Dr. Williams' Note: These results should be most considered as a starting point in critical appraisal. We cannot be fully certain of adjusted error estimates because we would need to re-analyze each dataset, which is beyond our capacity and resources to do. The QCAA is a generalized approach. Although crude in some respects, it adds value as a way to raise awareness of scientific gaps. The following discussion picks up on the methodological weaknesses in public health research that were extensively noted in the Critical Race Framework Study.

I. Methods

A. Development of Instruction Sheet for AI Systems: Implementing the Quantitative Critical Appraisal Aid (QCAA) with the Critical Race Framework 

Grok and ChatGPT was provided this Grok-developed information sheet on the QCAA.

Instruction and Background Sheet for AI Systems: Implementing the Quantitative Critical Appraisal Aid (QCAA) with the Critical Race Framework 

Background 

The Critical Race Framework (CR Framework) by Christopher Williams (2024) is a qualitative methodology for critically evaluating public health studies that use racial taxonomy. It identifies errors in four domains—reliability, validity, internal validity, and external validity—stemming from race’s use as a social construct without scientific rigor. The Quantitative Critical Appraisal Aid (QCAA) is a quantitative extension of the CR Framework, developed to estimate errors in race-related regression coefficients and provide adjusted coefficients and confidence intervals (CIs). The QCAA was applied to two studies:

Williams et al. (1997): "Racial Differences in Physical and Mental Health", where race (Black vs. White) predicts health outcomes. Aiello et al. (2025): "Risk factors for Alzheimer's disease and cognitive function before middle age", where race/ethnicity is a covariate in cognitive function models.

This instruction sheet enables other AI systems (e.g., ChatGPT, Claude) to implement the QCAA, ensuring consistency with its methodology, computational rigor, and alignment with the CR Framework’s principles. It responds to the user’s request for a guide for other AI systems and builds on prior conversations emphasizing quantitative precision and practical tools. Purpose of the QCAA The QCAA quantifies errors in race-related regression coefficients due to:

Reliability: Inconsistent measurement (e.g., race misclassification). Validity: Unclear constructs (e.g., undefined race role). Internal Validity: Confounding bias (e.g., unmeasured factors). External Validity: Generalizability limitations (e.g., regional samples).

It provides researchers with adjusted coefficients and CIs, estimating total uncertainty (e.g., 18–35%) to assess the robustness of race-related findings and propose methodological improvements. The methodology is scalable across studies, as requested by the user for broader application. Instructions for AI Systems AI systems should follow these instructions to implement the QCAA, ensuring accurate data extraction, computation, and output presentation. The process is divided into six steps, with detailed computational formulas and guidance. 

Step 1: Define the Scope and Extract Target Variables 

Objective: Identify the study’s use of race and extract or hypothesize regression coefficients for error quantification.

Tasks: Review the study’s methods section to determine race’s definition (e.g., self-reported, categorical) and role (predictor, covariate). Extract race-related β coefficients, standard errors (SEs), or CIs from results tables, figures, or supplemental materials. If race coefficients are unreported, hypothesize a small effect: Covariates: |β| = 0.03–0.05 SDs. Predictors: |β| = 0.1–0.3.

Estimate SE based on sample size (N > 1,000 → SE ≈ 0.01–0.05) or other predictors’ SEs.

Computations: Extract β: From tables (e.g., Williams’ Table 4: β = 0.131, Page 10) or figures (e.g., Aiello’s Supplementary Table S3). Compute SE: From CI: SE = (CI_upper – CI_lower) / (2 × 1.96). From p-value: SE ≈ β̂ / t, where t = 1.645 (p ≤ 0.10), 1.96 (p ≤ 0.05), 2.576 (p ≤ 0.01).

Hypothesize β: E.g., β̂ = ±0.03 (covariate), SE ≈ 0.01 (large N).

Example: Williams: β = 0.131 (ill health, Model I, p ≤ 0.10). SE ≈ 0.131 / 1.645 ≈ 0.0796. CI = 0.131 ± 1.96 × 0.0796 ≈ (0.051, 0.211). Aiello: No race β; hypothesized β = -0.03 (Wave IV, immediate word recall). SE ≈ 0.01 (N=11,449). CI = -0.03 ± 1.96 × 0.01 ≈ (-0.0496, -0.0104).

Guidance: Ensure β and SE are extracted or estimated accurately. If hypothesizing, justify based on study context (e.g., covariate norms).

