Methods and honest limits

Limits first

No ADHD diagnosis exists in this cohort. Nothing on this site is an ADHD prevalence or an ADHD diagnosis result. ADHD enters only as inherited (genetic) liability, either a score built from many genetic variants or the variants used in the Mendelian-randomisation analysis.
Single cohort. Every cohort-based finding comes from one research cohort of volunteers seen at memory clinics. Nothing was replicated in a different cohort, and rates there are higher than in the general population.
The 27-vs-34 instrument discrepancy is UNRESOLVED. An earlier Mendelian-randomisation report used 27 genetic instruments. The re-run could not reproduce that set: no earlier output, script or log could be found, so the original reference panel and filters are unknown. The standard recipe gave 35 variants, 34 after harmonisation. Other settings gave other counts; none gave 27. The analysis went ahead as a robustness check, not because that check passed. A stricter 26-variant sensitivity set is on the MR page. Until the original 27 are recovered, the MR result is not ready to publish.
Home-built estimator. The MR-RAPS package was not installed. The "MR-RAPS-like" row is the analyst's own implementation, not validated against the package, and must not be called MR-RAPS in public text.
Sample overlap between the ADHD and Alzheimer's studies in the MR analysis was not checked.

How well the models rank people

Concordance on 297 held-out people; bar = point estimate, whisker = 95% CI. The source says each added marker's gain is within chance.

How each result was produced

Conversion ladder: Take people who start with mild cognitive impairment and no dementia. Count how many are later diagnosed with dementia by each follow-up point, allowing for people who drop out of follow-up. Report the share with a 95% confidence interval.
Prediction ladder: Build a risk model on one group of people and test it on a separate group it has never seen. Start with age, sex, education and APOE4, then add memory and thinking tests, then spinal-fluid markers, MRI and PET one at a time. Performance is a concordance score: 0.5 is a coin toss, 1 is perfect. Several tests help define the diagnosis, which flatters them.
Cognition vs biomarkers: The same held-out group, two models: tests only and biomarkers only. Many biomarker values were filled in by imputation, which handicaps that side.
Tau and p-tau, ADAS-Cog, plasma p-tau217, executive function: Rank correlations (Spearman-style) between two measurements in the people who have both, each with a 95% confidence interval. Some of these agree partly by construction, which is why two are held back.
APOE genetic scan: A genome-wide association scan comparing people with normal cognition against people with dementia. It is small, so it cannot find new genes and its odds ratio is inflated by comparing two extreme groups.
ADHD genetic score and cognition: A polygenic score for ADHD liability was tested against memory and thinking scores and their change over time, in a sequenced sample, an independent array sample, and both pooled, with multiple-testing correction. It captures only a few percent of ADHD liability and covers European ancestry only.
DNA methylation: Methylation at ADHD-related genes compared by cognitive status. Only a small number of Alzheimer's participants and a cohort-wide shift mean small effects could not be detected, so this is a weak null.
Mendelian randomisation (MR): Uses inherited variants as natural experiments to ask whether genetic liability to ADHD changes Alzheimer's risk. Several estimators with different assumptions are run on several Alzheimer's datasets, plus the reverse direction as a sanity check. Agreement across estimators is what counts.

Numbers come from the source files; the site only rounds them for display (3 decimals for odds ratios, betas, CIs and SEs; 3 significant figures for p; 1 decimal for percentages). Exact MR values are at /mr.csv.