A Linear Algebraic Framework for Counterfactual Generation

Estimating individual treatment effects in clinical data is essential for understanding how different patients uniquely respond to treatments and identifying the most effective interventions for specific patient subgroups, thereby enhancing the precision and personalization of healthcare. However, counterfactual data are not accessible, and the true calculation of causal effects cannot be performed at the individual level. This paper proposes a linear algebraic framework to generate counterfactual longitudinal data that exactly matches pre-treatment factual data. Because causation travels forward in time, not in reverse, counterfactual predictability is further strengthened by blocking causal effects from flowing back to the past, thus limiting counterfactual dependence on the future. Using simulated LDL cholesterol datasets, we show that our method significantly outperforms the most cited methods of counterfactual generation. We also provide a formula that can estimate the time-varying variance of individual treatment effects, interpreted as a confidence level in the generated counterfactuals compared to true values.