No effect of additional education on long-term brain structure – a preregistered natural experiment in thousands of individuals

Education is related to a wide variety of beneficial health, behavioral, and societal outcomes. However, whether education causes long-term structural changes in the brain remains unclear. A pressing challenge is that individuals self-select into continued education, thereby introducing a wide variety of environmental and genetic confounders. Fortunately, natural experiments allow us to isolate the causal impact of increased education from individual (and societal) characteristics. Here, we exploit a policy change in the UK (the 1972 ROSLA act) that increased the amount of mandatory schooling from 15 to 16 years of age to study the impact of education on long-term structural brain outcomes in a large (n∼30.000, UK Biobank) sample. Using regression discontinuity – a causal inference method – we find no evidence of an effect from an additional year of education on any structural neuroimaging outcomes. This null result is robust across modalities, regions, and analysis strategies. An additional year of education is a substantial cognitive intervention, yet we find no evidence for sustained experience-dependent plasticity. Our results provide a challenge for prominent accounts of cognitive or ‘brain reserve’ theories which identify education as a major protective factor to lessen adverse aging effects. Our preregistered findings are one of the first implementations of regression discontinuity on neural data – opening the door for causal inference in population-based neuroimaging.


Introduc,on
Access to educa7on is codified as a fundamental human right with immense societal and economic benefits 1,2 .Individuals who experience more educa7on tend to show a wide variety of beneficial health, cogni7ve, and neural outcomes 3 .Correla7onal evidence across disparate contexts, countries, and demographics offers overwhelming support for these findings [4][5][6][7][8][9][10] .
Yet, strong causal evidence for the effect of educa7on on brain structure does not yet exist.Both ethical and prac7cal constraints mean that the effect of educa7on cannot be experimentally tested.This makes it unclear if any findings from educa7on are causal, or if instead, they reflect a complex web of preexis7ng, or amplifying, sociodemographic and individual characteris7cs 3,25 -many of which have been associated with brain structure (e.g., intelligence 26 , parental income 27 , neighborhood pollu7on 28 ).Among the plethora of environmental factors, there is also a substan7al (~40% heritability) gene7c component implicated in educa7onal a:ainment, further confounding poten7al effects 29,30 .In addi7on, access to higher educa7on involves substan7al selec7on processes at the level of the individual and educa7onal system which further complicate the causal pathways involved.One solu7on to this problem is using a natural experiment -a 'random-like' (exogenous) external event -allowing causal inference in observa7onal phenomena 31,32 .A crucial feature of this design is an assignment mechanism outside a par7cipant's control, usually of natural (e.g., geographical, weather events) or governmental (e.g., policy decisions, cutoff rules) origin.For instance, a law that increases the number of mandatory school years affects everyone equally, in turn, decoupling individual characteris7cs and other unmeasured confounders from the effects of addi7onal educa7on 33 .One of the most widely used causal inference analysis techniques is regression discon7nuity (RD), which is applicable when treatment is assigned via a cutoff of a par7cular score or running variable 31,32 .Recent advances in the field of econometrics have op7mized inference and largely standardized regression discon7nuity (RD) analysis 32,[34][35][36] .These methods have provided robust evidence that addi7onal educa7on causes an increase in intelligence (0.14 -0.35 SD) 12 .Despite the many strengths and poten7al causal insights natural experiments offer the field of cogni7ve neuroscience they have not been used to address such ques7ons.
On September 1 st 1972, the minimum mandatory age to leave school was raised from 15 to 16 years of age in England, Scotland, and Wales (called here 'ROSLA') 37 .The consequence of this law change was substan7al: it resulted in almost 100% of children aged 15 staying in school for an addi7onal year, in turn, increasing formal qualifica7ons, income, and cogni7on [38][39][40][41][42][43] .However, whether this substan7al interven7on also affected the long-term brain structure of those born right around the cut-off remains an open ques7on.This is unfortunate, as regression discon7nuity is a powerful tool to study phenomena that cannot (ethically or prac7cally) be randomized.Recent developments of increased large popula7on-based neuroimaging cohorts provide the sample size needed to make use of these cross-disciplinary methods.One such cohort, the UK BioBank, has recruitment criteria matching the geographic and birth window of the natural experiment ROSLA 44 .This provides the ideal opportunity to test, for the first 7me, the causal effect of a year of educa7on on long-term structural neuroimaging proper7es.
