Jonas Schöley
@jschoeley.com
jschoeley.com • Demographer @mpidr.bsky.social
Perinatal Demography • Mortality • Uncertainty • Dataviz
Perinatal Demography • Mortality • Uncertainty • Dataviz
Jim Oeppen showing latitudinal gradient in life expectancy at @hmdatabase.bsky.social symposium in Paris.
October 10, 2025 at 8:41 AM
Jim Oeppen showing latitudinal gradient in life expectancy at @hmdatabase.bsky.social symposium in Paris.
Sigh... another academic project website turned into an advert for online gambling. Give me 90s html not updated in decades over this anyday.
September 11, 2025 at 7:11 AM
Sigh... another academic project website turned into an advert for online gambling. Give me 90s html not updated in decades over this anyday.
Surprisingly, mortality selection only plays a minor role in explaining the rapid drop in the risk of death following birth. Even within relatively homogeneous subgroups, mortality changes rapidly with age, suggesting an intrinsically dangerous transition period following birth.
August 13, 2025 at 8:35 AM
Surprisingly, mortality selection only plays a minor role in explaining the rapid drop in the risk of death following birth. Even within relatively homogeneous subgroups, mortality changes rapidly with age, suggesting an intrinsically dangerous transition period following birth.
I estimated the changing distribution of mortality risk over the first year of life which has a massive right tail, so the average risk of death is a really bad estimator for the typical risk of death at any point in time. Should be enough heterogeneity for mortality selection...
August 13, 2025 at 8:35 AM
I estimated the changing distribution of mortality risk over the first year of life which has a massive right tail, so the average risk of death is a really bad estimator for the typical risk of death at any point in time. Should be enough heterogeneity for mortality selection...
To make this calculation I needed to have a reasonable estimate for the variability of mortality at various stages throughout infancy. So I estimated that using birthweight, APGAR score and gestation at birth as predictors, getting a discrete mixture distribution over >200 strata.
August 13, 2025 at 8:35 AM
To make this calculation I needed to have a reasonable estimate for the variability of mortality at various stages throughout infancy. So I estimated that using birthweight, APGAR score and gestation at birth as predictors, getting a discrete mixture distribution over >200 strata.
In my neonatal mortality paper I applied the Vaupel-Zhang equality to quantify how much the apparent change in the risk of death over the first days of life is merely mortality selection, and how much is due to actual changing risks in population subgroups.
August 13, 2025 at 8:35 AM
In my neonatal mortality paper I applied the Vaupel-Zhang equality to quantify how much the apparent change in the risk of death over the first days of life is merely mortality selection, and how much is due to actual changing risks in population subgroups.
The left side of the equation is how steeply the risk of death changes at age x for the whole population. It is equal to the average individual level change in the risk of death at that age minus the heterogeneity/variance of the risks of death across the population at that age.
August 13, 2025 at 8:35 AM
The left side of the equation is how steeply the risk of death changes at age x for the whole population. It is equal to the average individual level change in the risk of death at that age minus the heterogeneity/variance of the risks of death across the population at that age.
Why is that? Mortality selection. Those with a higher innate risk of death tend to die earlier, leaving those with a lower risk in the population. Over time, due to this selection, the average risk of death in a population declines, even without individual level decline.
August 13, 2025 at 8:35 AM
Why is that? Mortality selection. Those with a higher innate risk of death tend to die earlier, leaving those with a lower risk in the population. Over time, due to this selection, the average risk of death in a population declines, even without individual level decline.
The Vaupel-Zhang equality proves that we will observe a declining risk of death over infancy, even if individual risks do not change by age, as long as individuals differ in their risk of death. Jim called this "Heterogeneities Ruses".
August 13, 2025 at 8:35 AM
The Vaupel-Zhang equality proves that we will observe a declining risk of death over infancy, even if individual risks do not change by age, as long as individuals differ in their risk of death. Jim called this "Heterogeneities Ruses".
Think about infants during the first year of life. Their risk of death is highest at the day of birth, but rapidly falling afterwards. Question is: Is that only true in a statistical sense for the whole population or is it, true for individual infants as well?
August 13, 2025 at 8:35 AM
Think about infants during the first year of life. Their risk of death is highest at the day of birth, but rapidly falling afterwards. Question is: Is that only true in a statistical sense for the whole population or is it, true for individual infants as well?
In statistical parlance, it's a result about the relationship between the hazard function of a mixture distribution over the positive reals, and the hazards of the mixture components. I've re-derived it in that statistical sense in the paper: www.demographic-research.org/volumes/vol5...
August 13, 2025 at 8:35 AM
In statistical parlance, it's a result about the relationship between the hazard function of a mixture distribution over the positive reals, and the hazards of the mixture components. I've re-derived it in that statistical sense in the paper: www.demographic-research.org/volumes/vol5...
