Generalized Time-dependent Conditional Linear Models under Left Truncation and Right Censoring

Consider the model φ(S(z|X)) = β(z)t ~ X, where φ is a known link function, S(·|X) is the survival function of a response Y given a covariate X, ~ X = (1,X,X2, . . . ,Xp) and β(z) = (β0(z), . . . , βp(z)) t is an unknown vector of time-dependent regression coefficients. The response is subject to left truncation and right censoring. Under this model, which reduces for special choices of φ to e.g. Cox’s proportional hazards model or the additive hazards model with time dependent coefficients, we study the estimation of the vector β(z). A least squares approach is proposed and the asymptotic properties of the proposed estimator are established. The estimator is also compared with a competing maximum likelihood based estimator by means of simulations. Finally, the method is applied to a larynx cancer data set.