Using a preregistered design (h:ps://osf.io/rv38z/)with over 30,000 par7cipants we evaluate if an addi7onal year of educa7on, as mandated by ROSLA, causes changes in six global neural proper7es (total surface area, average cor7cal thickness, normalized total brain volume, mean weighted frac7onal anisotropy, white ma:er hyperintensi7es, and normalized cerebral spinal fluid volume) as compared to individuals born before the cut-off.It is also possible an effect from educa7on could manifest only in specific regions, in the absence of a broad, macro-neural effects.For this reason, we further tested 66 individual cor7cal regions for surface area and cor7cal thickness, 27 white ma:er fiber tracks for frac7onal anisotropy, and subcor7cal gray ma:er volume in 18 regions.Taken together, the combina7on of culng-edge quan7ta7ve methods, a large sample, a well-validated natural experiment and high-quality imaging allows us to examine, for the first 7me, if an addi7onal year of educa7on causes long-term structural reorganiza7on in the brain.

Results
To test if an addi7onal year of educa7on causes long-las7ng changes in neural proper7es we used fuzzy local-linear regression discon7nuity (RD) 34,35 .This con7nuity-based technique exploits the fact that ROSLA affected individuals based on a date of birth cutoff (September 1 st , 1957).More specifically, adolescents born aner this date had to spend one more year in school than those born only one day earlier.Local-linear RD analysis tests this by comparing the limits of two non-parametric func7ons, one fit using only par7cipants right before the policy change to another func7on fit on par7cipants right aner 32 .If an addi7onal year of educa7on affects neural outcomes, we assume that brain structure will be discon1nuous exactly at the cutoff.In contrast, if ROSLA does not affect long-term neural outcomes the func7ons should be con1nuous, or smooth around the cutoff.
Using fuzzy local-linear RD we fit a series of regressions to various measures of brain structure (Fig 1) to test for any discon7nuity at the cutoff.To determine the op7mal number of par7cipants to include, we use mean square error op7mized bandwidths to a maximal range of 10 years before and aner the cutoff (N > 30,000).Doing so, we observed no evidence of an effect from addi7onal educa7on on any of our preregistered global neuroimaging measures (p's > .05;Sup.Table 2).In other words, the rela7onship between the year of birth and neural outcomes was con1nuous around ROSLA's cutoff, indica7ng no differences in global structural measures from an extra year of educa7on.The op7mized bandwidths used in this analysis included par7cipants born 20 to 35 months around the cutoff (average N = 5124).The absence of a causal effect of educa7on was observed for all our global neuroimaging metrics: total surface area (SA), average cor7cal thickness (CT), normalized total brain volume (TBV), mean weighted frac7onal anisotropy (wFA), white ma:er hyperintensi7es (WMh), or normalized cerebral spinal fluid volume (CSF) (Figure 1; Sup.Fig. 3).These results did not change when impu7ng missing (~4%) covariate data.These findings strongly suggest that an addi7onal year of educa7on did not lead to changes detectable by MRI decades later.However, to ensure the validity of our (causal) inferences, a cri7cal step in any regression discon7nuity approach is to test the validity of the design 32 .For instance, if par7cipants can manipulate their treatment by sor7ng around the cutoff this severely limits the strength of causal claims.In the context of ROSLA, this is highly unlikely since the assignment was based on date of birth 37,45 .However, for completeness we tested this ques7on 46 , finding no evidence that individuals were somehow able to adjust their enrollment (Tq = -0.72,p = .47;Sup.Fig. 2).A second valida7on approach is to employ placebo outcome tests 32 .This approach uses variables that should not be causally related to your treatment (e.g., an addi7onal year of educa7on), to ensure the absence of spurious effects arising through unknown mechanisms.To accomplish this, we used all of our neuroimaging covariates (e.g., sex, head mo7on, site) as placebo outcomes, under the assump7on that ROSLA should not affect these variables.Other than one covariate (summer) which was determinis7cally related to ROSLA (therefore excluded), none of the placebo outcomes were related to ROSLA (Sup.Table 1).Our findings add to the exis7ng body of prior work 38,40,41,43 further solidifying ROSLA as a valid natural experiment.and d) weighted frac,onal anisotropy plo>ed by the par,cipant's date of birth in months (our running variable).Each dot reflects the average value for individuals born in that month.The dashed line corresponds to Sept. 1957 the date of birth inclusion cutoff for an addi,onal year of mandatory educa,on from ROSLA.We found no evidence of an effect from an addi,onal year of educa,on on any structural neuroimaging measures -illustrated here by a con,nuous line around the cutoff.Dark blue dots represent all individuals within the mean-squared error-op,mized bandwidths, in turn, reflec,ng par,cipants used for analysis with a local-linear fuzzy RD approach.Third-order polynomials (dark red lines) are fit on either side of the cutoff only for illustra,on purposes.Sup.Fig. 3 illustrates the two other preregistered global neuroimaging outcomes (total white ma>er hyperintensi,es and cerebral spinal fluid volume).
