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Abstract:
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This paper extends the latent promotion time cure rate marker model (Kim et al., 2009) for right-censored survival data. Instead of modeling the cure rate parameter as a deterministic function of risk factors, Kim et al. (2009) assumed the cure rate parameter of a targeted population be distributed over a number of ordinal levels according to the probabilities governed by the risk factors. In this work, 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 (LPTCR). 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. >70\%) of being cured?'' The proposed approach can accommodate a rich class of distributions for the cure rate parameter, while centered at Gamma densities. The algorithms developed in this work allow the fitting of LPTCR with several survival models for metastatic tumor cells.
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