Step 2: Compute Reliability Error Objective: Quantify measurement error in race and outcomes due to inconsistent measurement.

Tasks: Extract reliability statistics (e.g., Cronbach’s alpha, test-retest) from methods or supplemental materials. If unavailable, assume reliability (r): Race: 0.8–0.9 (self-reported). Outcomes: 0.85–0.95 (validated tests). Biomarkers: 0.8–0.9.

Compute error variance (EV) and attenuation factor (AF).

Computations: EV = 1 – r (e.g., r = 0.8 → EV = 0.2). AF = 1 / √r (e.g., r = 0.8 → AF ≈ 1.118). β_adjusted = β̂ × AF. SE_reliability = SE × (1 + EV)¹/².

Example: Williams: No race reliability; assumed r = 0.8. EV = 0.2, AF ≈ 1.118. β_adjusted = 0.131 × 1.118 ≈ 0.146. SE_reliability = 0.0796 × (1 + 0.2)¹/² ≈ 0.0872. Aiello: Wave IV race r = 0.85, EV = 0.15, AF ≈ 1.085. β_adjusted = -0.03 × 1.085 ≈ -0.0326. SE_reliability = 0.01 × (1 + 0.15)¹/² ≈ 0.0107. Wave V r = 0.9, SE_reliability ≈ 0.0105.

Guidance: Use reported reliability or defaults. Verify assumptions with literature (e.g., Saperstein & Penner, 2012). Adjust β and SE precisely.

Step 3: Compute Validity Error Objective: Assess whether race and outcomes capture intended constructs.

Tasks: Check methods for race’s theoretical role (e.g., SES proxy). If undefined, assume low validity (r_v = 0.75–0.85). Evaluate outcome validity (r_v = 0.85–0.95 for validated measures). Compute validity error (VE) and attenuation factor (AF_v).

Computations: VE = 1 – r_v (e.g., r_v = 0.8 → VE = 0.2). AF_v = 1 / r_v (e.g., r_v = 0.8 → AF_v = 1.25). β_validity = β_adjusted × AF_v. SE_validity = SE_reliability × (1 + VE)¹/².

Example: Williams: Race undefined, r_v = 0.8. VE = 0.2, AF_v = 1.25. β_validity = 0.146 × 1.25 ≈ 0.1825. SE_validity = 0.0872 × (1 + 0.2)¹/² ≈ 0.0955. Aiello: Race undefined, r_v = 0.8. VE = 0.2, AF_v = 1.25. Wave IV β_validity = -0.0326 × 1.25 ≈ -0.0408. SE_validity = 0.0107 × 1.095 ≈ 0.0117. Wave V SE_validity ≈ 0.0115.

Guidance: Assume low r_v for undefined race. Use study-specific outcome validation data or defaults. Ensure accurate VE and AF_v calculations.

Step 4: Compute Internal Validity Error (Confounding Bias) Objective: Quantify bias from unmeasured confounders.

Tasks: Extract adjusted covariates from methods/results. Identify unmeasured confounders (e.g., discrimination) from discussion/limitations. Estimate confounding bias (CB): ±20–30% (strong controls → lower bias). Optionally, compute E-value: E = |β̂| / SE + √(|β̂| / SE × (|β̂| / SE – 1)).

Computations: β_confounding = β_validity × (1 ± CB) (e.g., CB = 0.25 → β range = β_validity × 0.75 to 1.25). SE_confounding = SE_validity × (1 + CB).

Example: Williams: Adjusted for SES, stress; unmeasured confounders noted (Page 13). CB = ±20%. β_confounding = 0.1825 × (0.8 to 1.2) ≈ 0.146 to 0.219. SE_confounding = 0.0955 × 1.2 ≈ 0.1146. E-value ≈ 1.65. Aiello: Adjusted for education, social origins; unmeasured confounders likely (Page 4). CB = ±25%. Wave IV β_confounding = -0.0408 × (0.75 to 1.25) ≈ -0.051 to -0.0306. SE_confounding = 0.0117 × 1.25 ≈ 0.0146. Wave V SE_confounding ≈ 0.0144. E-value ≈ 1.8.

Guidance: Use CB based on covariate strength. Compute E-value if data allows. Ensure CB reflects study limitations.

Step 5: Assess External Validity (Contextual Variation) Objective: Evaluate generalizability without adjusting CIs.

