Imputation techniques for reliability analysis based on partly internal censored data

Abstract

In a conventional statistical analysis the term survival analysis or reliability analysis as it is known in engineering, has been used in a broad sense to describe collection of statistical procedures for data analysis for which the outcome variable of interest is time until an event occurs. The time to failure of a particular experimental unit might be censored and this censored can be right, left, and interval (Partly Interval Censored (PIC)). In this thesis the analysis of this particular model was based on non-parametric, semi-parametric Cox model, and parametric accelerated failure time model via PIC data. In these models several imputation techniques are used that is; midpoint, left & right point, random, mean, median, and Multiple Imputations (MI). The maximum likelihood estimate was considered to obtain the estimated survival function. These estimates were then compared to the existing model such as Turnbull and Cox model based on clinical trial data (breast cancer data), for which it showed the validity of our models. In contrast, the data needed to be modified to PIC data for the purpose of the researchers needs. Likewise, engineering failure rates data was also modified to represent PIC data and then simulation data was generated where the failure rates were taken based on engineering PIC data and was also used to further compare these three methods of estimation. From the simulation study for this particular case, we can conclude that the semi-parametric Cox model proved to be more superior in terms of estimating the survival function, likelihood ratio test and their P-value. In additional to that, based on imputation techniques, the MI, midpoint, random, mean and median showed better results with respect to estimate of the survival function. For the ultimate results, even though the semi-parametric model showed better output compared with the nonparametric and parametric models, all three models can easily be implemented based on engineering data set, medical data and simulation data.