Discordance Between Spatial and Population Correlations From Human Brain Imaging Data

It has become increasingly common to probe correlations between human brain imaging measures of receptor/protein binding and function using population-level brain maps, typically drawn from independent cohorts to estimate correlations across regions. This strategy raises issues of interpretation that we highlight here with both an empirical multimodal brain imaging dataset and simulation studies. Twenty-four healthy participants completed neuroimaging with both [11C]Cimbi-36 positron emission tomography and magnetic resonance imaging scans to estimate receptor binding potential (BP) and cerebral blood flow (CBF), respectively, in 18 cortical/subcortical regions. Correlations between BP and CBF were estimated in four ways: (1) Pearson correlation across regions of mean regional BP and CBF from a single or separate cohorts ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>ρ</mml:mi> <mml:mn>1.1</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$$ {\rho}_{1.1} $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>ρ</mml:mi> <mml:mn>1.2</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$$ {\rho}_{1.2} $$</mml:annotation></mml:semantics> </mml:math> , respectively), to mimic studies using data from independent cohorts; (2) Pearson correlation between BP and CBF across participants in each region ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>ρ</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$$ {\rho}_2 $$</mml:annotation></mml:semantics> </mml:math> ); or (3) the correlation between BP and CBF across participants across all regions within a single linear mixed effects model ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>ρ</mml:mi> <mml:mn>3</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$$ {\rho}_3 $$</mml:annotation></mml:semantics> </mml:math> ). We observed a significant positive correlation across regions ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mover><mml:mi>ρ</mml:mi> <mml:mo>̂</mml:mo></mml:mover> <mml:mn>1.1</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$$ {\hat{\rho}}_{1.1} $$</mml:annotation></mml:semantics> </mml:math> = 0.672, p = 0.0023; <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mover><mml:mi>ρ</mml:mi> <mml:mo>̂</mml:mo></mml:mover> <mml:mn>1.2</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$$ {\hat{\rho}}_{1.2} $$</mml:annotation></mml:semantics> </mml:math> = 0.659, p = 0.0030). Region-specific correlations across participants were substantively lower and not statistically significant ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mover><mml:mi>ρ</mml:mi> <mml:mo>̂</mml:mo></mml:mover> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$$ {\hat{\rho}}_2 $$</mml:annotation></mml:semantics> </mml:math> : mean = 0.140, range = -0.112-0.336; all p > 0.10), nor when estimated simultaneously within a linear mixed model ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mover><mml:mi>ρ</mml:mi> <mml:mo>̂</mml:mo></mml:mover> <mml:mn>3</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$$ {\hat{\rho}}_3 $$</mml:annotation></mml:semantics> </mml:math> = 0.138, p = 0.26). Our simulation study illustrated that regional differences in BP or CBF mean and variance can substantially bias across-regions correlations and inflate the type-1 error rate. Our observations allude to ambiguity in the meaning of across-regions correlations and suggest interpreting them as evidence for a biological relation, which implies a relation across participants, is problematic. Without validated methods that handle confounding and other biases, we urge caution in how future studies interpret across-regions correlations of population-level brain maps.