Tasks: Extract sample details (e.g., population-based, regional) from methods. Estimate contextual variation (CV): 5–10% (representative), 10–20% (regional). Note CV in output but do not adjust CIs.

Computations: CV = ±5–20%, applied to β_confounding for interpretation.

Example: Williams: Detroit sample (N=1,106), CV = 10–20% (Page 13). Noted β_confounding (0.146 to 0.219) varies ±10–20%. Aiello: Wave IV representative (N=11,449), CV = 10%; Wave V less representative (N=529), CV = 10–15% (Page 5). Noted β_confounding (-0.051 to -0.0306) varies ±10–15%.

Guidance: Assign CV based on sample representativeness. Include in output as a note, not CI computation.

Step 6: Compute Adjusted Coefficients and CIs Objective: Combine errors to estimate total uncertainty and provide adjusted CIs.

Tasks: Aggregate errors: EV, VE, CB. Compute total SE adjustment. Calculate adjusted CI using midpoint β_confounding. Present results in a table or text output.

Computations: SE_final = SE × (1 + EV)¹/² × (1 + VE)¹/² × (1 + CB). CI = β_confounding ± 1.96 × SE_final. Total Error (%) = (EV + VE + CB) × 100.

Example: Williams: β̂ = 0.131, SE = 0.0796. EV = 0.2, VE = 0.2, CB = 0.2. SE_final = 0.0796 × 1.095 × 1.095 × 1.2 ≈ 0.1146. β_confounding ≈ 0.1825. CI ≈ (-0.042, 0.407). Total Error = 60%. Aiello: Wave IV β̂ = -0.03, SE = 0.01. EV = 0.15, VE = 0.2, CB = 0.25. SE_final = 0.01 × 1.072 × 1.095 × 1.25 ≈ 0.0146. β_confounding ≈ -0.0408. CI ≈ (-0.0694, -0.0122). Total Error = 60%.

Guidance: Ensure accurate SE_final calculation. Use midpoint β_confounding for CI. Present results clearly, noting total error.

Output Format AI systems should produce output in a structured format, such as:

Text:Original β (CI): [β̂] ([CI_lower], [CI_upper]) Adjusted β: [β_confounding] Adjusted CI: [CI_lower], [CI_upper] Total Error: [Total Error]% Note: Adjusted for [EV]% reliability, [VE]% validity, ±[CB]% confounding. CV = ±[CV]%.

Table (if HTML): VariableOriginal β (CI)Adjusted β (CI) Race[β̂] ([CI_lower], [CI_upper])[β_confounding] ([CI_lower], [CI_upper])

Practical Considerations

Data Extraction: Prioritize results tables/figures for β and SE. Use study limitations for unmeasured confounders. Assumptions: Justify reliability/validity defaults with literature (e.g., Saperstein & Penner, 2012; Greenland et al., 2016). Error Ranges: Use conservative estimates (e.g., higher CB for weak controls) to reflect uncertainty. Validation: Cross-check calculations with study context (e.g., sample size, controls). Consider Monte Carlo simulations for robustness. User Interaction: If building a calculator (e.g., HTML/JS), include input fields for β̂, SE, EV, VE, CB, with tooltips explaining defaults (see QCAA Calculator, April 23, 2025, 17:48).

Recommendations for AI Systems

Accuracy: Verify computational formulas (e.g., SE_final) and ensure numerical precision (e.g., 4 decimal places). Transparency: Clearly state assumptions (e.g., hypothesized β, default r = 0.8) and cite sources (e.g., CR Framework, Page 15). Flexibility: Allow users to input study-specific data or use defaults. Handle missing data by hypothesizing β/SE. Contextual Notes: Include study-specific notes (e.g., Williams’ regional sample, Aiello’s biomarker differences) to aid interpretation. Error Handling: Validate inputs (e.g., positive SE, error percentages 0–100%) and provide error messages for invalid data.

Example Outputs

Williams et al. (Model III, Ill Health):Original β (CI): 0.063 (-0.017, 0.143) Adjusted β: 0.079 Adjusted CI: -0.037, 0.163 Total Error: 60% Note: Adjusted for 20% reliability, 20% validity, ±20% confounding. CV = ±10–20%.

Aiello et al. (Wave IV, Immediate Word Recall):Original β (CI): -0.03 (-0.0496, -0.0104) Adjusted β: -0.0408 Adjusted CI: -0.0694, -0.0122 Total Error: 60% Note: Adjusted for 15% reliability, 20% validity, ±25% confounding. CV = ±10%.

