Nonparametric Tests of the Markov Model for Survival Data

Abstract

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Semiparametric inference for an accelerated failure time model with dependent truncation

“…However, empirical evidence has shown that truncation may reveal useful information on the lifetime of interest (Tsai 1990;Jones and Crowley 1992;Chen et al 1996;Martin and Betensky 2005;Emura and Wang 2010;Rodríguez Girondo and de Uña-Álvarez 2012). In this article, we explicitly include the truncation variable, along with other covariates, in the proposed semiparametric AFT regression model.…”

“…We implement computing routines for the proposed method in R depend.truncation package which is freely available through the Comprehensive R Archive Network (CRAN) http://cran.rproject.org/". Jones and Crowley (1992) also included the truncation variable as a covariate based on their models. However, their paper focused only on testing the assumption of quasiindependence without estimating the models.…”

“…In contrast to independent censorship which is not a testable condition, there exist several nonparametric tests for verifying the quasi-independence assumption on the truncation variable (Tsai 1990;Jones and Crowley 1992;Chen et al 1996;Martin and Betensky 2005;Emura and Wang 2010;Uña-Álvarez 2012;Rodríguez Girondo and de Uña-Álvarez 2012). From these articles, we see an interesting phenomenon that the null hypothesis of quasi-independence was often rejected in some common real-world examples.…”

Survival Curve Estimation with Dependent Left Truncated Data Using Cox's Model

“…Individuals are right censored if they were alive as of 2006. We tested the independence of the left-truncation time and age at death using Jones and Crowley's (1992) approach based on the Cox model. There was a significant association (P¡0.0001).…”

“…A test based on the productmoment correlation has been proposed by Chen et al (1996). Alternatively, Jones and Crowley (1992) proposed the use of Cox's model for testing the association. In particular, they model the conditional distribution of time-to-event given truncation time using Cox's model for left-truncated data (Andersen et al, 1997).…”