Semiparametric estimation for the additive hazards model with left-truncated and right-censored data

Survival data from prevalent cases collected under a cross-sectional sampling scheme are subject to left-truncation. When fitting an additive hazards model to left-truncated data, the conditional estimating equation method (Lin & Ying, 1994), obtained by modifying the risk sets to account for left-truncation, can be very inefficient, as the marginal likelihood of the truncation times is not used in the estimation procedure. In this paper, we use a pairwise pseudolikelihood to eliminate nuisance parameters from the marginal likelihood and, by combining the marginal pairwise pseudo-score function and the conditional estimating function, propose an efficient estimator for the additive hazards model. The proposed estimator is shown to be consistent and asymptotically normally distributed with a sandwich-type covariance matrix that can be consistently estimated. Simulation studies show that the proposed estimator is more efficient than its competitors. A data analysis illustrates application of the method.