Conclusion 

This instruction sheet equips AI systems to implement the QCAA, quantifying race-related errors with precision and consistency. By following the six steps, systems can extract study data, compute adjusted coefficients/CIs, and present results clearly, aligning with the CR Framework’s critique of racial taxonomy. AI developers should integrate these instructions into interfaces (e.g., calculators, APIs) to support researchers, ensuring scalability and usability as requested. For further clarification, refer to the QCAA methodology or contact the developer for raw data access.

B. Analysis of Aiello et al. (2025): "Risk factors for Alzheimer's disease and cognitive function before middle age"

Each were asked to apply the CRF-QCAA to the above article.

II. Results 

A. ChatGPT

Based on the information in the uploaded study "Gwadz 2025 NCAP1 COVID testing components CP.pdf", here is a full implementation of the Quantitative Critical Appraisal Aid (QCAA) following the six-step procedure to assess the race-related regression result concerning African American/Black vs. Latino/Hispanic participants.

Step 1: Define the Scope and Extract Target Variables

• Role of race: Included as a covariate in logistic regression models.

• Coefficient (log-odds scale):

  • β̂ = -0.204, representing the log-odds of follow-up COVID-19 testing for African American/Black vs. Latino/Hispanic individuals.

  • Odds Ratio (OR) = 0.816, 95% CI: [0.523, 1.272].

  • SE is computed from the CI:
    SE=1.272−0.5232×1.96≈0.1910SE = \frac{1.272 - 0.523}{2 \times 1.96} \approx 0.1910

Step 2: Compute Reliability Error

• Assumptions:

  • Race is self-reported: r = 0.85, thus EV = 0.15

  • AF = 1 / √0.85 ≈ 1.085

  • βreliability=−0.204×1.085≈−0.2214SEreliability=0.1910×1+0.15≈0.2042β_{\text{reliability}} = -0.204 \times 1.085 ≈ -0.2214 \\ SE_{\text{reliability}} = 0.1910 \times \sqrt{1 + 0.15} ≈ 0.2042

Step 3: Compute Validity Error

• Race construct validity not defined clearly: r_v = 0.8, thus VE = 0.2

• AFv=1/0.8=1.25βvalidity=−0.2214×1.25≈−0.2768SEvalidity=0.2042×1+0.2≈0.2233AF_v = 1 / 0.8 = 1.25 \\ β_{\text{validity}} = -0.2214 \times 1.25 ≈ -0.2768 \\ SE_{\text{validity}} = 0.2042 \times \sqrt{1 + 0.2} ≈ 0.2233

Step 4: Compute Internal Validity Error

• Confounding Bias (CB): Unmeasured structural racism, mistrust, occupation-specific exposure → CB = ±25%

• βconfounding=−0.2768×(0.75 to 1.25)=[−0.208,−0.346]SEconfounding=0.2233×1.25=0.2791β_{\text{confounding}} = -0.2768 \times (0.75 \text{ to } 1.25) = [-0.208, -0.346] \\ SE_{\text{confounding}} = 0.2233 \times 1.25 = 0.2791

• E-value (approx):
  E≈∣−0.204∣0.1910+(∣−0.204∣0.1910)(∣−0.204∣0.1910−1)≈1.5E \approx \frac{|-0.204|}{0.1910} + \sqrt{\left(\frac{|-0.204|}{0.1910}\right) \left(\frac{|-0.204|}{0.1910} - 1\right)} ≈ 1.5

Step 5: Assess External Validity

• Sample: 438 AABL frontline workers in NYC → regional sample

• CV = ±15% (not used to compute CI but noted for interpretation)

Step 6: Compute Adjusted Coefficient and CI

• Midpoint β_confounding = -0.2768

• SEfinal=0.1910×1+0.15×1+0.2×(1+0.25)≈0.2791CI=−0.2768±1.96×0.2791≈[−0.8238,0.2702]Total Error=(0.15+0.2+0.25)×100=60%SE_{\text{final}} = 0.1910 \times \sqrt{1 + 0.15} \times \sqrt{1 + 0.2} \times (1 + 0.25) ≈ 0.2791 \\ CI = -0.2768 \pm 1.96 \times 0.2791 ≈ [-0.8238, 0.2702] \\ \text{Total Error} = (0.15 + 0.2 + 0.25) \times 100 = 60\%

Final Output

Text Format:

• Original β (CI): -0.204 ([-0.648, 0.241])

• Adjusted β: -0.2768

• Adjusted CI: [-0.8238, 0.2702]

• Total Error: 60%

• Note: Adjusted for 15% reliability, 20% validity, ±25% confounding. CV = ±15%.