Next, we tested whether there may be any regionally specific neuroimaging effects.It is possible that an addi7onal year of educa7on caused localized neural changes that are not picked up globally.As preregistered, we used the Desikan-Killiany cor7cal atlas 47 to test the effect of an addi7onal year of educa7on on 33 bilateral regions for both cor7cal thickness (CT) and surface area (SA).These analyses included on average 5080 effec7ve par7cipants (N range = 3884 -7771) for CT and 5392 par7cipants (N range = 3739 -8727) for SA.Despite these rela7vely high par7cipant numbers, we did not find an addi7onal year of educa7on to cause changes in any regions for CT or SA (p'sFDR > .05).This was also the case for weighted mean frac7onal anisotropy in all 27 tracks tested 48 (p'sFDR > .05;mean n = 4766).Lastly, we tested the volume of 18 subcor7cal regions, finding none to be related to an addi7onal year of educa7on (p'sFDR > .05,mean n = 5174).To summarize, there was no evidence of an addi7onal year of educa7on affec7ng any regional neuroimaging measures with fuzzy local-linear regression discon7nuity (Sup.Figure 4).

Bayesian Local Randomiza1on Robustness Analysis
As an addi7onal preregistered robustness test, we used a slightly different approach, onen referred to as 'local randomiza7on', to analyze natural experiments.This approach works under the assump7on that individuals close to the cutoff are exchangeable and similar except for the treatment (in our case an addi7onal year of school) 32,49 .To implement this analysis, we compared par7cipants born exactly right before the cutoff (August 1957; n ≈ 130) to those born right aner the cutoff (September 1957; n ≈ 100).An addi7onal benefit is that we implemented this analysis in a Bayesian framework, allowing us to more readily interpret the strength of evidence either in favor of the null or alterna7ve hypothesis.Our preregistered default point null Bayes factors were too wide, arguably providing rela7vely strong evidence in favor of the null.Taking a more conserva7ve approach, we report these analyses with a narrower normal prior (mean=0, sd=1).Doing so, we replicated and extended our findings from fuzzy local-linear RD analysis, observing strong evidence in favor of the null hypothesis for total surface area (BF01 = 18.21), average cor7cal thickness (BF01 = 15.09),total brain volume (BF01 = 13.61),weighted frac7onal anisotropy (BF01 = 11.63),white ma:er hyperintensi7es (BF01 = 13.26), and cerebral spinal fluid volume (BF01 = 14.50).In addi7on, we tested across a range of priors which did not meaningfully affect our inferences, as each showed evidence in favor of the null (Sup.Table 4 &  6).
The two quan7ta7ve RD approaches described here (local-linear and local randomiza7on) have strengths and challenges similar to the widespread bias versus variance tradeoff.As the number of months on either side of the cutoff increases, bias is introduced as par7cipants become less similar, yet at the same 7me, the sample size increases, thereby lowering the variance of the es7mate.Our local randomiza7on approach runs a negligible risk of bias, but at the cost of a rela7vely modest sample size: One could argue the 230 par7cipants included in our 1-month window are too few for neuroimaging outcomes.To examine the consequences of this tradeoff, we therefore expanded the boundary to a 5-month window around September 1 st , 1957 (n per group ≈ 600).This larger par7cipant pool provided further evidence in support of the null hypothesis of educa7on not affec7ng global neural measures (Figure 2 & 3, Sup.Table 6).Lastly, we repeated our placebo outcome tests for both a one-and five-month window local randomiza7on analysis, finding no associa7ons (Sup Table 5 & 7), demonstra7ng the robustness of the natural experiment ROSLA and our analysis approach.
Figure 2 Bayes factors for surface area per region using a local randomiza,on analysis with a 5-month window around the onset of ROSLA (September 1st, 1957).Illustra,ng widespread evidence against the effect of a year of educa,on on total surface area.The regionally specific analysis of these bayes factors [reported prior: normal(0, 1)] was not preregistered and serves to illustrate our global neural findings.

Correla1onal Effect of Educa1on
The above analyses employed an RD design allowing us to inves7gate the hypothesized causal effect of (addi7onal) educa7on on differences in brain structure independent of confounding pathways.To ensure our sample is at least in principle sensi7ve to observing brain-behavior associa7ons (cf. 50), we reran the analysis as a simple associa7on instead.This allows us to examine whether more years of educa7on are associated with differences in brain structure.Notably, such an observa7onal analysis (and resul7ng parameter es7mate) would reflect an indeterminate mixture of causal effects as well as any indirect, sociodemographic, and individual pathways.These associa7ons would s7ll be of considerable poten7al scien7fic interest, but could not be interpreted as causal effects of educa7on on brain structure.Crucially, this was done using the same subset of par7cipants as in the local randomiza7on analysis.Resul7ng in an es7mate of how much one addi7onal year of educa7on correlates with brain structure.
