A Latent Promotion Time Cure Rate Model using Dependent Tail-Free Mixtures

Abstract

Summary The paper extends the latent promotion time cure rate marker model of Kim, Xi and Chen for right‐censored survival data. Instead of modelling the cure rate parameter as a deterministic function of risk factors, they assumed that the cure rate parameter of a targeted population is distributed over a number of ordinal levels according to the probabilities governed by the risk factors. We propose to use a mixture of linear dependent tail‐free processes as the prior for the distribution of the cure rate parameter, resulting in a latent promotion time cure rate model. This approach provides an immediate answer to perhaps one of the most pressing questions ‘what is the probability that a targeted population has high proportions (e.g. greater than 70%) of being cured?’. The approach proposed can accommodate a rich class of distributions for the cure rate parameter, while centred at gamma densities. The algorithms that are developed in this work allow the fitting of latent promotion time cure rate models with several survival models for metastatic tumour cells.

Inclusion of Time-Varying Covariates in Cure Survival Models with an Application in Fertility Studies

“…Recently, several extensions of the promotion time model have been proposed in the literature; see for example Liu and Shen (), Kim et al . (), Lopes and Bolfarine (), Li and Lee () and Bremhorst et al . ().…”

“…5/ Tsodikov (2002) proposed, in a frequentist framework, a non-parametric estimator of the baseline survival function S 0 .t/, whereas Yin and Ibrahim (2005), using a piecewise exponential distribution, and , using P-splines, suggested a flexible specification of S 0 .t/ in a Bayesian framework; see Gressani and Lambert (2018) for fast inference in that Bayesian setting. Recently, several extensions of the promotion time model have been proposed in the literature; see for example Liu and Shen (2009), Kim et al (2009), Lopes and Bolfarine (2012), Li and Lee (2017) and Bremhorst et al (2019). Our paper is motivated by the analysis of data from the German Socio-Economic Panel (Wagner et al, 2007) studying the transition to second and third births.…”

Nonparametric double additive cure survival models: An application to the estimation of the non-linear effect of age at first parenthood on fertility progression

“…Within the Bayesian paradigm, Yin and Ibrahim (2005) assumed a piece-wise exponential distribution, while (Bremhorst and Lambert 2016) opted for a flexible specification of S0false(tfalse) using P-splines (Eilers and Marx, 1996, 2010). For recent articles using or extending the promotion time model, we refer the interested reader to Liu and Shen (2009), Kim et al (2009), Lopes and Bolfarine (2012) and Li and Lee (2017).…”