KETO-CTA Study

An Audit with the Actual Data

John | The John & Calvin Podcast

Dataset of Plaque Metrics

Longitudinal Data From the KETO-CTA Study: Plaque Predicts Plaque, ApoB Does Not


Plaque Data released by organization funding the study:

https://citizensciencefoundation.org/keto-cta/

No cholesterol (ApoB), demographic or other clinical data


All code, figures, data, studies available at:

https://github.com/SloughJE/keto_cta_analysis_check

Incorrect Figure 1B

Figure 1B from Study

Figure 1B from Data

Individual Change in Plaque Volume

(B) The red line represents the median change (0.8%), and the shaded area represents the IQR (0.3%-1.7%).

Incorrect Figure 1A

Figure 1A from Study

Figure 1A from Data

Individual Change in Plaque Volume

(A). The red line represents the median change (18.9 mm3), and the shaded area represents the IQR (9.3-47.0 mm3).

Incorrect Figures 2D, 2E, 2F

Figure 2F from Study

Figure 2F from Data

Changes in Total Plaque Score vs Coronary Artery Calcium

(C, F) Only CAC is associated with changes in NCPV and TPS. The regression line was fitted with the function “lm,” which regresses y~x, and the shaded area represents the standard error.

Linear Model Assumptions

4 Simple Linear Regression Assumptions

3 are tested with data (in this situation)

  • Linearity: between the predictor and the outcome

  • Constant variance (homoscedasticity) of residuals

  • Normally distributed residuals

These linear assumptions are quantifiable and objectively testable.

  • If the assumptions don’t hold, statistical significance and uncertainty estimates aren’t trustworthy
  • Results may be invalid

Visual checks are standard first step; sometimes preferable in very small or very large samples.

Here I focus on the tests because they give a clear yes/no answer.
With n = 100, they’re generally reliable and well-calibrated, not overly sensitive.

LM Assumptions (claims vs tests)

“all linear model assumptions were corroborated with the R function performance::check_model.”

- Direct quote from the study

Actual Linear Model Assumption Tests

Model β Linearity Constant Variance Residual Normality
ΔNCPV ~ CACbl β = 0.18
p = <0.001		 Violation
p = 0.031		 Violation
p = 0.001		 Violation
p = <0.001
ΔNCPV ~ NCPVbl β = 0.25
p = <0.001		 OK
p = 0.198		 Violation
p = <0.001		 Violation
p = <0.001
ΔNCPV ~ PAVbl β = 5.48
p = <0.001		 Borderline
p = 0.050		 Violation
p = <0.001		 Violation
p = <0.001
ΔNCPV ~ TPSbl β = 7.37
p = <0.001		 OK
p = 0.132		 Violation
p = <0.001		 Violation
p = 0.001

Objective tests show all 4 models failed at least 2 tests each.

Letter to Editor and Response

“The validity of the regression models is also questionable. Despite claims of meeting assumptions, variables were reported using medians, suggesting non-normal distributions. Visual inspection of scatter plots shows clustering and no clear linear trends. Robust or nonparametric methods might have been more appropriate, and model diagnostics would improve transparency.”

- quote from letter to the editor

“we are aware of the relevance of linear assumptions to obtain accurate estimators. Because residual plot evaluation can also be subjective, we followed their suggestion and reran all models with robust linear regression (using the MASS::rlm function in R version 4.4.3 [R Foundation]). While, as expected, there were small differences with the published estimates, all models using robust regression were consistent with what was reported.”

- quote from the reply to a letter to the editor

“residual plot evaluation can also be subjective”

- quote from the reply to a letter to the editor

“we are aware of the relevance of linear assumptions to obtain accurate estimators. Because residual plot evaluation can also be subjective, we followed their suggestion and reran all models with robust linear regression (using the MASS::rlm function in R version 4.4.3 [R Foundation]). While, as expected, there were small differences with the published estimates, all models using robust regression were consistent with what was reported.”

- quote from the reply to a letter to the editor

LM Assumptions: Objective Tests

  • Calling residual plot evaluation “subjective” is evasive.

  • Visual checks are interpretive, but these assumptions are objectively testable with quantifiable methods.

  • Just show the diagnostics.