First, we es7mated the associa7on between educa7on (in years of a:ainment) and global neuroimaging measures using the same sample of par7cipants from the one-month window local randomiza7on analysis (i.e., August & September 1957; n ~ 230).Similar to the causal approach, five of the six measures showed evidence in support of the null hypothesis (Sup.Table 4).In contrast, total surface area showed weak evidence in support of a posi7ve associa7on of educa7on (BF10 = 2.3, n = 229).To increase power, we expanded our observa7onal analysis to par7cipants born in a five-month window around the ROSLA cutoff (Fig. 3).This considerably increased the strength of evidence in support of a posi7ve associa7on between years of educa7on and total surface area (BF10 = 41.7,N = 1185).In addi7on, the larger pool of par7cipants provided extreme evidence in support of an associa7on between years of educa7on and cerebral spinal fluid volume (BF10 = 80.7, n = 1193).This analysis highlights the stark difference between a causal and associa7onal approach, while also providing evidence of sensi7vity to brain-behavioral associa7ons in the same sample.Of the remaining four global measures, three meaningful decreased in their strength of evidence (in terms of Jeffrey criteria 51 ) in favor of the null when compared to the causal es7mate (Fig. 3; Sup.Table 6).The only global neuroimaging measure that provided a similar amount of evidence (in favor of the null) between a causal and correla7ve approach was mean cor7cal thickness (BF01 = 7.22 & BF01 = 8.81 respec7vely).

Discussion
In a large, preregistered study we find converging evidence against a causal effect of educa7on on long-term structural neuroimaging outcomes.This null result is present across imaging modali7es, different regions, and analysis strategies.We find no issues with the design of the 1972 ROSLA, substan7a7ng it as a valid natural experiment, in agreement with prior work 38,40- 43 .Despite a large sample (min N = 4238), we find no evidence of an effect of educa7on on any of the global neuroimaging measures with a con7nuity-based RD analysis.Confirming this result, we find strong evidence in support of the null hypothesis for these global neuroimaging measures using a Bayesian local randomiza7on analysis.Moreover, we find no regionally specific effect of educa7on on local mean cor7cal thicknesses or surface area across 66 cor7cal regions.This lack of localized effects was further confirmed in weighted mean frac7onal anisotropy for 27 white ma:er tracks, as well as subcor7cal gray ma:er volume in 18 regions.Moreover, we demonstrate the ability to find strong evidence in favor of observa7onal associa7ons between educa7on and brain structure at this resolu7on, sugges7ng our findings are not due to lack of sensi7vity more generally.
Our robust null result is seemingly at odds with causal inference findings of educa7on's posi7ve behavioral effect on intelligence 11,14,39 -which is sustained throughout decades 12,38 .This juxtaposi7on suggests that, to the extent that the addi7onal year of educa7on induced longterm changes in cogni7ve abili7es, the neural manifesta7on is at a level of resolu7on not detectable with conven7onal MRI field strengths.However, this would seem to contrast with a range of influen7al findings demonstra7ng that high-intensity experimental behavioral interven7ons (e.g.juggling, studying, memory training) lead to measurable differences in brain structure (with similar imaging pipelines) in much smaller samples [52][53][54] .Moreover, compared to even these high-intensity interven7ons, a year of educa7on is an extensive period of learning.The 1972 ROSLA was well implemented, schools had 7me to prepare and were given addi7onal funding, increasing standardized formal qualifica7ons of those affected 41,42 .This leaves open the ques7on of how to interpret this constella7on of findings.
One poten7al explana7on to account for this discrepancy is the concept of expansion-renormaliza1on 55,56 , which posits following a period of skill acquisi7on, the cortex ini7ally expands and then renormalizes over the course of a few months.In our context, this would suggest that the addi7onal year would have manifested at a level detectable in MRI when the difference in educa7onal exposure between children pre-and post-ROSLA was most pronounced and recent.In other words, MRI effects at the macro-scale might have been detectable immediately post-ROSLA in 16-year-old adolescents, before renormalizing, to a micro-scale, leaving in place permanent, but microstructural changes.Possible cellular candidates for ini7al experience-dependent plas7city are an increase in dendri7c spines, the swelling of astrocytes, and intracor7cal myelin adapta7ons 57,58 .These structural changes may be detectable using other approaches such as in vivo cellular work (cf. 59), extreme high field strengths 56,60 , or postmortem histology 61,62 .
Addi7onally, the long period of 7me between addi7onal educa7on and neuroimaging offers both strengths and weaknesses for our design.First, it could be the case that 46 years is too long and any poten7al effect faded out over the years.That is, rather than having a micro-neural effect, it may be that there simply are no lingering effects at the brain level at all.In this case, it may be be:er to think of the (causal) impact of addi7onal educa7on as more akin to fitness or strength interven7ons which are also unlikely to persist across such a period.However, we note that prominent aging-related theories of heterogeneity argue directly against this ra7onale, instead posi7ng life course experiences offer a reserve or 'brain buffer' that leads to an increasing cascade of processes limi7ng adverse aging effects [15][16][17] .Here, the 7ming between our interven7on (ROSLA) and scanning makes our design par7cularly well-powered to test these theories, since educa7on would contribute to an ini7al brain buffer (intercept) and any cumula7ve educa7onal effect (slope) over 46 years.While our results are at odds with prior conceptual and observa7onal work, a recent longitudinal study found prior educa7on to not affect the rate of brain aging 63 -in alignment with our findings.
