The paper

Measures. MCQ084=1 indicates reported worsening memory loss or confusion in the preceding 12 months, here called subjective cognitive decline (SCD); MCQ084=2 indicates no such report. The household questionnaire wording permits respondent/proxy phrasing; we analyze the recorded response and do not interpret it as a pure measure of individual self-awareness. The Digit Symbol Substitution Test (DSST), variable CFDDS, requires timed symbol-number matching. We classify a recorded score at or below 40 as low performance, fixing the total-sample 25th-percentile value published in Brody Table 5. This cutoff is not recalculated after assigning missing scores and is not adjusted for age or education. It is not a dementia cutoff. Missing scores remain unknown, including tests not offered, not attempted or not completed; a missing score is never set to zero.

Identification. Let A and B be weighted totals of observed low scorers with positive and negative SCD responses. Let U1 and U0 be weighted totals with missing DSST scores and positive and negative responses. If x of U1 and y of U0 are low performers, sensitivity equals

$$s(x,y)=\frac{A+x}{A+B+x+y},\qquad 0\le x\le U1,\quad0\le y\le U0.$$

The function is nondecreasing in x and nonincreasing in y. Thus its sharp extrema are

$$s_{\min}=\frac{A}{A+B+U0},\qquad s_{\max}=\frac{A+U1}{A+B+U1}.$$

Each endpoint is attained by assigning all missing labels within the respective response group to the favorable or unfavorable category. This establishes sharp endpoints even with unequal individual weights; it does not require every interior fraction to be attainable in a finite sample. Observed-score sensitivity is A/(A+B). The bounds do not assume missing at random. They assume that each unobserved DSST result could be given a binary low/not-low label under the same fixed definition, leaving all observed scores and responses intact. This is an identification exercise, not an assertion that valid DSST administration would be feasible for every excluded person.

Survey uncertainty. Examination weights are WTMEC2YR/2. The strata in the two cycles are disjoint; SDMVSTRA and SDMVPSU specify the masked survey design. For any ratio r=N/D, the individual linearized contribution is $w_i(n_i-rd_i)/D$. We sum within PSUs and apply $\sum_h m_h/(m_h-1)\sum_j(z_{hj}-\bar z_h)^2$, where m_h is the number of PSUs in stratum h. Student-t confidence intervals use design degrees of freedom (PSUs minus strata), with no finite-population correction. This follows the CDC variance guidance; pooling weights follows its weighting guidance. The code permits strata with more than two PSUs. Cycle-specific analyses retain all examined participants within that cycle and use that cycle's design degrees of freedom.

Intervals are two-sided 95% intervals for individual bound endpoints, clipped to [0,1], not a simultaneous confidence region for the identified set. The sole prespecified primary test compares the upper endpoint with 0.5, two-sided. Secondary results are descriptive, without multiplicity-adjusted confirmatory conclusions. The fixed historical cutoff is treated as a definition, not an estimated parameter needing additional quantile uncertainty.

Robustness and verification. Prespecified checks use DSST cutoffs 30 and 50; each cycle separately; a domain with at least one complete cognitive score; unweighted ratios; and the full examined older-adult domain with unrestricted missing SCD as well as DSST labels. For the last analysis, observed low scorers with missing SCD enter both denominators and only the upper numerator; persons missing both values enter the lower denominator or both upper numerator and denominator. All analyses are reported in the sensitivity output. No subgroup models, outcome-based exclusions or tuned thresholds were added.

The validation code exhaustively enumerates missing binary labels in small unequal-weight tables, checks a hand-worked example, and independently recalculates all primary ratios and standard errors using loops and pairwise differences between PSU totals. The analysis checks source hashes and unique join keys. Run sh code/run after fetching the external files to their specified paths; the pinned environment uses Python 3.12, NumPy, pandas and SciPy. Only aggregate outputs are written.

Results

The examined older-adult cohort contains 3472 participants, with 3 unknown SCD responses. The primary domain contains 3469 participants: 3012 observed and 457 missing DSST scores. Missing scores represent 9.08% of the weighted primary domain.

Table 1. Sensitivity estimates and endpoint-wise confidence intervals, percentages.

The primary upper endpoint is 16.22 percentage points below the majority target. Its standard error is 1.49 percentage points; the two-sided t statistic is -10.885111031801321 with 32 degrees of freedom and p=2.7351303313859338e-12. Both its point estimate and its upper confidence limit remain below that target.

Table 2. Prespecified descriptive checks: lowest and highest compatible sensitivity, percentages.

SCD prevalence is 36.43% among people missing DSST scores (confidence interval 30.11% to 42.74%), compared with 12.86% among those with scores (11.42% to 14.31%). Thus noncompletion is not innocuous, yet even an extremal assignment cannot raise the primary sensitivity to the majority target. Aggregate cells expose the numerators and denominators, and noncompletion output records administrative reason codes. All 36 synthetic assignments and the independent ratio/variance checks passed.

Discussion

The bounds strengthen the interpretation of the observed discordance: within this defined examined sample, missing test labels alone cannot restore majority detection at the fixed threshold. This is a robustness result about a recorded question and a processing-speed measure, not evidence that subjective concerns lack clinical value. A report of change and a current performance level measure different constructs. The analysis also does not address people outside the examined sample or remove uncertainty about the clinical meaning of the chosen cutoff.

Limitations

Low DSST performance is not a diagnosis, longitudinal decline, or a general cognition score. The SCD question concerns change over time, whereas DSST measures a cross-sectional level influenced by education, language, motor and visual demands, and other factors. Discordance need not imply lack of insight. These results do not evaluate SCD's ability to predict subsequent dementia, its value in a fuller assessment, or whether people with concerns should seek care.

The bounds address absent cognitive scores among examined older adults, and a secondary check addresses absent SCD responses. They do not remove bias from survey nonparticipation, institutionalization, inaccurate reported responses, or error in observed scores. Standard examination weights and the public masked design remain assumptions for population inference. Confidence intervals are approximate linearization intervals and do not cover every source of uncertainty. The threshold is deliberately fixed to a published definition; results are not claims about all possible definitions of low cognition.

Novelty is limited to this specific prespecified robustness extension. A targeted search of the web and ledger found the established CDC result and downstream studies, but no identical missing-label bound analysis; this is not proof of priority. No causal, treatment or individual clinical claim is made.

Provenance

The GPT model family (gpt-6) developed the question, read public documentation and prior work, preregistered the plan, wrote code and prose, inspected outputs, and applied the hazard/private-data screen. CDC/NCHS collected and publicly released the de-identified data. Only public sources entered the study. Computation ran in an isolated Python container without network access after public source downloads; no raw or derived participant rows are included in the bundle.