  • “reran all models with robust linear regression…MASS::rlm”
  • Robust Linear Regression mainly just down-weights outliers.
  • Does not deal with non-linearity, heteroskedasticity and non-normality of residuals.



check_model output:



check_model output:



check_model output:



check_model output:

Conclusions Without Supporting Models

“CONCLUSIONS In lean metabolically healthy people on KD, neither total exposure nor changes in baseline levels of ApoB and LDL-C were associated with changes in plaque.”

“there is no association between NCPV vs LDL-C or ApoB and TPS vs LDL-C or ApoB.”


Abstract claim component Model Model reported
Δ-plaque vs ΔLDL-C Δ-NCPV ~ ΔLDL-C Not reported
Δ-plaque vs LDL-C exposure Δ-NCPV ~ LDL-C exposure Not reported
Δ-plaque vs LDL-C baseline Δ-NCPV ~ LDL-C baseline Not reported
Δ-plaque vs ΔApoB Δ-NCPV ~ ΔApoB Reported
Δ-plaque vs ApoB exposure Δ-NCPV ~ ApoB exposure Not reported
Δ-plaque vs ApoB baseline Δ-NCPV ~ ΔApoB Reported
N/A NCPV_final ~ LDL-C exposure Reported (NCPV_final, PAV_final)

Missing TPS Models and Results

“Results Neither change in ApoB …, baseline ApoB, nor total LDL-C exposure … were associated with the change in noncalcified plaque volume (NCPV) or TPS.”

“Neither … change in ApoB nor the ApoB level … were associated … with TPS (Figures 2D and 2E, Table 3).” - “changes in and baseline levels of ApoB were not associated with changes in NCPV or TPS”


Figures 2D–2F are Δ-TPS (outcome) panels (vs ΔApoB, ApoB, CAC_bl)


Table 3 Model Results has no Δ-TPS models

No Δ-TPS ~ LDL-C, LDL-C exposure, or ApoB model results anywhere.

TPS association with CAC

“CAC is associated with changes in NCPV and TPS”


\(\Delta \text{TPS} \sim \text{CAC}_{\text{baseline}}\)

β (95% CI) P Value R² adj
0.002 (-0.0004, 0.0038) 0.11 0.016


CAC is not associated with \(\Delta\)TPS

Figure 2F from Data

Changes in Total Plaque Score vs Coronary Artery Calcium

(C, F) Only CAC is associated with changes in NCPV and TPS. The regression line was fitted with the function “lm,” which regresses y~x, and the shaded area represents the standard error.

Bayes Factor rscale is not Moderate

“Bayes factors were calculated…with…an ~ rscale value of 0.8 to contrast a moderately informative prior with a conservative distribution width (to allow for potential large effect sizes) due to the well-documented association between ApoB changes and coronary plaque changes.”

Calling rscale = 0.8 “moderately informative” is inaccurate.

R package docs: “medium”, “wide”, “ultrawide” = 0.354, 0.5, 0.707

  • rscaleCont = 0.8 is wider than “ultrawide”
  • substantial evidence needed to show a non-null effect
  • Same r-scale apparently used for all models. No sensitivity analysis on r-scale.

“the addition of Bayesian inference adds credence to finding that there is no association between NCPV vs LDL-C or ApoB and TPS vs LDL-C or ApoB”

  • only “justification” for Bayesian modeling
  • no indication of prespecification

LDL-C Exposure Calculation

“LDL-C exposure on a KD was calculated by summing the products of the reported days on a KD prior to study commencement and baseline LDL-C on a KD plus the study follow-up days by their final LDL-C.”

\[ \text{LDL-C}_{\text{exp}} = Days_{\text{KD}}\cdot LDL_{\text{baseline}} \;+\; Days_{\text{follow-up}}\cdot LDL_{\text{final}} \]


  • one baseline value for all pre-study Keto Diet time and one final value for all follow-up is a coarse simplification
  • relies on recall of KD start
  • standard AUC/time-weighted approach (need multiple measurements)
  • limitation due to resources

Lifetime LDL-C Formula Doesn’t Add Up

“LDL-C exposure on a KD was calculated by summing the products of the reported days on a KD prior to study commencement and baseline LDL-C on a KD plus the study follow-up days by their final LDL-C.”

\[ \text{LDL-C}_{\text{exp}} = Days_{\text{KD}}\cdot LDL_{\text{baseline}} \;+\; Days_{\text{follow-up}}\cdot LDL_{\text{final}} \]

“Estimated lifelong LDL-C additionally included the product of age upon commencing a KD and pre-KD LDL-C.”