The Vaupel-Zhang equality features in my recent publication on mortality selection and convergence in neonatal mortality. JimV mentioned that he'd like this equation inscribed on his tombstone. It's a super general consequence of unobserved heterogeneous mortality, his speciality. Let me show you:
August 13, 2025 at 8:35 AM
The Vaupel-Zhang equality features in my recent publication on mortality selection and convergence in neonatal mortality. JimV mentioned that he'd like this equation inscribed on his tombstone. It's a super general consequence of unobserved heterogeneous mortality, his speciality. Let me show you:
You're right. On a gestational age scale we see a continuos exponential increase in the risk of death from post- to pre-natality. This does not extrapolate to conception though. @jnobles.bsky.social knows about the very early part. epc2024.eaps.nl/uploads/241135
August 5, 2025 at 10:53 AM
You're right. On a gestational age scale we see a continuos exponential increase in the risk of death from post- to pre-natality. This does not extrapolate to conception though. @jnobles.bsky.social knows about the very early part. epc2024.eaps.nl/uploads/241135
Taylor's law holds for heterogeneity in the risk of neonatal death.
As the average death rate in a cohort of newborns declines over the first month of life, the variance of death rates declines as well in a power-law fashion. Read more in my piece on post-natal mortality selection and convergence.
As the average death rate in a cohort of newborns declines over the first month of life, the variance of death rates declines as well in a power-law fashion. Read more in my piece on post-natal mortality selection and convergence.
August 5, 2025 at 10:48 AM
Taylor's law holds for heterogeneity in the risk of neonatal death.
As the average death rate in a cohort of newborns declines over the first month of life, the variance of death rates declines as well in a power-law fashion. Read more in my piece on post-natal mortality selection and convergence.
As the average death rate in a cohort of newborns declines over the first month of life, the variance of death rates declines as well in a power-law fashion. Read more in my piece on post-natal mortality selection and convergence.
Kitagawa's decomposition uses the product rule for finite differences. Thus it applies to every demographic statistic expressible as a difference of weighted sums. Below, I use it to decompose changes in the variance of mortality rates into mortality selection and convergence components.
August 5, 2025 at 10:31 AM
Kitagawa's decomposition uses the product rule for finite differences. Thus it applies to every demographic statistic expressible as a difference of weighted sums. Below, I use it to decompose changes in the variance of mortality rates into mortality selection and convergence components.
Average mortality rates are a horrible measure of typical mortality during the first weeks of life. On the day of birth modal mortality is 189 times lower than average mortality. Read more in my recent piece on selection in neonatal mortality.
August 4, 2025 at 11:57 AM
Average mortality rates are a horrible measure of typical mortality during the first weeks of life. On the day of birth modal mortality is 189 times lower than average mortality. Read more in my recent piece on selection in neonatal mortality.
In this piece in honour of Jim Vaupel I pull the veil from hidden heterogeneity. I show how the observed distribution of frailties changes in a cohort of newborns over the first month of life and quantify mortality selection and its impact on the age pattern of neonate mortality. Fully reproducible.
August 1, 2025 at 11:49 AM
In this piece in honour of Jim Vaupel I pull the veil from hidden heterogeneity. I show how the observed distribution of frailties changes in a cohort of newborns over the first month of life and quantify mortality selection and its impact on the age pattern of neonate mortality. Fully reproducible.
All of this discrete modeling on time series of counts can also be expressed in the continuous language of survival analysis. The distribution of the observed lifetimes is then a convolution of the distribution of expected lifetimes with a distribution of displacement times.
July 3, 2025 at 9:41 AM
All of this discrete modeling on time series of counts can also be expressed in the continuous language of survival analysis. The distribution of the observed lifetimes is then a convolution of the distribution of expected lifetimes with a distribution of displacement times.
A single slice of the time-varying distribution of displacement times allows for some relevant inference on the life-time lost of those who died at that time.
July 3, 2025 at 9:41 AM
A single slice of the time-varying distribution of displacement times allows for some relevant inference on the life-time lost of those who died at that time.
The displacement matrix can be transformed into a time-varying distribution of displacement times.
July 3, 2025 at 9:41 AM
The displacement matrix can be transformed into a time-varying distribution of displacement times.
I use a simple heuristic to estimate the displacement matrix whereby I proportionally distribute all deficit to the excess time points. Other and better solutions are possible. The resulting model is one, where the observed deaths are expressed as expected deaths re-shuffled in time.
July 3, 2025 at 9:41 AM
I use a simple heuristic to estimate the displacement matrix whereby I proportionally distribute all deficit to the excess time points. Other and better solutions are possible. The resulting model is one, where the observed deaths are expressed as expected deaths re-shuffled in time.
Excess death modeling suggests a huge excess during the heatwave followed by a persistent moderate death deficit in the following fall and winter.
July 3, 2025 at 9:41 AM
Excess death modeling suggests a huge excess during the heatwave followed by a persistent moderate death deficit in the following fall and winter.
I apply the method to time series of daily French deaths following the 2003 European heatwave (data by @rchung.bsky.social).
July 3, 2025 at 9:41 AM
I apply the method to time series of daily French deaths following the 2003 European heatwave (data by @rchung.bsky.social).