Why am I getting old and fat? Age-period-cohort effects

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The morning after a day spent in London running the CLOSER workshop, Using multiple longitudinal studies for age-period-cohort investigations, I woke feeling happy with how things went but exhausted. Two noisy children and a headache, from the rare occasion I have a few beers, didn’t help. I used to be able to work hard, party harder, and wake up early the next morning, often to play field-hockey (which has now resulted in hip operations and arthritis). Such ageing unfortunately happens to us all and is in many ways irreversible.

As an epidemiologist focusing mainly on childhood growth and development, I am interested in how different biological measures and systems change with age, from conception to maturity and beyond. These are age effects because we are talking about how some measure is related to chronological (and sometimes biological) age. Body mass index (BMI), for example, generally increases from birth to a peak at around six months of age, before decreasing to a nadir called the adiposity rebound at around 5-6 years of age, before increasing again into and throughout most of adulthood.

This is of course the average, crude pattern. There are huge differences between different people and much shorter-term fluctuations occur. The ways in which we apply statistical models to data in order to describe, and explore variation, in this type of age-related trajectory are advanced and rapidly evolving. Anyone wanting to understanding age effects, which naturally requires information on the same person or people measured at different ages (i.e., longitudinal data), will likely be tasked with learning at least the basic methods available to create trajectories during their career. This is the bread and butter of many birth cohort and longitudinal study researchers, and a central theme in life course epidemiology research.

The big assumption when investigating a person’s trajectory is that it is actually being driven by age rather than changes in the environment in which the person lives. I might gain weight after the 29th March 2019 because I am getting older and at an age (35 years) and life stage (married, two kids, full-time job) when weight gain is common. This would be an age effect.

Alternatively, I might gain weight because Brexit, if it happens, causes a recession and a crash in the housing market, leaving us unable to pay our mortgage, so we move to Portugal (my wife is Portuguese) where I always put on weight when we visit. This would be a period effect, which can essentially be thought of as a historical event that occurs at a discrete point in time and impacts on everyone, but not necessarily in the same way or to the same extent. My example is a very specific period effect that won’t apply to many people, but nonetheless it is a period effect.

Say my weight ends up being 5 kg more on the 29 March 2020 compared to the 29 March 2019. Is this because I am one year older or because Brexit occurred? There is no way to know. You would have to decide what the most likely explanation was (age effect, period effect, or some mixture of the two) based on knowledge/theory, circumstances, and perhaps other variables. The problem arises because age and year are perfectly colinear, such that a one-year increase in age corresponds to a one-year increase in year. The same principle applies regardless of whether you are looking at one person or one million people. The only real solution is to have a sample of people who reach different ages at different points in time. Put differently, age and year are no longer perfectly colinear if you have a sample of individuals born at different points in time.

For me, year of birth is one of the single most informative variables we can have. It essentially acts as a proxy for all the known and unknown environmental exposures and conditions that a person experiences across their life. I was born in 1984 and at age 35 years my BMI is around 28 kg/m2, whereas someone born in 1884 might have a BMI closer to 20 kg/m2 at 35 years of age. This is a clearly recognisable cohort effect. Of course, we all know this difference in BMI is due to range of preconception, prenatal, postnatal, and later life exposures and conditions that have changed over time, but birth year encapsulates them all into a single contrast (1984 vs 1884).

If we have data on different birth year cohorts then we can make such contrasts and document changes over time (i.e., secular trends). There is a long history and huge literature on, for example, obesity trends but most of this is based on cross-sectional data. By working with multiple longitudinal studies born at different points in time it is possible to investigate how some age-related process has changed over time in response to shifts in the behavioural, socioeconomic, and political landscape. This could be done by modelling trajectories (age effect) and seeing how they differ according to birth year (cohort effect), as we have done for BMI in the UK birth cohort. With this design, it is also possible to see how a risk factor distribution and its effects on an outcome might have changed over time. A lot of our work, for example, has focused on how the relationship of socioeconomic position with BMI has changed over time (see also). Importantly, this can help understand the extent to which a risk factor could have contributed to the secular trend in the outcome of interest. We have recently, for example, demonstrated that the association of infant weight gain with adolescent BMI has strengthened over time, and that this process explains 23% of the secular increase in BMI at age 11 years between 1957 and 2012. While cross-sectional cohort effects are well documented for many things, cohort effects in longitudinal processes and relationships are largely unknown.

At our workshop last week, we heard from Andrew Bell about the complexity of age, period, and cohort effects and the impossibility of being able to investigate all three in any single analysis. I would tell you more, but you would be better off reading Andy’s forthcoming book on the topic. There were three other fantastic applied talks, plus mine. Liina Mansukoski presented her PhD research on how inequalities in adolescent growth in Guatemala have changed over the second half of the 20th Century. Anamaria Brailean spoke on cohort differences in cognitive ageing in Amsterdam. And Alice Goisis demonstrated how the association of older maternal age (40+) with adverse offspring health has declined over time, largely due to older mothers now having higher socioeconomic background than before. Tom Norris and Silvia Costa also ran a practical in which groups had to draw age-related trajectories for two different birth cohorts, before adding on period effects. The one on probability of full-time employment according to years since PhD perhaps struck the strongest chord with the audience. You can download the slides from all the presentations here.

Gladly, I am not sitting here finishing this blog worried about ageing and all that that ensues. Instead, the workshop reaffirmed my fascination with wanting to investigate/understand what leads to us all being different and how the responsible life course factors and processes are not static in time. By pooling data across multiple longitudinal cohort studies, as many large initiatives and consortia now do, we increase statistical power. But we should also welcome, embrace, and properly explore the variation and heterogeneity created by doing this. If the cohorts are born at different points in time, then consideration of age, period, and cohort effects is clearly important and incredibly interesting, at least to me.


Dr Will Johnson is a Lecturer in Human Biology and Epidemiology at Loughborough University’s School of Sport, Exercise and Health Sciences. You can follow Will on Twitter @W_O_Johnson