\[ \text{Life-LDL-C}_{\text{exp}} = Days_{\text{KD}}\cdot LDL_{\text{baseline}} \;+\; Days_{\text{follow-up}}\cdot LDL_{\text{final}} \;+\; \boldsymbol{\big( Age_{\text{at-KD-start}}\cdot LDL_{\text{pre-KD}} \big)} \]

  • This equation is dimensionally inconsistent.
  • It adds days and age together. It’s like adding miles and inches.
  • pre-KD term is down-scaled by ~365× relative to the day-based terms.
  • any associations with outcomes are dominated by keto diet exposure.
  • if they did convert age, “lifetime” exposure just reflects how old someone was at KD

This isn’t an Age Mediation Analysis

“Estimated lifetime LDL-C exposure was only a significant predictor of final NCPV in the univariable analysis but lost significance when age was included as a covariate (Table 3). Both age and lifetime LDL-C exposure lost significance when baseline CAC was included in the model (Table 3).”

A mediation analysis is a specific statistical method that:

  • tests how an exposure affects an outcome through a middle step (the mediator)
  • estimates an indirect effect (through the mediator) and a direct effect (everything else).
  • requires a pre-specified pathway and proper statistical testing (usually with CIs or bootstraps).

This is not a mediation analysis.

  • No indirect effect was estimated or tested. No causal model specified.
  • Age can’t be a mediator of LDL exposure (age isn’t caused by LDL); it’s a confounder.
  • They only compared p-values after adding variables.

This isn’t an Age Mediation Analysis

“Estimated lifetime LDL-C exposure was only a significant predictor of final NCPV in the univariable analysis but lost significance when age was included as a covariate (Table 3). Both age and lifetime LDL-C exposure lost significance when baseline CAC was included in the model (Table 3).”

They ran (reported) three regressions with sequential covariate adjustment and concluded:

after adjusting for baseline CAC, neither age nor lifetime LDL-C predicts NCPV_final.

- CAC explains the association; age / lifetime LDL-exposure don’t matter.

“Loses significance” ≠ mediation. Collinearity since lifetime LDL-C embeds age.

Age is a common cause/proxy of both lifetime LDL-C exposure and NCPV. It’s a confounder, not a mediator.


Adding baseline CAC (a downstream variable) blocks the mediation pathway and biases effects.


They did NOT report NCPV_final ~ lifetime LDL-C exposure.

Nonstandard Percent Change

“The median change in NCPV was 18.9 mm3 (IQR: 9.3-47.0 mm³) and the median change in PAV was 0.8% (IQR: 0.3%-1.7%). Compared to baseline, these represent a 43% and 50% change, respectively.”

Standard percent change: \(\operatorname{median}\!\left(\frac{NCPV_{1y}-NCPV_{bl}}{NCPV_{bl}}\right)\times 100\%\)

“What was the typical relative change per subject?”


They computed a ratio of median change to baseline median: \(\frac{\operatorname{median}(NCPV_{1y}-NCPV_{bl})}{\operatorname{median}(NCPV_{bl})}\times 100\%\)

  • NCPV: \(18.9/44 \approx 43\%\); and PAV: \(0.8/1.6 \approx 50\%\)


Standard percent change vs. reported ratio-of-medians:

Outcome “ratio-of-medians” Median % change Mean % change
NCPV 43% 49.2% 81.4%
PAV 50% 47.3% 80.7%


Likely chosen because some baselines were zero.

Their “percent change” metric is nonstandard and should be labeled and justified.

Univariable Change Models Can Mislead

“Linear models on the primary (NCPV) and secondary outcomes were univariable”

All conclusions based on independent univariable change score models

Δ-NCPV ~ ApoB; Δ-NCPV ~ NCPV_baseline

  • Basic confounding unchecked (age, sex, BP)
  • Δ-NCPV contains baseline NCPV, biasing associations (mathematical coupling)
  • Δ results in less power, compounded noise
  • ignores starting plaque
  • baseline imbalance and shared correlates can increase, reduce, or even reverse associations

Consensus in biostatistics: use baseline-adjusted regression, ANCOVA style model: follow-up ~ baseline + covariates for analyses.

NCPV_follow-up ~ NCPV_baseline + ApoB_baseline + age + sex

ANCOVA Answers Relevant Question

ΔNCPV ~ ApoB_baseline (unadjusted change score)

Question: Among all participants, is baseline ApoB associated with the raw change in plaque over 1 year, without accounting for where people started or other factors?

