The Intercensal Method: hacking Healthy Life Expectancy.
A methodological note on estimating healthy life expectancy when you have two cross-sectional snapshots rather than full individual longitudinal histories.
Tracking individuals longitudinally to calculate Healthy Life Expectancy is fantastic if you have infinite time, infinite patience and a population that never moves house. For the rest of us, there is the intercensal method.
The problem
Robust healthy life expectancy models, such as IMaCh, demand multistate longitudinal data. You need to know exactly when someone transitions from healthy to unhealthy and finally to dead. But what if you only have two independent cross-sectional snapshots of a population, such as two censuses or two adjacent waves of a survey?
Michel Guillot and Yan Yu showed that, under reasonable demographic assumptions, you do not necessarily need to follow every individual. You can work with cohort proportions.
The sweet spot: this approach sits between the Sullivan method, which only requires a single cross-section but cannot calculate conditional health expectancies, and full multistate discrete-time models, which offer deeper dynamic insight but require expensive longitudinal panel data.
The maths
The intercensal method uses the exact relationship linking the proportion of healthy individuals at two dates. Here is the core operational equation:
The terms are:
- \(\Pi(x,t)\): 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.
- \({}_{n}q_{x}^{HD}\): the probability of a healthy individual dying.
- \({}_{n}q_{x}^{UH}\): the probability of recovering from unhealthy to healthy.
- \({}_{n}q_{x}\): the overall mortality probability for the cohort.
By solving this non-linear system of equations, we can extract 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, highly accurate age-specific mortality probabilities can be obtained from external life tables, such as those produced by the ONS, and used as inputs for the intercensal framework.
The proposal: the interventional workflow
I do not only want to describe reality. I want to engineer it.
Once we use the intercensal method to recover transition probabilities, \({}_{n}q_{x}^{HU}\) and \({}_{n}q_{x}^{UH}\), between survey waves, we have a functional engine. My proposed interventional workflow goes further by injecting policy modifiers directly into the matrix.
Suppose a public health initiative boosts physical activity. We do not just guess the impact. We apply a relative risk multiplier, \({}_{n}RR_{x}^{HU}\), to suppress the healthy-to-unhealthy transition probability, then regenerate the multistate life table to estimate the impact on Healthy Life Expectancy.
That moves healthy life expectancy away from being solely a static descriptive measure and toward being a dynamic forecasting model.