CAUSAL INFERENCE FOR CONTINUOUS-TIME PROCESSES WHEN COVARIATES ARE OBSERVED ONLY AT DISCRETE TIMES

Area of Science:

• Causal Inference
• Longitudinal Data Analysis
• Biostatistics

Background:

• Traditional causal inference methods often assume discrete-time data generation.
• Observational studies may involve continuous-time processes with discrete observations, violating key assumptions.
• The sequential randomization assumption for discrete-time g-estimation may be unreasonable in such cases.

Purpose of the Study:

• To investigate causal inference methods for longitudinal data generated from continuous-time processes.
• To address limitations of discrete-time g-estimation when underlying data generation is continuous.
• To propose and evaluate alternative methods for consistent causal effect estimation.

Main Methods:

• Exploration of assumptions guaranteeing consistency for discrete-time g-estimation under deterministic models.
• Development and proposal of a "controlling-the-future" method for more general cases.
• Application and comparison of methods using simulated data and a real-world dataset on diarrhea and child height.

Main Results:

• The "controlling-the-future" method demonstrates robust performance, matching or exceeding g-estimation in many scenarios.
• The proposed method provides consistent estimation in situations where discrete-time g-estimation is severely inconsistent.
• Comparative analysis highlights the strengths of the new method in both simulated and real-world applications.

Conclusions:

• Discrete-time g-estimation assumptions may not hold for continuous-time data generation.
• The "controlling-the-future" method offers a valuable alternative for causal inference in complex longitudinal data.
• The study provides practical tools for analyzing observational data with continuous underlying processes.