The Intercensal Method:
Hacking Healthy Life Expectancy

Tracking individuals longitudinally to calculate Healthy Life Expectancy (HLE) is fantastic if you have infinite time, infinite patience, and a populace that never moves house. For the rest of us, there is the intercensal method.

The Problem

Most robust HLE models (like IMaCh) demand greedy multistate longitudinal data. You need to know exactly when John Smith transitioned from 'healthy' to 'unhealthy' and finally to 'dead'. But what if you only have two independent cross-sectional snapshots of a population (say, two censuses, or two adjacent waves of a survey like ELSA)?

Enter Michel Guillot and Yan Yu (2009), who demonstrated that under reasonable demographic assumptions, you do not actually need to follow John Smith. You just need to look at the cohort proportions.

The Math(s)

The intercensal method cleverly exploits the exact relationship linking the proportion of healthy individuals at two dates. Here is the core operational equation:

Where the terms are defined as follows:

• $\Pi(x,t)$: The prevalence of healthy individuals at age $x$ and time $t$.
• $\Pi(x+n, t+n)$: The prevalence of healthy individuals at age $x+n$ and time $t+n$.
• ${}_{n}q_{x}^{HU}$: The probability of transitioning from healthy to unhealthy between age $x$ and $x+n$.
• ${}_{n}q_{x}^{HD}$: The probability of a healthy individual dying between age $x$ and $x+n$.
• ${}_{n}q_{x}^{UH}$: The probability of recovering from unhealthy to healthy between age $x$ and $x+n$.
• ${}_{n}q_{x}$: The overall probability of mortality for the cohort between age $x$ and $x+n$, regardless of health status.

By solving this non-linear system of equations, we can extract the hidden transition probabilities without relying on computationally and financially expensive individual-level tracking.

The Clean Truth: Reducing Data Burden

From a data-burden and governance perspective, this is one of the method's genuine strengths. Because the equation only requires the cohort mortality probability ${}_{n}q_{x}$, not person-level death histories, studies using the intercensal method do not need to observe or share individual mortality data.

Instead, you can obtain highly accurate age-specific mortality probabilities from external life tables (e.g., the ONS). Those are entirely suitable inputs for the intercensal framework.

The Proposal: The Interventional Workflow

But I don't just want to describe reality. I want to engineer it.

Once we use the intercensal method to recover those transition probabilities (${}_{n}q_{x}^{HU}$, ${}_{n}q_{x}^{UH}$) between ELSA Wave 10 and 11, we have a fully functional engine. My proposed Interventional Workflow takes this a step further by injecting policy modifiers directly into the matrix.

We stop calculating HLE solely as a static descriptive measure, and start leveraging it as a dynamic forecasting model.

Essential Reading

• Guillot M, Yu Y. (2009). Estimating health expectancies from two cross-sectional surveys: the intercensal method.