Slope interpretation: Average difference in change (mm³) per 1 mg/dL higher ApoB, unadjusted.

Clinically limited: Doesn’t condition on starting plaque, age, sex, BP; easily distorted by baseline differences and extra noise in change scores.
It doesn’t tell an individual with given baseline/risk profile what their 1-year plaque will be.


NCPV_follow-up ~ NCPV_baseline + ApoB_baseline + age + sex (ANCOVA)

Question: Among people with the same starting plaque, age, and sex, do those with higher ApoB tend to have more plaque in 1 year?

Slope interpretation: Expected difference in 1-year NCPV (mm³) per 1 mg/dL higher ApoB, holding baseline NCPV and covariates fixed.

Clinically relevant: What a patient wants to know; “Given where I start and my risk factors, does higher ApoB mean more plaque next year, and by how much?”

Univariable Models are not the Norm

CCTA plaque-progression studies — model types & links

Study Author Model
Association of Statin Treatment With Progression of Coronary Atherosclerotic Plaque Composition van Rosendael Linear mixed-effects regression with a random intercept; baseline plaque volume included (with statin×baseline interaction).
Longitudinal Quantitative Assessment of Coronary Atherosclerotic Plaque Burden Related to Serum Hemoglobin Levels Won Multiple linear regression (annualized change) and logistic regression; adjusted including baseline total plaque volume.
Association of Cardiovascular Disease Risk Factor Burden With Progression of Coronary Atherosclerosis Han Multivariable linear regression of annualized PAV change; adjusted including baseline PAV; logistic for incident adverse plaque.
Assessment of Coronary Plaque Progression in Coronary CT Angiography Using a Semi-Quantitative Score Lehman Longitudinal regression (multivariable); adjusted for age, sex, and follow-up interval; baseline plaque presence included as a predictor.
The impact of baseline calcified plaque volume on coronary rapid plaque progression by serial coronary computed tomography angiography in patients with type 2 diabetes Jian Multivariable logistic regression for rapid plaque progression (binary) with odds ratios; adjusted for baseline variables; baseline calcified plaque volume as key predictor.
Comparison of mineral oil and non-mineral oil placebo on coronary plaque progression by coronary computed tomography angiography Lakshmanan Analysis of covariance (ANCOVA) comparing plaque progression rates; final model adjusted for baseline plaque volume.
Polygenic Risk Is Associated With Long-Term Coronary Plaque Progression and High-Risk Plaque Nurmohamed Linear mixed-effects models for plaque progression (change in PAV and % noncalcified plaque) adjusted including baseline plaque volume and conventional risk factors; logistic regression for HRP presence at baseline and follow-up.

The Norm: ANCOVA

  • Observational (pre–post) studies almost always include baseline plaque when modeling progression. Not doing so risks confounding and regression to the mean (baseline imbalance).

  • In RCTs randomization handles bias on average, but ANCOVA still gives cleaner, more precise estimates; it’s the usual choice.

  • Baseline adjustment with change scores (Δ)?
    • Better than not including it, ANCOVA still preferred
    • Compounds measurement error, noisier and more biased

ΔNCPV vs Follow-up NCPV

β (95% CI) P Value R² adj
0.251 (0.200, 0.302) <0.001 0.488

β (95% CI) P Value R² adj
1.251 (1.200, 1.302) <0.001 0.960

ΔNCPV vs Follow-up NCPV

β (95% CI) P Value R² adj
5.483 (4.224, 6.741) <0.001 0.427

β (95% CI) P Value R² adj
26.569 (23.864, 29.273) <0.001 0.793

ΔNCPV vs Follow-up NCPV

β (95% CI) P Value R² adj
0.181 (0.130, 0.232) <0.001 0.330

β (95% CI) P Value R² adj
0.764 (0.600, 0.927) <0.001 0.462

ΔNCPV vs Follow-up NCPV

β (95% CI) P Value R² adj
7.371 (5.453, 9.288) <0.001 0.366

β (95% CI) P Value R² adj
31.924 (26.098, 37.749) <0.001 0.542

Low R² = No Association!

But consider the Partial R²

NCPV_follow-up ~ NCPV_baseline + ApoB

  • R² is the fraction of total variance explained by the model

  • Baseline R²: % of variation explained baseline-only model, very high due to serial (auto)correlation

  • Partial R²: % of the remaining variation explained by another covariate(s) (e.g., ApoB)

If baseline explains a lot, a small R² can still be a large share of what’s explainable beyond baseline.

