Abstract
The Cox proportional hazards model is a widely used statistical method for the censored data that model the hazard rate rather than survival time. To overcome complexity of interpreting hazard ratio, quantile regression was introduced for censored data with more straightforward interpretation. Different methods for analyzing censored data using quantile regression model, have been introduced. The quantile regression approach models the quantile function of failure time and investigates the covariate effects in different quantiles. In this model, the covariate effects can be changed for patients with different risk and is a flexible model for controlling the heterogeneity of covariate effects. We illustrated and compared five methods in quantile regression for right censored data included Portnoy, Wang and Wang, Bottai and Zhang, Yang and De Backer methods. The comparison was made through the use of these methods in modeling the survival time of breast cancer. According to the results of quantile regression models, tumor grade and stage of the disease were identified as significant factors affecting 20th percentile of survival time. In Bottai and Zhang method, 20th percentile of survival time for a case with higher unit of stage decreased about 14 months and 20th percentile of survival time for a case with higher grade decreased about 13 months. The quantile regression models acted the same to determine prognostic factors of breast cancer survival in most of the time. The estimated coefficients of five methods were close to each other for quantiles lower than 0.1 and they were different from quantiles upper than 0.1.
Highlights
The Cox proportional hazards model is a widely used statistical method for the censored data that model the hazard rate rather than survival time
Other methods such as accelerated failure time (AFT) models and censored quantile regression (CQR) models were introduced for censored data with a more straightforward interpretation[3]
The AFT model allows a direct interpretation of covariate effects on event time, it requires a strong assumption of homogeneous treatment effect[4]
Summary
The Cox proportional hazards model is a widely used statistical method for the censored data that model the hazard rate rather than survival time. The Cox proportional hazards (Cox) model is a widely used statistical method for the censored data This model is limited by the assumption of a constant hazard ratio (HR) over time (i.e., proportionality), and models the hazard rate rather than the survival time d irectly[2]. The complexity of the HR estimate interpretation was recognized as a problem in the Cox models To overcome this limitations, other methods such as accelerated failure time (AFT) models and censored quantile regression (CQR) models were introduced for censored data with a more straightforward interpretation[3]. The effect of a covariate is to accelerate or decel- direct interpretation of covariate effects on event erate the life course of a disease by some constant time
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