple properties.

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On the collapsibility of lifetime regression models

Advances in Applied Probability ◽

10.1239/aap/1059486827 ◽

2003 ◽

Vol 35 (3) ◽

pp. 755-772 ◽

Cited By ~ 7

Author(s):

Thierry Duchesne ◽

Jeffrey S. Rosenthal

Keyword(s):

Failure Time ◽

Traumatic Event ◽

Accelerated Failure Time ◽

Time To Failure ◽

Wear Process ◽

Accelerated Failure Time Models ◽

Accelerated Failure ◽

Collapsible Model ◽

Time Varying Covariates ◽

Accumulation History

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A New Compromise Design Plan for Accelerated Failure Time Models with Temperature as an Acceleration Factor

Mathematics ◽

10.3390/math9080836 ◽

2021 ◽

Vol 9 (8) ◽

pp. 836

Author(s):

Irene Mariñas-Collado ◽

M. Jesús Rivas-López ◽

Juan M. Rodríguez-Díaz ◽

M. Teresa Santos-Martín

Keyword(s):

Failure Time ◽

Failure Process ◽

Accelerated Life Test ◽

Accelerated Failure Time ◽

Time To Failure ◽

Middle Point ◽

Accelerated Life ◽

Accelerated Failure Time Models ◽

Accelerated Failure ◽

Compromise Design

An accelerated life test of a product or material consists of the observation of its failure time when it is subjected to conditions that stress the usual ones. The purpose is to obtain the parameters of the distribution of the time-to-failure for usual conditions through the observed failure times. A widely used method to provoke an early failure in a mechanism is to modify the temperature at which it is used. In this paper, the statistically optimal plan for Accelerated Failure Time (AFT) models, when the accelerated failure process is described making use of Arrhenius or Eyring equations, was calculated. The result was a design that had only two stress levels, as is common in other AFT models and that is not always practical. A new compromise plan was presented as an alternative to the widely used “4:2:1 plan”. The three-point mixture design proposed specified a support point in the interval that was optimal for the estimation of the parameters in AFT models, rather than simply the middle point. It was studied in comparison to different commonly used designs, and it proved to have a higher D-efficiency than the others.

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Effects of covariates on alternating recurrent events in accelerated failure time models

The International Journal of Biostatistics ◽

10.1515/ijb-2019-0099 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Moumita Chatterjee ◽

Sugata Sen Roy

Keyword(s):

Recurrent Events ◽

Failure Time ◽

Likelihood Method ◽

Model Parameters ◽

Accelerated Failure Time ◽

Survival Times ◽

Copula Functions ◽

Event Time ◽

Accelerated Failure Time Models ◽

Accelerated Failure

AbstractIn this article, we model alternately occurring recurrent events and study the effects of covariates on each of the survival times. This is done through the accelerated failure time models, where we use lagged event times to capture the dependence over both the cycles and the two events. However, since the errors of the two regression models are likely to be correlated, we assume a bivariate error distribution. Since most event time distributions do not readily extend to bivariate forms, we take recourse to copula functions to build up the bivariate distributions from the marginals. The model parameters are then estimated using the maximum likelihood method and the properties of the estimators studied. A data on respiratory disease is used to illustrate the technique. A simulation study is also conducted to check for consistency.

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