  • Clinical ≠ high R²: small effects add up over time and can still push patients past treatment thresholds and risk classification
  • Baseline R² ≈ 0.96: 96% of follow-up NCPV variance is explained by baseline NCPV.
  • Residual R² after baseline: 4% (for risk factors + measurement error + noise)
  • ApoB effect: ΔR² ≈ 0.02 ⇒ Partial R² (ApoB | baseline) = 0.02 / 0.04 = 0.50
  • ApoB explains 50% of the variance remaining after baseline.

“Plaque predicts plaque; ApoB does not” is a consequence of study design and model choice.

R² metrics are seldom shown here

Total/adjusted/partial R²: common in simple linear models; not standard for more advanced models

There isn’t one standard R² (beyond ordinary linear regression)

  • Model dependence & collinearity: partial R² unstable.
  • Small samples: partial R² can be very noisy
  • Mixed model families: GLM/mixed/hurdle lack a single standard R²
  • Plaque progression convention: report \(\beta\)/OR with 95% CI and p-values.
  • Clinical interpretability: “Δ outcome per 10 mg/dL ApoB” (not R²)

Example: Each 10 mg/dL higher ApoB is associated with a +0.25 percentage-point increase in plaque progression.

In this study, models violate OLS assumptions: R² can be high or low for the wrong reasons, misrepresenting model adequacy.

Weakest model choice


  • Among reasonable ways to test an ApoB~plaque association

    • with two timepoints, with this dataset


  • ΔNCPV ∼ ApoB is the weakest plausible choice

\(\Delta\)NCPV ~ \(\Delta\)ApoB                \(\Delta\)NCPV ~ ApoB

\(\Delta\)NCPV ~ \(\Delta\)ApoB: \(\beta\) = 0.01, P Value = 0.91            \(\Delta\)NCPV ~ ApoB: \(\beta\) = 0.06, P Value = 0.33

“changes in and baseline levels of ApoB were not associated with changes in NCPV”

  • Claim of “no association” is overstated.

  • Slope of \(\beta\) = 0.06 still allows clinically non-trivial increases.

  • Wide uncertainty? effects compatible with zero or clinically meaningful increases.

  • Correct interpretation: inconclusive, not null.

  • They do not report CI of \(\beta\).

Conclusions

  1. Claims and charts contradict the data.

  2. Multiple conclusions lack supporting analyses/results.

  3. Some metrics are nonstandard or conceptually unsound.

  4. “Assumptions corroborated”.
    — FALSE. Model assumptions were violated.

  5. The model results are invalid.

  6. Proper and relevant analysis is baseline-adjusted ANCOVA.

Miscellaneous issues

Location Study Text Issue
Figure 1 caption “…the shaded area represents the IQR (9.3-47.0 mm³)…” Imprecise. The quoted IQR is the ΔNCPV IQR; shaded band is 25th–75th percentile band at baseline and 1-year.
Figures 2D–F Caption “(D to F) Change in ApoB, baseline ApoB, and baseline CAC vs NCPV.” Axes/legend appear to be TPS, not NCPV → label/data mismatch
Table 3 caption “R² = squared correlation coefficient (explained variability).” Reports negative values, must be adjusted R²
Table 3 β = 0.18 No reporting of CIs for β.
KD Duration Table 1 vs Table 3 KD duration mean 1,642.7 days (≈4.5 y) vs caption “LDL-C exposure … mean 5.7 y.” Inconsistent durations.
KD Duration Abstract vs Table 1 LDL-C exposure median 1,302 d (984–1,754) vs KD duration median 1,427 d (1,002–1,938). Metrics conflated. exposure should be in units like mg/dL·days, not days.
Table 1 (Total cholesterol) Median 338, IQR (301–337). Impossible IQR (Q3 < median)
Follow-up Characteristics? Baseline table provided. No follow-up characteristics table. ApoB significantly changed in 1 year. Did LDL? Are participants still “LMHR”?
multiple “changes in baseline levels” Baseline doesn’t change.
Software statement “using R 4.0.3 (2020)… with the last available version for Sept 2024.” Unclear what version was used.
Central Illustration shows \(\Delta\)TPS ~ ApoB as main chart Why? Not primary outcome. TPS model results not reported
Central Illustration (quote) “Neither total exposure nor changes in baseline levels of ApoB and mg/dL were associated with changes in plaque. Conversely, baseline plaque but ApoB was not associated…” Incoherent/grammatical errors
Main text (Results/Discussion) “…baseline values magnify their percentual changes…” percent change or percentage-point change
“Prediction” vs “Association Study interchangably uses Prediction and Association Prediction ≠ Association in statistics. Prediction needs out-of-sample validation
Change on Change Regressions \(\Delta\)NVPC ~ \(\Delta\)ApoB I cannot understand why they would even test this.

