Abstract: This article presents a general single-index hazard regression model to assess the effects of covariates on a failure time. Based on left-truncated and right-censored survival data, a new partial-rank correlation function is proposed to estimate the index coefficients in the presence of covariate-dependent truncation and censoring. Furthermore, an efficient computational algorithm is proposed for the computation that maximizes the constructed target function. The developed approach can be extended to include right-truncation and left-censoring under a reverse-time hazard regression model. Based on the maximum rank correlation estimator in the literature, we establish the consistency and asymptotic normality of the maximum partial-rank correlation estimator. A series of simulations shows that the proposed estimator has satisfactory finite-sample performance compared with that of its competitors. Lastly, we demonstrate our methodology by applying it to data from the US Health and Retirement Study.

Key words and phrases: Asymptotic normality, consistency, left-censoring, left-truncation, partial-rank correlation estimation, rank correlation estimation, random weighted bootstrap, right-censoring, right-truncation, U-statistic.