Analysis of transformation models with censored data

Abstract

In this paper we consider a class of semi-parametric transformation models, under which an unknown transformation of the survival time is linearly related to the covariates with various completely specified error distributions. This class of regression models includes the proportional hazards and proportional odds models. Inference procedures derived from a class of generalised estimating equations are proposed to examine the covariate effects with censored observations. Numerical studies are conducted to investigate the properties of our proposals for practical sample sizes. These transformation models, coupled with the new simple inference procedures, provide many useful alternatives to the Cox regression model in survival analysis.

Partial rank estimation of duration models with general forms of censoring

“…See for example Cox (1975)'s partial maximum likelihood estimator (PMLE), Cuzick (1988), and more recently Chen, Jin and Yin (2002). Cheng, Wei and Ying (1995), Fine, Ying andWei (1998), andCai, Wei andWilcox (2000) are more restrictive in the sense that in addition to parametrically specifying the distribution of i , they do not allow the censoring variable to depend on x i . The other group, of which examples include the important single-index estimators in Han (1987) and Cavanagh and Sherman (1998), 2 do not impose distributional assumptions on i , but for consistency requires that the censoring variable be independentof the covariates.…”

Consistency of the NPML Estimator in the Right‐Censored Transformation Model

“…These models are coextensive with model (1), as can be seen from the formula g(S(t|z)) ¼ h(t) + z¢b (1.3 of Cheng et al, 1995), where g is known and h unknown, through the correspondence g(x) " log(G )1 () log x)), h(t) " log K(t). Throughout this paper, we are concerned with models S(t|z) in formula (1) defined in terms of a known function G, about which we assume that: (G.1) G is three times continuously differentiable, strictly increasing, and concave on (0, 1),…”

“…As an indication of the overall consistency result in this case, we state only one result. In that result, a specific preliminary estimator is cited in equation (38), but any of the others of Cheng et al (1995) would do just as well.…”

“…Klaassen (1993) proved existence of a consistent and efficient estimator of b in the uncensored Clayton-Cuzick model. Cheng et al (1995) and Bagdonavicius & Nikulin (1997) established asymptotic properties for estimating equation-based estimators in general transformation models. Parner (1998) has shown the joint NPMLE for (b, K) in the right-censored Clayton-Cuzick model to be consistent, asymptotically Gaussian, and semiparametric efficient.…”

Statistical Diagnosis for General Transformation Model with Right Censored Data Based on Empirical Likelihood

“…In this paper, we will consider statistical diagnostic for a class of very general survival models-general transformation models with right censored data in the form of [20]; Fine et al [21]). …”