Statistical Inference Method For Competitive Risk Data With Failure Reason For Failure Reason In Accelerated Failure Time Model

Abstract:Competing risk data is very common in survival analysis. In clinical trials and other applications, the cause of failure may be missing for some rea-sons. Inappropriate analysis method may lead to biased result. Recently, many researchers proposed statistical inference methods of competing risk data with missing cause of failure. However, there is no research for analyzing compet-ing risk data with missing cause of failure under accelerated failure time model, which is a valuable semiparametric model with ease of interpretation. This is a blank in the previous research.This paper considers analyzing competing risks data with missing cause of failure under the accelerated failure time model. The missing mechanism is as-sumed to be missing at random. After introducing some basic knowledge of accelerated failure time model and missing data, two situations are considered, one is missing with parametric model, the other is missing with nonparametric model. In the third chapter of this paper, when missing model is parametric model, the inverse probability weighted and double robust techniques are used to modify the rank based estimating functions for competing risks data with com-complete observations on cause of failure. Proper optimization technique is utilized to obtain the desired estimators. The asymptotic properties of the pro-posed estimators are established. A simulation study is carried out to assess the finite sample performance of the proposed method and validate the theoretical findings. The proposed estimating method is finally adopted to analyze two data sets from two clinical trials for illustration. In the fourth chapter, when missing model is nonparametric model, kernel smoothing technique is used to estimate the probability of missing. Estimating equation is established accordingly. The asymptotic properties of the proposed estimators are then studied and simula-tion is carried out. The proposed method is also adopted to analyze those two data sets. The proposed method can be used for analyzing competing risk free data with missing censoring indicators as well.