Estimation for semiparametric transformation models with length-biased sampling

For length-biased and right-censored data, we propose an estimation method to assess the effects of risk factors under the semiparametric linear transformation model. Unlike the existing method of Shen et al. (2009) based on the ranks of observed failure times, the new estimators are obtained from counting process-based unbiased estimating equations. Consistency and asymptotic normality for the estimators are derived under suitable regularity conditions. We evaluate the finite sample performance of the proposed method and make a comparison with that of Shen et al. (2009) by simulation studies. A real data example is analyzed to illustrate the proposed method.