Analysis of Transformation Models with Censored Data

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARYIn 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.

Probabilistic Index Models

“…Bickel and Ritov (1997) proposed an efficient estimation of β based on rank statistic methods. Cheng et al (1995) proposed a class of estimating equations for β under possibly right-censored observations. Moreover, Han (1987) even allowed F " to be unknown and gave the maximum rank correlation estimatê…”

“…The first involves inverse probability weighting and the second makes use of pseudo-pseudovalues. Here we mention only that inverse probability weighting has already been described by Cheng et al (1995) in a class of semiparametric linear transformation models that generalize Cox proportional hazard models that make use of estimating equations similar to ours. In passing we note that the discussants Chenlei Leng and Guang Cheng made this observation too.…”

Maximum Likelihood Estimation in Semiparametric Regression Models with Censored Data

“…This approach can also be applied to the general transformation models that are given in equations (2)-(4). The inverse probability of censoring weighting (Robins and Rotnitzky, 1992) approach was used by Cheng et al (1995) and Cai et al (2002) for linear transformation models, and by Kalbfleisch and Lawless (1988), Borgan et al (2000) and Kulich and Lin (2004) for casecohort studies. These estimators are not asymptotically efficient.…”

“…Both the proportional hazards and the proportional odds models belong to the class of linear transformation models which relates an unknown transformation of the failure time linearly to covariates , page 241). Dabrowska and Doksum (1988), Cheng et al (1995) and Chen et al (2002) proposed general estimators for this class of models, none of which are asymptotically efficient. The class of linear transformation models is confined to traditional survival (i.e.…”

Semiparametric Models: A Generalized Self-Consistency Approach

“…. 27/ The class of NTMs includes the class of linear transformation models (Cheng et al, 1995(Cheng et al, , 1997. It is easy to show that a linear transformation model can be represented as γ.x|β, z/ = p[log{θ.β, z/} + q.x/], where p is a parametrically specified tail function, q is an inverse tail function and θ is a predictor (it is convenient to specify q as the inverse of p; then θ = 1 corresponds to the base-line γ.x|·/ = x).…”