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Background  This study aimed to introduce recursively imputed survival trees into multistate survival models (MSRIST) to analyze these types of data and to identify the prognostic factors influencing the disease progression in patients with intermediate events. The proposed method is fully nonparametric and can be used for estimating transition probabilities.    Methods  A general algorithm was provided for analyzing multi-state data with a focus on the illness-death and progressive multi-state models. The model considered both beyond Markov and Non-Markov settings. We also proposed a multi-state random survival method (MSRSF) and compared their performance with the classical multi-state Cox model. We applied the proposed method to a dataset related to HIV/AIDS patients based on a retrospective cohort study extracted in Tehran from April 2004 to March 2014 consist of 2473 HIV-infected patients.    Results  The results showed that MSRIST outperformed the classical multistate method using Cox Model and MSRSF in terms of integrated Brier score and concordance index over 500 repetitions. We also identified a set of important risk factors as well as their interactions on different states of HIV and AIDS progression.    Conclusions  There are different strategies for modelling the intermediate event. We adapted two newly developed data mining technique (RSF and RIST) for multistate models (MSRSF and MSRIST) to identify important risk factors in different stages of the diseases. The methods can capture any complex relationship between variables and can be used as a useful tool for identifying important risk factors in different states of this disease.

Multistate recursively imputed survival trees for time-to-event data analysis: an application to AIDS and mortality post-HIV infection data