Lastly, to demonstrate the importance of controlling for unobserved confounders we conducted a simple correla7on analysis -using the same subset of par7cipants -rela7ng educa7on to differences in brain structure.We found evidence to support an associa1on between more years of educa7on and greater surface area and cerebral spinal fluid volume.This result emphasizes the need for cau7on in a:ribu7ng causa7on in non-causal designs, as unobserved confounders can masquerade as an effect of interest.For instance, more educa7on is frequently highlighted as offering behavioral and neural protec7on against the adverse effects of aging [15][16][17] -while we replicate this inference associa7onally, we find no causal evidence for any neuroprotec7ve effects.This suggests a more complex pathway of effects unfolding over 7me.Environmental causes are most likely very small and addi7ve, which makes them not only difficult to study 64 but also equally hard to adequately control 65 .Our findings suggest that to truly understand the neural and behavioral processes that unfold aner interven7ons such as educa7on we need a mul7pronged, mixed methods approach that combines deep phenotyping, longitudinal imaging and behavioral follow-up [66][67][68] , as well as more sophis7cated models that can capture gene-by-environment-interplay 14,64,69 .Only then will we be able to iden7fy idiosyncra7c environmental effects and individual characteris7cs underlying heterogenous lifespan development.
Here, we report a lack of causal evidence of a year of school on long-term neural outcomes in thousands of par7cipants.An addi7onal year of educa7on is a substan7al interven7on and our preregistered findings are robust across imaging modali7es, different regions, and analysis strategies.While our design cannot inform us of any short-term neural effects of educa7on, our results call into ques7on sustained experience-dependent plas7city, with significant ramifica7ons for prominent theories of aging-related heterogeneity.The recent availability of large neuroimaging cohort data paired with culng-edge methods from econometrics offers new avenues in studying neural effects.Causal inference is a new tool to the neuroimager's toolkit -opening novel, societally relevant phenomena -with the poten7al to move the field of popula7on neuroscience from one of associa1on to one of causa1on.

Methods
On September 1 st , 1972 the minimum age to leave school was increased from 15 years of age to 16 in England, Scotland, and Wales 37 .This law, henceforth ROSLA, mandated children born aner September 1 st , 1957 to stay in school for an addi7onal year.In contrast, a child born only one day earlier was unaffected and legally allowed to stop formal schooling at 15 years of age.The consequence of this law change was substan7al: it resulted in almost 100% of children aged 15 staying in school for an addi7onal year, in turn, increasing formal qualifica7ons (Sup.Fig 2) 40,41 .1][42] ) high design validity.A sizable body of prior work has found behavioral effects from the 1972 ROSLA 38,[40][41][42][43] .
In this study, we leverage ROSLA to study the causal effect of an addi7onal year of educa7on on the brain.To do so, we will use the neuroimaging sub-sample of the UK BioBank -the largest neuroimaging study to date -which also lines up perfectly with geographic and birth window (~1935-1971) requirement characteris7cs for ROSLA 70 .We followed our preregistra7on (h:ps://osf.io/rv38z)closely, yet some minor devia7ons were necessary and explicitly outlined in 'devia1ons from preregistra1on' (code: h:ps://github.com/njudd/eduBrain).

Structural neuroimaging outcomes
It is very plausible that a broad interven7on like educa7on could affect the brain in either a global, or more regionally specific manner.For this reason, we examined both whole-brain averaged measures in addi7on to regional specificity in atlas-based regions and tracts.We tested the following global measures; total surface area (SA), average cor7cal thickness (CT), total brain volume normalized for head size (TBV), mean weighted frac7onal anisotropy (wFA), white ma:er hyperintensi7es (WMh), and cerebral spinal fluid volume normalized for head size (CSF).Next, we examined cor7cal thickness (CT) and surface area (SA) regionally using the Desikan-Killiany Atlas 47 .The temporal pole was not included by the UK BioBank making the total number of regions 66.We will also test weighted mean frac7onal anisotropy (wFA) with a global average and, regionally on 27 white ma:er tracks 48 .Lastly, we examine subcor7cal volume in 18 regions 71 .
