Pilot Statistical Analysis and Sample-Size Justification
MRI-based T1 mapping in chronic liver disease
Aim 2B: Explanted human livers
Statistical analysis. The primary estimand will be the mean bias of SR-CSE T1 relative to the prespecified reference method. A linear mixed-effects model will include method, contrast level, and relevant tissue characteristics as fixed effects and liver as a random effect, thereby accounting for repeated contrast levels, segments, and methods within each liver. Bias and 95% confidence intervals will be reported overall and across the T1 range; Bland–Altman limits of agreement will supplement the model-based results. Associations of R1 with gadolinium concentration will be evaluated in the same framework.
Sample size. This is a technical pilot study emphasizing precision. Treating the 40 livers as the independent units and using the preliminary 3.0T test-retest SD of 18.2 ms as a conservative planning proxy, the 95% confidence interval for mean bias has an approximate half-width of 5.8 ms. This precision is sufficient for pilot purposes to characterize the magnitude of bias and inform the design of a future definitive validation study. Repeated measurements within each liver should further improve precision but are not counted as independent sample-size units.
Aim 3A: Native T1 in MASLD/MASH
Statistical analysis. Whole-liver T1 will be the primary measurement; segment-level results will be supportive. Test-retest data will be analyzed with a mixed-effects variance-components model to estimate within-subject SD and the repeatability coefficient, with Bland–Altman plots for display. Method bias relative to STEAM-MRS and between-protocol reproducibility will be summarized with estimates and 95% confidence intervals. Associations with fibrosis stage will be estimated using regression, with the F0–F1 versus F2–F3 comparison and AUC treated as exploratory. Sex will be included as a covariate; sex-specific estimates will be descriptive because this pilot is not powered for subgroup inference.
Sample size. Forty patients (approximately 20 with F0–F1 and 20 with F2–F3 fibrosis) plus 10 healthy controls will provide pilot estimates of repeatability, between-subject variability, and fibrosis-related effect size. The preliminary F0–F1 versus F2–F4 contrast corresponds to a standardized difference of 0.54; with 20 patients per fibrosis group, its estimated 95% confidence interval would have a half-width of approximately 62 ms. With 40 paired observations, the 95% confidence limits for a repeatability coefficient are approximately 0.82 to 1.28 times its observed value. These data are intended to support planning of a future definitive diagnostic-performance study, not definitive sensitivity or specificity claims.
Aim 3B: Post-contrast T1 in cirrhosis
Statistical analysis. The primary analysis will estimate the Spearman association between a single prespecified biomarker, \(\Delta R1=1/T1_{post}-1/T1_{pre}\), and ICG-R15, with a 95% confidence interval. A regression model will provide an adjusted analysis including prespecified clinical covariates. Other T1- and R1-derived measures, associations with MELD, and comparisons across Child–Pugh groups will be secondary or exploratory. Repeatability and between-protocol reproducibility will be summarized as in Aim 3A.
Sample size. Among 40 patients with cirrhosis, the preliminary correlation of -0.52 corresponds to approximately 93% power for a two-sided test at the 0.05 level using the Fisher-z approximation; correlations of magnitude 0.43 or greater provide at least 80% power. If the observed correlation is -0.52, the approximate 95% confidence interval is -0.71 to -0.24. Ten healthy controls will provide descriptive reference values but are not included in this primary calculation.