[Paper Review] A general dynamical statistical model with possible causal interpretation

Daniel Commenges, Anne Gégout‐Petit|ArXiv.org|Oct 24, 2007

Bayesian Modeling and Causal Inference41 references3 citations

TL;DR

This paper proposes a general dynamical statistical model based on stochastic processes and Doob-Meyer decomposition to formalize causal influence with physical interpretability. It distinguishes between system models (mechanistic ODEs) and observation models, demonstrating that conventional joint models fail to capture causal mechanisms—while mechanistic HIV models with explicit biological pathways (e.g., infected vs. uninfected T cells, viral load dynamics) successfully represent causal influences through differential equations and directed graphs.

ABSTRACT

We develop a general dynamical model as a framework for possible causal interpretation. We first state a criterion of local independence in terms of measurability of processes involved in the Doob-Meyer decomposition of stochastic processes, as in Aalen (1987); then we define direct and indirect influence. We propose a definition of causal influence using the concepts of ``physical system''. This framework makes it possible to link descriptive and explicative statistical models, and encompasses quantitative processes and events. One of the features of this paper is the clear distinction between the model for the system and the model for the observation. We give a dynamical representation of a conventional joint model for HIV load and CD4 counts. We show its inadequacy to capture causal influences while on the contrary known mechanisms of HIV infection can be expressed directly through a system of differential equations.

Motivation & Objective

• To develop a general framework for causal inference in dynamic systems using stochastic processes.
• To formalize causal influence via physical systems and laws, moving beyond correlation.
• To clarify the distinction between the model of the underlying biological system and the model of observed data.
• To demonstrate that mechanistic ODE models better capture causal influences than standard joint models in HIV dynamics.
• To integrate event processes (e.g., opportunistic disease) with continuous markers using proportional hazards within the dynamical framework.

Proposed method

• Uses Doob-Meyer decomposition of special semimartingales to define local independence via measurability of predictable processes.
• Defines direct and indirect influence through the predictable variation component of the Doob-Meyer decomposition.
• Introduces causal influence via the concept of a 'physical system' governed by physical laws, ensuring interpretability.
• Constructs a system model using a system of stochastic differential equations (SDEs) or ODEs to represent biological mechanisms (e.g., HIV infection dynamics).
• Separates the system model (unobserved processes) from the observation model (measured markers like CD4 and viral load).
• Uses directed graphs to represent causal influences, with edges indicating dynamic dependencies derived from the ODE system.

Experimental results

Research questions

• RQ1 How can causal influence be formally defined in a continuous-time stochastic process framework with physical interpretability?
• RQ2 What distinguishes a model of the underlying biological system from a model of the observed data in longitudinal studies?
• RQ3 Why do conventional joint models of HIV markers fail to capture causal mechanisms despite better fit?
• RQ4 How can mechanistic ODE models of HIV dynamics be embedded in a statistical framework that supports causal inference?
• RQ5 How can treatment decisions influenced by measurements be represented in a causal graph when treatment is not randomized?

Key findings

• Conventional joint models of HIV load and CD4 counts, while fitting data well, fail to represent causal influences due to lack of mechanistic structure.
• Mechanistic ODE models that distinguish quiescent and activated CD4+ T cells, and infectious vs. non-infectious virus, successfully encode known biological mechanisms and causal pathways.
• The system of ODEs proposed by Ho et al. (1995) and Perelson et al. (1996), extended by Guedj et al. (2007), provides a time-homogeneous, physically interpretable model of HIV dynamics.
• The model allows for causal interpretation through the structure of the ODEs and the resulting influence graph, with clear pathways from viral load to CD4 decline.
• In observational studies, treatment decisions influenced by measured viral load and CD4 counts can be modeled by including the doctor’s decision process, with measurement-induced influences shown via dotted lines in the causal graph.
• The integration of a counting process for opportunistic disease with the ODE system via a proportional hazards model allows for joint modeling of events and continuous markers under the same causal framework.