Regression Estimation for Length-Biased Data: A Review and Comparative Study

Length-biased sampling has been widely recognized in various fields, including economics, industrial reliability, applications in etiology, and studies related to epidemiology, genetics, and cancer screening. The assessment of the relationship between risk factors and survival time in the presence of biased data, particularly length-biased right-censored (LBRC) data, has long been a statistical challenge. Since the structure of observed length-biased data differs from that of the target population, using traditional methods to estimate covariate effects based on the observed length-biased data is inappropriate. This chapter focuses on discussing existing methods for estimating regression coefficients under commonly used semiparametric models, specifically the Cox proportional hazard (Cox) and accelerated failure time (AFT) models, when dealing with LBRC data. To compare the efficacy of available methods, a simulation study is conducted. In summary, the results indicate that all the estimating methods proposed to accommodate LBRC data exhibit better performance than the traditional approach for estimating coefficients of Cox model, which ignores bias in sampling. Furthermore, the composite partial likelihood method outperforms all other methods in terms of bias and standard error. For AFT model, the inverse weighted estimating equation approach is more efficient in the presence of LBRC data compared to other existing methods. Additionally, to illustrate the practical performance of these methods, a real dataset is analyzed.