Preprint vs Published: What Changed

Pre-print title: Plaque Begets Plaque, ApoB Does Not; Longitudinal Data From the KETO-CTA Trial

Published title: Longitudinal Data From the KETO-CTA Study; Plaque Predicts Plaque, ApoB Does Not

In text: find and replace ‘begets’ with ‘predicts’.


Description of main figure, and primary outcome:

“Most participants presented with stable NCPV (Figures 1A and 1B), with 1 participant exhibiting a decrease in NCPV (Figures 2A to 2C) and 6 participants showing decreases in TPS scores over 1 year”

Removed and replaced with:

“The median change in NCPV was 18.9 mm3 (IQR: 9.3-47.0 mm3) and the median change in PAV was 0.8% (IQR: 0.3%-1.7%). Compared to baseline, these represent a 43% and 50% change, respectively.”


In CONCLUSIONS section: “In an exploratory analysis, changes in and baseline levels of ApoB were not associated with changes in NCPV or TPS…”

“exploratory” added in published version. Only mention in entire paper.


Table 1 median (Q1–Q3) PAV at baseline changed from 1.25% (0.5–3.6) to 1.6% (0.5–4.9).

Record of pre-print is unavailable. All links go to new version. It is available here.

Appendix: Plaque Metrics

Baseline, follow-up, and paired change in plaque metrics at 1 year
Metric N1
Median (Q1–Q3)
Mean ± SD
Baseline Follow-up Change2 Baseline Follow-up Change2
Noncalcified plaque volume (mm³) 100 44.0 (15.5–102.2) 66.0 (25.2–163.2) 18.8 (9.3–46.6) 75.9 ± 88.3 107.4 ± 112.7 31.5 ± 31.5
Coronary artery calcium score 100 0.0 (0.0–54.2) 0.0 (0.0–56.0) 0.0 (0.0–5.0) 50.3 ± 100.9 58.8 ± 120.4 8.5 ± 25.5
Percent atheroma volume (%) 100 1.6 (0.5–5.0) 2.6 (1.0–6.8) 0.8 (0.3–1.7) 3.2 ± 3.8 4.4 ± 4.6 1.2 ± 1.2
Total plaque score 100 0.0 (0.0–2.2) 1.0 (0.0–3.0) 0.0 (0.0–1.0) 1.7 ± 2.6 2.2 ± 3.0 0.5 ± 1.1
Calcified plaque volume (mm³) 100 0.3 (0.0–19.8) 0.9 (0.0–24.2) 0.5 (0.0–4.2) 18.7 ± 37.4 22.7 ± 42.5 4.0 ± 7.4
1 N = number of paired scans per metric.
2 Change = follow-up − baseline, summarized across participants.
Relative percent change from baseline to follow-up in plaque metrics at 1 year
Metric N (nonzero baseline)2
Percent change from baseline1
Median (Q1–Q3) Mean ± SD
Noncalcified plaque volume (mm³) 96 49.2 (26.0–104.4) 81.4 ± 85.5
Coronary artery calcium score 43 15.6 (1.8–45.7) 23.4 ± 56.6
Percent atheroma volume (%) 96 47.3 (25.9–100.0) 80.7 ± 86.3
Total plaque score 47 25.0 (0.0–50.0) 33.0 ± 77.4
Calcified plaque volume (mm³) 56 25.9 (10.8–64.7) 60.9 ± 104.2
1 Percent change = (follow-up − baseline) / baseline × 100; calculated per participant and summarized across participants.
2 N counts participants with a nonzero baseline for the metric.
Zeros, incidence (0→>0), and resolution (>0→0) by metric
Metric N Baseline = 0 Follow-up = 0 0 → >0 >0 → 0
Noncalcified plaque volume (mm³) 100 4 1 3 0
Coronary artery calcium score 100 57 54 6 3
Percent atheroma volume (%) 100 4 1 3 0
Total plaque score 100 53 46 10 3
Calcified plaque volume (mm³) 100 44 27 18 1
Percent change from baseline to follow-up: medians and trimmed mean
Metric N2 N baseline > 02
Median (Q1–Q3) % change1
Trimmed mean, 10%3
Overall (offset) Baseline > 0
Noncalcified plaque volume (mm³) 100 96 44.9 (23.7–77.8) 49.2 (26.0–104.4) 51.0
Coronary artery calcium score 100 43 0.0 (0.0–13.4) 15.6 (1.8–45.7) 5.1
Percent atheroma volume (%) 100 96 33.3 (19.9–56.3) 47.3 (25.9–100.0) 37.8
Total plaque score 100 47 0.0 (0.0–14.3) 25.0 (0.0–50.0) 5.0
Calcified plaque volume (mm³) 100 56 4.1 (0.0–18.1) 25.9 (10.8–64.7) 9.1
1 Overall % change = ((follow-up + c)/(baseline + c) - 1) × 100. BL>0 % change = ((follow-up - baseline)/baseline) × 100. c = 0.5 × the 5th percentile of non-zero values across visits for that metric, with floors: percentages 0.5; CAC 10; volumes 5. Positive values indicate increase vs baseline; negative indicate decrease.
2 N = paired participants; N baseline > 0 = number with nonzero baseline.
3 Trimmed mean removes 10% from each tail before averaging; computed on the Overall (offset) % change.