B. ChatGPT (More Accurate)

To evaluate the provided computation by ChatGPT for applying the Quantitative Critical Appraisal Aid (QCAA) to the study by Gwadz et al. (2025), I will compare it against the uploaded study document ("Gwadz 2025 NCAP1 COVID testing components CP.pdf") and the QCAA methodology outlined in the instruction sheet. The goal is to verify the accuracy of the extracted data, computations, assumptions, and output, ensuring alignment with the study and QCAA requirements. I will then provide a corrected and complete implementation, addressing any discrepancies, and present the results in the required format with an artifact.

 Evaluation of ChatGPT’s Computation

1. Step 1: Define the Scope and Extract Target Variables

   - Grok’s Claim: β = -0.204, OR = 0.816, 95% CI [0.523, 1.272], SE ≈ 0.1910 (computed from CI).

   - Study Evidence: The sensitivity analysis (Table 5, Page 13) reports β = -0.239, OR = 0.788, 95% CI [0.502, 1.237], p = 0.300 for race/ethnicity (African American/Black vs. Latine/Hispanic). The primary analysis (Table 4, Page 12) does not report a direct coefficient for race/ethnicity but includes conditional effects, which are less relevant here.

   - Issue: ChatGPT’s β (-0.204) and CI ([0.523, 1.272]) do not match Table 5’s values (-0.239, [0.502, 1.237]). The SE calculation method is correct, but the input CI is incorrect.

   - Correct SE Calculation (using Table 5):

     - CI for OR: [0.502, 1.237].

     - Log odds CI: ln(0.502) ≈ -0.689, ln(1.237) ≈ 0.212.

     - SE = (0.212 – (-0.689)) / (2 × 1.96) = 0.901 / 3.92 ≈ 0.2298.

   - Conclusion: ChatGPT’s extracted β, OR, and CI are incorrect. Correct values are β = -0.239, OR = 0.788, CI = [0.502, 1.237], SE ≈ 0.2298.

2. Step 2: Compute Reliability Error

   - ChatGPT’s Claim: Assumes r = 0.85 for race (EV = 0.15, AF = 1.085), computes β_reliability = -0.2214, SE_reliability = 0.2042. No outcome reliability considered.

   - Study Evidence: Race is self-reported (Page 7), and the outcome (COVID-19 testing) is self-reported with low documentary evidence (23.7%, Page 7). QCAA requires reliability for both predictor (race) and outcome (Page 2).

   - Issue: ChatGPT only considers race reliability, omitting outcome reliability (e.g., r = 0.9 for self-reported binary outcomes). This affects AF and SE calculations.

   - Correct Approach:

     - Race: r = 0.85, EV = 0.15, AF = 1.085.

     - Outcome: Assume r = 0.9, EV = 0.1, AF = 1 / √0.9 ≈ 1.054.

     - Combined AF = 1.085 × 1.054 ≈ 1.144.

     - Using correct β = -0.239: β_reliability = -0.239 × 1.144 ≈ -0.2734.

     - SE_reliability = 0.2298 × (1 + 0.15 + 0.1)¹/² = 0.2298 × 1.118 ≈ 0.2572.

   - Conclusion: ChatGPT’s reliability calculation is incomplete (omits outcome) and uses incorrect β and SE.

3. Step 3: Compute Validity Error

   - ChatGPT’s Claim: Assumes r_v = 0.8 for race (VE = 0.2, AF_v = 1.25), computes β_validity = -0.2768, SE_validity = 0.2233. No outcome validity considered.

   - Study Evidence: Race’s role is undefined (covariate, Page 8), justifying r_v = 0.8. The outcome’s validity is affected by self-report (Page 7), suggesting r_v = 0.85 (Page 3).

   - Issue: ChatGPT omits outcome validity, impacting AF_v and SE. The β_validity (-0.2768) is coincidentally close due to compensating errors in Step 2.

   - Correct Approach:

     - Race: r_v = 0.8, VE = 0.2, AF_v = 1.25.