All measures are derived from the image preprocessing pipeline from the UKB, further preprocessing details are outlined elsewhere 44,72 .All outliers were iden7fied if they were either above quar7le 3 plus 1.5 7mes the interquar7le range (IQR) or below quar7le 1 minus 1.5 7mes the IQR and brought to the fence by manually recoding them to this limit (Tukey/Boxplot Method).Our alpha level for global neuroimaging measures (mean CT, total SA, average FA, WM hyper-intensi7es, normalized TBV & normalized CSF) is 0.05.The regional metrics (SA, CT, wFA & subcor7cal structures) are false discovery rate (FDR) corrected using the number of regions per modality (e.g., 66 regions for SA) with a q value less than 0.05 considered significant.Neuroimaging measures are reported in raw units.

Con1nuity-based framework: Local-linear fuzzy regression discon1nuity
Regression discon7nuity (RD) is a technique we use to es7mate the effect of an interven7on on an outcome where assignment (usually binary) is based on a cutoff of a running or 'forcing' variable 31,32 -in our case, age in months.One major design issue in RD is if par7cipants select into (or out of) the treatment group by sor7ng around to the cutoff of the running variable.However, as the 1972 ROSLA law was not pre-announced, generally strictly enforced, and affected teenagers, such alterna7ve explana7ons are highly improbable 45 .Nevertheless, we conducted a density test of the running variable to check for bunching near the cutoff 46 .Although the design validity of the 1972 ROSLA is well established 38,[40][41][42][43] we s7ll tested a variety of placebo outcomes (outlined in 'covariates of no interest') -outcomes implausible to be affected by the interven7on.
RD analysis broadly falls into two separate but complementary frameworks 36,49 .The first, con7nuity-based approach defines the es7mand as the difference between the limits of two con7nuous non-parametric func7ons: one fit using only par7cipants right before the policy change to another func7on fit on par7cipants right aner.The other, so-called local randomiza1on approaches assume par7cipants are 'as if random' in a small window () around the cutoff (described more in detail in the sec7on "Bayesian Local Randomiza7on analysis").In this case, the es7mand is the mean group difference between par7cipants before and aner the cutoff within .As  approaches zero around the cutoff, the es7mand becomes conceptually more similar to con7nuity-based approaches.
To empirically test whether an addi7onal year of educa7on caused long-las7ng global and regional neural changes we used a fuzzy local linear regression discon7nuity design (a con7nuity-based approach) with robust confidence intervals from the RDHonest package 31,34,35 .Our outcome variables are the neuroimaging metrics described above, which were adjusted to increase sta7s7cal precision (see sec7on 'covariates of no interest').The running variable (X) is a par7cipant's date of birth in months (mDOB), as is conven7on, it was centered at zero around the birth cutoff of ROSLA (September 1 st , 1957).Our first-stage (fuzzy) outcome was a dummy coded variable of whether the par7cipant completed at least 16 years of educa7on.Par7cipants who indicated they completed college were not asked this ques7on, therefore we recorded their response as 21 years 38 .Our choice of using the RDHonest package was primarily due to its ability to provide accurate inference with discrete running variables (in our case mDOB).We used the default selngs of local-linear analysis on MSE-derived bandwidths with triangular kernels 34,35 .
We included par7cipants born in England, Scotland, or Wales 10 years on either side of the September 1 st , 1957 cutoff (dob Sept. 1 st , 1947 -Aug 31 st , 1967) with neuroimaging data.The range of the running variable (age in our case) to include on either side of the cutoff (known as the bandwidth; z) is one of the most consequen7al analy7cal decisions in regression discon7nuity designs.Prior work using ROSLA in the UK BioBank has analyzed bandwidths as large as 10 years 43 to as small as a year 38 .Large bandwidths include more par7cipants (decreasing variance) yet these par7cipants are also further away from the cutoff, in turn, poten7ally increasing bias in the es7mand 36,49 .Conversely, smaller bandwidths provide a less biased, yet noisier es7mates.State-of-the-art con7nuity-based RD methods use data-driven bandwidth es7ma7on such as mean squared error (MSE) op7mized bandwidths 73 .Since we used this approach the op7mal bandwidth range and, in turn, the number of included par7cipants, will differ per fi:ed model.This also makes it logically incompa7ble to sensi7vity test our bandwidths 36 , since they are mean squared error derived -widening them will lower variance and, in turn, increase bias while 7ghtening them will have the opposite effect.Lastly, the use of triangular kernels means par7cipants further away from the cutoff will be weighted less than those closer 36 .Both MSE-op7mized bandwidths and triangular kernels determine the number of 'effec7ve observa7ons' to be fit by a fuzzy local linear RD model.
For our global con7nuity-based analysis we made sure the results did not change due to missing covariate data.This was accomplished by impu7ng missing covariate data (≈4%) with classifica7on and regression trees from the MICE package 74 .We imputed using informa7on from only the variables included in each analysis and did not use the running variable (DOB in months) or our first-stage instrument for predic7on.We did this ten 7mes checking the es7mates and inferences across each itera7on to ensure robustness.