Plaque Metrics Charts

Plaque Baseline and Follow-up metrics are highly correlated


Follow-up NCPV was modeled as a linear function of baseline NCPV using generalized least squares (GLS): \(Y_i=\beta_0+\beta_1 X_i+\varepsilon_i\), with a power-of-the-mean residual variance \(\operatorname{Var}(\varepsilon_i)=\sigma^2\lvert\mu_i\rvert^{2\delta}\) (nlme varPower), where \(\mu_i=\mathbb{E}[Y_i\mid X_i]\).

Candidate variance structures (same fixed effects) were compared by likelihood-ratio tests under maximum likelihood.

The selected structure was refit by restricted maximum likelihood (REML) for parameter estimates and uncertainty.

Pointwise 95% confidence bands for \(\mathbb{E}[Y\mid X]\) were obtained from the model-based covariance of the fitted mean.

Fit statistics (REML): AIC = 874.15; BIC = 884.49; \(\log L=-433.08\)

Variance function: \(\hat\delta=0.526\) (95% CI 0.357–0.695)

Residual SD: \(2.097\) (df = 98; 95% CI 1.029–4.273)

Term Estimate 95% CI p-value
Intercept 8.547 5.504 to 11.590 <0.001
Baseline NCPV 1.304 1.231 to 1.378 <0.001

Robustness check (OLS with HC3 SEs): \(\hat\beta_1=1.251\) (SE 0.041), \(p<0.001\), consistent with the GLS slope

Diagnostics were acceptable: on the normalized GLS scale residuals were approximately homoscedastic and centered, with only mild tail departures; inferences were robust to tail behavior (HC3-robust SEs and pairs bootstrap CIs).

Plaque Baseline and Follow-up metrics are highly correlated


R² (baseline → follow-up, with linear mean): Baseline alone explains ≈ 96% of the variation (GLS weighted “R²” ≈ 93%) in follow-up values. Only ~4% (or 7%) is left after accounting for baseline.

ICC = Intraclass Correlation Coefficient — Proportion of total variance due to differences between people (vs within-person change).

ICC ≈ 0.91: about 91% of variability is between individuals; within-person year-to-year change is small.

This is Autocorrelation, more specifically serial (auto)correlation, or within-person persistence, not insight. Baseline plaque “predicts” follow-up mainly because the measure is relatively stable over time (high R², high ICC).

If we use baseline-adjusted regression, we could answer the question: “What explains the extra change beyond baseline?”

baseline-adjusted model (ANCOVA):

Follow-up ~ Baseline + ApoB (+ covariates)

– Test ApoB’s incremental value (partial F-test / ΔR²)

– still need to check model assumptions

Effect modification check:

Follow-up ~ Baseline + ApoB + (+ covariates) + Baseline*ApoB

– If the interaction is non-significant, ApoB’s association with follow-up does not depend on baseline level.