Second order Markov multistate models

The GRBIO research group on biostatistics and bioinformatics is currently inviting applications for a PhD position. The main focus of this research project will be extending the initial definitions and results for second order Markov multistate models.

PhD Project:

The PhD project will focus on working with second order Markov multistate models. A multistate model (MSM) is a model for a stochastic process which at any time occupies one of a few possible states. MSM provides a flexible framework to describes complex clinical processes over time. MSM are well developed for continuous and discrete times under a first order Markov assumption where the future of the process only depends on the current state. Second order Markov models assume that the process not only depends on the current but also on the preceding state. This is a new approach when the first order Markov assumption cannot be assumed. So far, only estimations for the transition probabilities for complete data have been obtained.
The project will aim to study and extend MSM models under a second order Markov, to develop inference methods of estimation and hypothesis testing and to apply them to different datasets.

Tasks:

The successful candidate will be expected to carry out the following tasks:

• Prove Chapman-Kolmogorov equations for second order Markov models in continuous time.
• Estimate transition probabilities and transition intensities, accounting for right censoring.
• Develop a test for the second order Markov property.
• Define a Cox-based multistate model with covariates with second order Markov condition.
• Implement in R the previous estimations and test.
• Interpret the results and communicate findings in academic papers and presentations

Requirements:

The ideal candidate should have a master's degree in biostatistics, statistics, mathematics, data science or a related field. Strong skills in mathematics and in theoretical probability theory are needed. The candidate should have excellent written and verbal communication skills in English and be able to work independently and as part of a team.

Application:

Interested candidates should send their CV, academic transcripts, a letter of motivation, and contact details of two referees to the project supervisors, Dr. Mireia Besalú (mbesalu@ub.edu) and Dr. Guadalupe Gómez (lupe.gomez@upc.edu) by the 15th of July 2023. Shortlisted candidates will be invited for an interview, either in person or via video conference, and the successful candidate will be notified by the end of July 2023.

We welcome applicants from all backgrounds, genders, and nationalities. The university is committed to promoting a diverse and inclusive community, and we encourage candidates to apply who will contribute to this goal.