Statistics

Machine learning

Replication (statistics)

Radiology

Sample size determination

Magnetic resonance imaging

Brain morphometry

Psychology

Virology

Multivariate statistics

Neuroscience

Cognition

Imaging genetics

Multiple comparisons problem

Univariate

Functional magnetic resonance imaging

Population

Brain function

Mathematics

Computer science

Neuroimaging

Brain size

Medicine

Environmental health

Nature

Magnetic resonance imaging (MRI) has transformed our understanding of the human brain through well-replicated mapping of abilities to specific structures (for example, lesion studies) and functions1–3 (for example, task functional MRI (fMRI)). Mental health research and care have yet to realize similar advances from MRI. A primary challenge has been replicating associations between inter-individual differences in brain structure&nbsp;or&nbsp;function and complex cognitive or mental health phenotypes (brain-wide association studies (BWAS)). Such BWAS have typically relied on sample sizes appropriate for classical brain mapping4 (the median neuroimaging study sample size is about 25), but potentially too small for capturing reproducible brain–behavioural phenotype associations5,6. Here we used three of the largest neuroimaging datasets currently available—with a total sample size of around 50,000 individuals—to quantify BWAS effect sizes and reproducibility as a function of sample size. BWAS associations were smaller than previously thought, resulting in statistically underpowered studies, inflated effect sizes and replication failures at typical sample sizes. As sample sizes grew into the thousands, replication rates began to improve and effect size inflation decreased. More robust BWAS effects were detected for functional MRI (versus structural), cognitive tests (versus mental health questionnaires) and multivariate methods (versus univariate). Smaller than expected brain–phenotype associations and variability across population subsamples can explain widespread BWAS replication failures. In contrast to non-BWAS approaches with larger effects (for example, lesions, interventions and within-person), BWAS reproducibility requires samples with thousands of individuals. Combined data from three large studies, with a total sample size&nbsp;of&nbsp;around 50,000 individuals,&nbsp;indicate that many previous studies linking the brain to complex phenotypes&nbsp;have been statistically underpowered, producing inflated and&nbsp;irreproducible effects.

Reproducible brain-wide association studies require thousands of individuals