On the role of Martingales in continuous-time causal inference, Pål Christie Ryalen

You are all invited to an exciting seminar at Biostats on Monday, December 09 @ 15:15: 

Pål Christie Ryalen, University of Oslo and Oslo University Hospital

"On the role of Martingales in continuous-time causal inference”

A number of works on causal inference with counting process data have attempted to draw on well-established conditions such as consistency, exchangeability, and positivity for identifying causal effects. Despite multiple claimed or conjectured identification conditions and formulas in the literature, counting process analogues of these identifying conditions have not yet been established. There is consequently a lack of tools to formally reason about identification, and it remains unclear when, or if, existing proposed identification formulas can be derived. There are furthermore no existing definitions of potential outcomes for counting process data, and characterizations of dynamic treatment regimes are lacking.

In this talk, I define dynamic regimes and associated potential outcomes for data described by marked point processes (MPPs), and introduce MPP analogues of the commonly used consistency, exchangeability, and positivity conditions, which prove to be sufficient for identifying effects in MPP data structures. The conditions are martingale-centered, showing the critical role of martingale theory in identifying causal effects for data described by  stochastic processes. The definitions and conditions align with well-established discrete-time conditions in the special cases where alignment is expected, and the results thus bridge the vast literature on survival (event history) analysis with counting processes in continuous time and discrete-time causal inference. Having established a set of identification conditions, I derive and characterize marginal g-formulas, and obtain formulas that are generally quite different from those that have been posed in related works on causal inference with stochastic processes. I discuss the relation with related work, the classical survival literature and the discrete-time causal inference literature.

Room: Biostat library (5.2.46) 

For more information and to see the abstracts go to https://biostatistics.dk/seminars/

Unless otherwise stated, seminars will be held at CSS (det gamle Kommunehospital), Øster Farimagsgade 5, 1353 Copenhagen K, room 5.2.46. Tea will be served in the library of the section of Biostatistics half an hour before the seminar starts.