Bayesian Local Randomiza1on Analysis
As a robustness test and to provide evidence for the null hypothesis, we conducted a Bayesian analysis using the local randomiza7on framework for RD 32 .This alterna7ve framework assumes a small window () around the cutoff (c) where the running variable is treated "as if random" 49 .While the local randomiza7on framework invokes stricter assump7ons on the assignment mechanism, placing more importance on the window around the cutoff ( = [c − w, c + w]) it handles discrete running variables well 49 .As the number of months on either side of the cut-off increases, bias is introduced as subjects become less similar, yet at the same 7me, the sample size increases, thereby lowering the variance of the es7mate.
As recommended 32,49 , we included par7cipants within the smallest window possible ( = 1 month; August vs September 1957), then expanded to a 5-month window around September 1 st , 1957.A dummy variable (ROSLA) was constructed to reflect if a par7cipant was impacted by the policy change.We then tested the effect of this variable on our six global neuroimaging measures while correc7ng for the covariates listed above.A few neuroimaging covariates did not have sufficient observa7ons to be included (see 'devia7ons from preregistra7on').Models were fit in R (v. 4.3.2) with rstanarm with Markov Chain Monte Carlo sampling of 80,000 itera7ons over 4 chains 75 .All priors (p) used a normal distribu7on centered at 0 with autoscaling [p*sd(y)/sd(x)].Our preregistra7on referred to using the 'default' weakly informa7ve prior of STAN (i.e., 2.5 SDs).However, this is a rela7vely wide prior for point null Bayesian hypothesis tes7ng, and at odds with the defaults from packages meant for this purpose (e.g., BayesFactor).We therefore deviated from our preregistra7on and reported Bayes Factors with a normal prior centered at 0 with a standard devia7on of 1 (medium informa7ve).We also report strongly informa7ve (SD = .5)and weakly informa7ve (SD = 1.5) normal priors.Model diagnos7cs were checked with trace plots, posterior distribu7ons, and rhat values (<1.05) 76 .We then computed log Bayes Factors using the bayestestR package 77 using the Savage-Dickey density ra7o with a point-null of 0 for each of the 3 priors.The strength of evidence was interpreted on a graded scale using the criteria preregistered 51 .If the two frameworks disagree our primary inference will be based on the con7nuity-based framework.
Similarly to our con7nuity-based approach, we conducted placebo outcome tests within both windows ( = 1 & 5 months) using each included covariate as the outcome being predicted by ROSLA.In addi7on, we preregistered four placebo cutoffs -an analysis where the cutoff is ar7ficially moved to test the specificity of the effect -yet null findings made this test no longer necessary (see 'devia7ons from preregistra7on').

Correla1onal Analysis
To compare our results to a correla7onal approach, we tested self-reported years of total educa7on (EduYears) on the six global neuroimaging measures using the same par7cipants as the local randomiza7on analysis ( = 1 & 5 months).The analysis pipeline is iden7cal to the local randomiza7on approach, except the dummy coded term ROSLA was subs7tuted for con7nuous EduYears.

Covariates of no interest
In neuroimaging it is common to include covariates.However, for iden7fica7on in a valid regression discon7nuity design covariates by defini1on should be equal on either side of the cutoff 36 .We used standard neuroimaging covariates for two purposes, 1) to further test the validity of the 1972 ROSLA and 2) to increase sta7s7cal precision in our RD analysis.For instance, there are large sex differences in certain neural measures mostly related to head size 78 , therefore we included a dummy variable for sex.We expect ROSLA to not affect the propor7on of males and females, yet including this measure as a covariate will increase the es7ma7on precision for measures sensi7ve to sex-related head size differences (e.g., surface area1 ).
Children born in July and August could technically leave school at 15 aner 1972 ROSLA due to the exam period ending in mid-June and the school year star7ng on September 1 st 40 .This is an ar7fact of asking 'What age did you complete full-1me educa1on?',rather than 'How many years of educa1on did you complete?'.This ar7fact predates and is not influenced by ROSLA 79 , yet to account for this we included a dummy variable for children born in July or August.
Lastly, Neuro-UKB recruitment is s7ll ongoing and started in April 2014 70 .In turn, there is a wide range of intervals in terms of the period between when someone was born and the age at which they were scanned.We control for this discrepancy by including a variable 'date of scanning' (DoS).This was done by coding the earliest date a (included) par7cipant was scanned to 0 and coun7ng the number of days un7l the last included par7cipant.This resulted in a value for each par7cipant that was the number of days they were scanned aner the first par7cipant.We also include this variable squared, so we can model quadra7c effects, resul7ng in two variables (DoS & DoS 2 ).Other (preregistered) neuroimaging quality control measures were included such as scanning site, head mo7on, whether a T2 FLAIR sequence was used, T1 intensity scaling, and 3 diffusion measures recommended 80 .No addi7onal covariates other than those preregistered (h:ps://osf.io/rv38z)were added.
