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📋 '''Controlled direct effect (CDE)''' is a causal quantity that measures the impact of a treatment or exposure on an outcome when a mediating variable is held fixed at a specified level, rather than allowed to vary naturally. In the insurance context, CDE is particularly relevant when analysts want to understand how a pricing decision, [[Definition:Underwriting | underwriting]] rule, or policyholder characteristic affects [[Definition:Claims | claims]] outcomes through a specific pathway — net of any indirect channels that operate through an intermediate factor. For example, an insurer might ask how a change in [[Definition:Deductible | deductible]] level directly affects [[Definition:Claims frequency | claims frequency]] when the policyholder's risk-taking behavior (a mediator) is held constant at a particular value.

⚙️ Estimating the CDE requires an analyst to specify a [[Definition:Directed acyclic graph (DAG) | directed acyclic graph]] or similar structural model that maps out how variables relate to one another, then intervene — conceptually or statistically — to fix the mediator at a chosen level. In practice, this might involve stratifying the analysis by the mediator's value or using regression adjustment under carefully stated assumptions about confounding. Consider an [[Definition:Insurtech | insurtech]] firm investigating whether a [[Definition:Telematics | telematics]]-based [[Definition:Premium | premium]] discount causally reduces accident severity (the outcome). Driving behavior improvement is a natural mediator: discounts might encourage safer driving, which in turn reduces severity. The CDE isolates the portion of the discount's effect that operates through channels other than driving behavior — perhaps through the type of vehicle a policyholder chooses to insure, or through changes in mileage — by fixing driving behavior at a particular level.

💡 Understanding direct versus indirect causal pathways is far from academic for insurers navigating an increasingly regulated environment around [[Definition:Algorithmic fairness | algorithmic fairness]] and [[Definition:Discrimination | discrimination]]. Regulators in the European Union, the United Kingdom, and several U.S. states are scrutinizing whether [[Definition:Rating factor | rating factors]] such as credit scores or geographic location affect premiums through legitimate risk pathways or through channels that proxy for protected characteristics like race or ethnicity. The CDE gives [[Definition:Actuarial science | actuarial]] teams a formal tool to decompose a variable's total effect into the portion that flows directly to the outcome versus the portion mediated by potentially problematic intermediaries. This decomposition can strengthen [[Definition:Rate filing | rate filing]] justifications, support compliance with anti-discrimination mandates, and inform product design decisions that are both profitable and equitable.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Direct effect]]
* [[Definition:Counterfactual]]
* [[Definition:Directed acyclic graph (DAG)]]
* [[Definition:Algorithmic fairness]]
* [[Definition:Risk classification]]
* [[Definition:Do-calculus]]
{{Div col end}}

Definition:Controlled direct effect (CDE) - Revision history

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