Utrecht University

Department of Social and Behavioural Sciences

**Project**

**Transition models for individual causal effects**

The individual causal effect is the difference between potential outcomes under all possible treatment conditions for a single unit (Hernan & Robins, 2019). Under the potential outcomes framework, causality is associated with an intervention applied to a unit, and the individual causal effect is measured by the difference between a measured potential outcome and an unmeasured, but estimated potential outcome. The individual causal effect may vary

across different units. Therefore, if the scientificc interest is whether a unit would benefit from treatment, it is necessary to estimate the unit’s individual causal effect. The individual casual effect is of great interest in many disciplines such as biomedical, public health and social sciences.

Although the individual causal effect is the essential element of the potential outcomes framework, many researchers in causal inference estimate the average causal effect instead of the individual causal effect (Splawa-Neyman, Dabrowska, & Speed, 1990). The reason is that we can only observe one of those potential outcomes for an individual which means all other outcomes are missing (Holland, 1986). Thus, it is impossible to estimate the individual causal effect from the observed data directly. Obviously, if we assume that the effect varies between individuals, it would be inappropriate to extrapolate an average causal effect in one population to an individual. A solution would be to estimate the individual’s causal effect by imputing the unobserved potential outcome. Multiple imputation (Rubin, 1987) seems a promising technique for estimating potential outcomes. In multiple imputation, several imputed datasets are generated to reflect the uncertainty about the true, but unobserved value. After imputing missing values in potential outcomes, we could estimate the individual causal effect on the imputed dataset.

I will explore a new class of transition models which could describe the individual causal effect using the imputation models for unobserved potential outcomes. The transition model consists of three components: 1) imputation, 2) causal modeling and aggregation, and 3) analysis and decision-making. With this modular framework, researchers would conveniently perform causal

inference. Moreover, the result of the causal inference could be presented less ambiguously. I expect that novel transition models could be applied to both experimental and observational studies.

On 7 October 2022 Mingyang Cai defended his thesis at the University of Utrecht.

**Supervisors **

Prof. dr. S. van Buuren, dr. G. Vink

**Financed by**

Utrecht University

**Period**

1 August 2018 – 7 October 2022