Our first aim, known as a placebo outcome test, involved tes7ng the effect of an addi7onal year of educa7on on each covariate.This was accomplished iden7cally to our neuroimaging outcomes (see sec7on 'Con7nuity-based framework') using RDHonest.We expect there to be no effect of ROSLA on any covariate.This was also tested for the Local-Randomiza7on Framework ( = 1 & 5 months).
For our second aim, increasing the precision of the RD es7mand we used covariate-adjusted outcomes (Y).This was done by filng a local linear regression for each MSE-derived bandwidth  with a matrix of covariates (′) on the unadjusted outcome (uY) using Equa7on 1 below.Let X denote the running variable (date of birth in months) which is centered around the ROSLA cutoff (i.e., September 1 st , 1957 = 0).In the second step, this matrix of covariates is then mul7plied by the fi:ed coefficients (β * ' ) and subtracted from the unadjusted outcome (uY) to make a covariate-adjusted outcome (Y).Since our assignment mechanism is probabilis7c (i.e., fuzzy RD) we also corrected our first-stage outcome, a dummy coded variable reflec7ng if the par7cipant stayed in school un7l 16, in an iden7cal manner.This method was used aner personal communica7on with Prof. Michal Kolesar the package creator of RDHonest.For the Bayesian local randomiza7on analysis and correla7onal analysis, we simply included the covariates in the model.Devia1ons from the preregistra1on The study closely followed the preregistra7on pipeline (h:ps://osf.io/rv38z),yet in a few minor cases it was not possible to follow.For instance, our ini7al plan involved placebo cutoffs -a sensi7vity test where the cutoff is ar7ficially moved to check if a significant result may also appear (for whatever reason) at other, non-hypothesized dates.Due to our lack of findings, we did not conduct this analysis as it was not necessary.
Some covariates lacked variance in specific specifica7ons due to very few observa7ons and therefore could not be included.In the global con7nuity analysis, this only impacted weighted frac7onal anisotropy, where the variable 'T2_FLAIR' was not used.This dummy-coded variable, indica7ng if a par7cipant had a T2-weighed MRI scan, was also not used in the regional con7nuity-based analysis nor for the local-randomiza7on analysis.The local randomiza7on analysis included a small number of par7cipants around September 1 st 1957 therefore we did not include the covariate "summer" as this would have been isomorphic to our effect of interest (ROSLA).Lastly, for the one-month window analysis, there were not enough observa7ons to include imaging center 11028.

Choice of priors
The Savage-Dickey density ra7o is the height of the posterior divided by the height of the prior at a par7cular point (0 in our case for Point null Bayes Factors).This makes them par7cularly sensi7ve to the prior used.Our preregistra7on referred to using a 'default weakly informa1ve prior'.While not specified this was referencing the default prior of STAN (i.e., normal of 2.5 SDs).However, this is arguably too wide for adequate point null Bayesian hypothesis tes7ng and at odds with the defaults from packages meant for this purpose (e.g., BayesFactor package).If we used the default prior from STAN it would have given us unrealis7cally strong support for the null hypothesis.We therefore deviated from our preregistra7on and reported Bayes Factors with a normal prior centered at 0 with a standard devia7on of 1 (mediumly informa7ve).We also report strongly informa7ve (SD = .5)and weakly informa7ve (SD = 1.5) normal priors both also centered at 0. All of our priors supported the null hypothesis they just varied in the amount of evidence in support of the null.Lastly, for illustra7on purposes, we ran the 5-month local randomiza7on analysis for surface area regions using the mediumly informa7ve prior (Figure 2).

Figure 1
Figure1Regression discon,nuity (RD) plot of monthly averaged a) total surface area, b) average cor,cal thickness, c) total brain volume, and d) weighted frac,onal anisotropy plo>ed by the par,cipant's date of birth in months (our running variable).Each dot reflects the average value for individuals born in that month.The dashed line corresponds to Sept. 1957 the date of birth inclusion cutoff for an addi,onal year of mandatory educa,on from ROSLA.We found no evidence of an effect from an addi,onal year of educa,on on any structural neuroimaging measures -illustrated here by a con,nuous line around the cutoff.Dark blue dots represent all individuals within the mean-squared error-op,mized bandwidths, in turn, reflec,ng par,cipants used for analysis with a local-linear fuzzy RD approach.Third-order polynomials (dark red lines) are fit on either side of the cutoff only for illustra,on purposes.Sup.Fig.3illustrates the two other preregistered global neuroimaging outcomes (total white ma>er hyperintensi,es and cerebral spinal fluid volume).