Journal of Data Science

We fit a Cox proportional hazards (PH) model to interval-censored survival data by first subdividing each individual's failure interval into nonoverlapping sub-intervals. Using the set of all interval endpoints in the data set, those that fall into the individual's interval are then used as the cut points for the sub-intervals. Each sub-interval has an accompanying weight calculated from a parametric Weibull model based on the current parameter estimates. A weighted PH model is then fit with multiple lines of observations corresponding to the sub-intervals for each individual, where the lower end of each sub-interval is used as the observed failure time with the accompanying weights incorporated. Right-censored observations are handled in the usual manner. We iterate between estimating the baseline Weibull distribution and fitting the weighted PH model until the regression parameters of interest converge. The regression parameter estimates are fixed as an offset when we update the estimates of the Weibull distribution and recalculate the weights. Our approach is similar to Satten et al.'s (1998) method for interval-censored survival analysis that used imputed failure times generated from a parametric model in a PH model. Simulation results demonstrate apparently unbiased parameter estimation for the correctly specified Weibull model and little to no bias for a mis-specified log-logistic model. Breast cosmetic deterioration data and ICU hyperlactemia data are analyzed.

Abstract: Accelerated life testing (ALT) has gained greater importance because of dealing with high reliability units. As a result, there is a big need to use a goodness of fit (GOF) technique for testing the underlying lifetime distribution. But there is a difficulty due to the existence of several stress levels with different samples of units at each level. Then, the choice of a certain GOF technique is based on its capability to combine the failure times from all stress levels to reach a conclusion about the adequacy of a certain lifetime distribution at each stress level. In this paper, the extended Neyman’s smooth test (ENST) is chosen. It is then modified in order to be used in validating the distributional assumption of accelerated failure time (AFT) model. This modified method is called; the adapted extended Neyman’s smooth test (AENST). It is applied to test for both Weibull and exponential distributions in case of constant stress under complete sampling. To check the performance of the AENST, a comparison is made with the conditional probability integral transformation test (CPITT) via a simulation study. Moreover, a real data set is provided to illustrate the application of the introduced AENST. The results revealed that the AENST is a powerful test comparing with the CPITT. Thus, the AENST is recommended for testing the AFT models.