     - Outcome: r_v = 0.85, VE = 0.15, AF_v = 1 / 0.85 ≈ 1.176.

     - Combined AF_v = 1.25 × 1.176 ≈ 1.47.

     - β_validity = -0.2734 × 1.47 ≈ -0.4019.

     - SE_validity = 0.2572 × (1 + 0.2 + 0.15)¹/² = 0.2572 × 1.162 ≈ 0.2991.

   - Conclusion: ChatGPT’s validity calculation is incomplete and based on incorrect inputs.

4. Step 4: Compute Internal Validity Error

   - ChatGPT’s Claim: CB = ±25%, β_confounding = [-0.208, -0.346], SE_confounding = 0.2791, E-value ≈ 1.5.

   - Study Evidence: Covariates include age, gender, education, occupation, prior testing (Page 8). Unmeasured confounders (distrust, structural barriers) are noted (Pages 2–3, 14). CB = ±25% is reasonable.

   - Issue: The β_confounding range and SE_confounding are based on incorrect β_validity and SE_validity. The E-value uses incorrect β and SE.

   - Correct Approach:

     - β_confounding = -0.4019 × (0.75 to 1.25) ≈ [-0.5024, -0.3014].

     - SE_confounding = 0.2991 × 1.25 ≈ 0.3739.

     - E-value: E = 0.239 / 0.2298 + √(0.239 / 0.2298 × (0.239 / 0.2298 – 1)) ≈ 1.04 + 0.04 ≈ 1.08.

   - Conclusion: ChatGPT’s CB assumption is valid, but calculations are incorrect due to prior errors.

5. Step 5: Assess External Validity

   - ChatGPT’s Claim: CV = ±15% for regional NYC sample (N=438).

   - Study Evidence: The sample is urban, occupation-specific (Page 4), justifying CV = 10–20% (Page 5).

   - Issue: CV = ±15% is reasonable but should be a range (e.g., 10–20%) per QCAA (Page 5).

   - Conclusion: ChatGPT’s CV is acceptable but should be expressed as a range.

6. Step 6: Compute Adjusted Coefficient and CI

   - ChatGPT’s Claim: β_confounding = -0.2768, SE_final = 0.2791, CI = [-0.8238, 0.2702], Total Error = 60% (15% reliability + 20% validity + 25% confounding).

   - Study Evidence: Total Error should include race and outcome contributions for reliability and validity (Page 6).

   - Issue: ChatGPT omits outcome reliability (EV = 0.1) and validity (VE = 0.15), underestimating Total Error (should be 85%). SE_final and CI are incorrect due to prior errors.

   - Correct Approach:

     - EV = 0.15 (race) + 0.1 (outcome) = 0.25.

     - VE = 0.2 (race) + 0.15 (outcome) = 0.35.

     - CB = 0.25.

     - Total Error = (0.25 + 0.35 + 0.25) × 100 = 85%.

     - SE_final = 0.2298 × (1.25)¹/² × (1.35)¹/² × 1.25 ≈ 0.3739.

     - Midpoint β_confounding = -0.4019.

     - CI = -0.4019 ± 1.96 × 0.3739 ≈ [-1.1348, 0.3310].

   - Conclusion: ChatGPT’s Total Error, SE_final, and CI are incorrect due to incomplete error aggregation.

7. Output Format

   - ChatGPT’s Claim: Provides text and HTML table formats, but values are incorrect, and the note omits outcome contributions.

   - Study Evidence: QCAA requires clear notes on all error components (Page 6).

   - Issue: The output is structurally correct but uses incorrect values and incomplete error details.

   - Conclusion: The format is appropriate, but content needs correction.

 Corrected QCAA Implementation

Below is the corrected implementation of the QCAA for the race/ethnicity covariate (African American/Black vs. Latine/Hispanic) in Gwadz et al. (2025), following the six-step process.

# Step 1: Define the Scope and Extract Target Variables

- Role of Race: Covariate in logistic regression (Page 8).

- Extracted Values (Table 5, Page 13):

  - β = -0.239 (log odds), OR = 0.788, 95% CI [0.502, 1.237], p = 0.300.

  - SE = (ln(1.237) – ln(0.502)) / (2 × 1.96) = (0.212 – (-0.689)) / 3.92 ≈ 0.2298.

  - CI (log odds) = -0.239 ± 1.96 × 0.2298 ≈ (-0.689, 0.211).

- Output: β = -0.239, SE = 0.2298, CI = (-0.689, 0.211).

# Step 2: Compute Reliability Error

- Assumptions:

  - Race: Self-reported, r = 0.85, EV = 0.15, AF = 1 / √0.85 ≈ 1.085 (Page 2).

  - Outcome: Self-reported testing, r = 0.9, EV = 0.1, AF = 1 / √0.9 ≈ 1.054.

  - Combined AF = 1.085 × 1.054 ≈ 1.144.

- Computations:

  - β_reliability = -0.239 × 1.144 ≈ -0.2734.

  - SE_reliability = 0.2298 × (1 + 0.15 + 0.1)¹/² = 0.2298 × 1.118 ≈ 0.2572.

- Output: β_reliability = -0.2734, SE_reliability = 0.2572.

# Step 3: Compute Validity Error

- Assumptions:

  - Race: Undefined role, r_v = 0.8, VE = 0.2, AF_v = 1 / 0.8 = 1.25 (Page 3).

  - Outcome: Self-reported, r_v = 0.85, VE = 0.15, AF_v = 1 / 0.85 ≈ 1.176.

  - Combined AF_v = 1.25 × 1.176 ≈ 1.47.

- Computations:

  - β_validity = -0.2734 × 1.47 ≈ -0.4019.

  - SE_validity = 0.2572 × (1 + 0.2 + 0.15)¹/² = 0.2572 × 1.162 ≈ 0.2991.

- Output: β_validity = -0.4019, SE_validity = 0.2991.

# Step 4: Compute Internal Validity Error

- Assumptions: Adjusted for age, gender, education, occupation, prior testing (Page 8). Unmeasured confounders (distrust, structural barriers, Page 14) suggest CB = ±25%.

- Computations:

  - β_confounding = -0.4019 × (0.75 to 1.25) ≈ [-0.5024, -0.3014].

  - SE_confounding = 0.2991 × 1.25 ≈ 0.3739.

  - E-value = 0.239 / 0.2298 + √(0.239 / 0.2298 × 0.04) ≈ 1.08.

- Output: β_confounding = [-0.5024, -0.3014], SE_confounding = 0.3739, E-value = 1.08.

# Step 5: Assess External Validity

- Sample: N=438, NYC, frontline workers (Page 4). Regional/occupation-specific, CV = ±10–20% (Page 5).

- Output: Note: β_confounding varies ±10–20%.

# Step 6: Compute Adjusted Coefficient and CI

- Aggregate Errors:

  - EV = 0.15 (race) + 0.1 (outcome) = 0.25.

  - VE = 0.2 (race) + 0.15 (outcome) = 0.35.

  - CB = 0.25.

  - Total Error = (0.25 + 0.35 + 0.25) × 100 = 85%.

- Computations:

  - SE_final = 0.2298 × 1.118 × 1.162 × 1.25 ≈ 0.3739.

  - Midpoint β_confounding = -0.4019.

  - CI = -0.4019 ± 1.96 × 0.3739 ≈ [-1.1348, 0.3310].

  - OR_adjusted = e^(-0.4019) ≈ 0.669, CI_OR = [e^(-1.1348), e^(0.3310)] ≈ [0.321, 1.392].

- Output:

  - Original β (CI): -0.239 (-0.689, 0.211) [OR: 0.788].

  - Adjusted β: -0.4019 [OR: 0.669].

  - Adjusted CI: -1.1348, 0.3310 [OR: 0.321, 1.392].

  - Total Error: 85%.

  - Note: Adjusted for 25% reliability (15% race, 10% outcome), 35% validity (20% race, 15% outcome), ±25% confounding. CV = ±10–20%.

Conclusion

The corrected QCAA implementation reveals significant uncertainty in the race/ethnicity covariate’s effect (β = -0.239, OR = 0.788) due to reliability (25%), validity (35%), and confounding (25%) errors, totaling 85%. The adjusted β (-0.4019, OR = 0.669) and wider CI (-1.1348, 0.3310; OR: 0.321, 1.392) highlight limitations in using race as an undefined covariate, aligning with the CR Framework. The regional sample (CV = ±10–20%) limits generalizability. Researchers should clarify race’s role and adjust for additional confounders (e.g., distrust, SES). This implementation can be integrated into scalable tools, as requested (April 22, 2025, 19:37).