MRI-based Quantification of Perfusion and Microstructure

Sample size and power considerations

Detection of fibrosis

Read data from Ren et al. (2024):

Fibrosis	N	Dslow_Mean	Dslow_SD	Dfast_Mean	Dfast_SD	F_Mean	F_SD
0	13	0.623	0.146	65.361	10.605	0.413	0.086
1	27	0.551	0.149	62.099	8.433	0.393	0.062
2	23	0.584	0.104	58.070	8.724	0.345	0.061
3	25	0.602	0.150	52.355	7.462	0.312	0.072
4	18	0.707	0.214	42.871	8.422	0.291	0.058

• Group 1 (F0–1): F0 => 13 obs, F1 => 27 obs, total 40
• Group 2 (F2–3): F2 => 23 obs, F3 => 25 obs, total 48
• Group 3 (F4): F4 => 18 obs

Hence the ratio is 40 : 48 : 18 (sum = 106).

Keep this ratio and calculate sample size based on one-way ANOVA for each parameter.

Dslow

Dslow: Group-wise means and SDs

Group	N	Mean	SD
G1_F0_1	40	0.574400	0.1500861
G2_F2_3	48	0.593375	0.1289758
G3_F4	18	0.707000	0.2140000

• For 80% power, total \(n=\) 106;
• For 90% power, total \(n=\) 137.

Dfast

Dfast: Group-wise means and SDs

Group	N	Mean	SD
G1_F0_1	40	63.15915	9.187459
G2_F2_3	48	55.09344	8.507805
G3_F4	18	42.87100	8.422000

[1] 8.757669

• For 80% power, total \(n=\) 22;
• For 90% power, total \(n=\) 24.

F

F: Group-wise means and SDs

Group	N	Mean	SD
G1_F0_1	40	0.3995000	0.0702023
G2_F2_3	48	0.3278125	0.0683114
G3_F4	18	0.2910000	0.0580000

• For 80% power, total \(n=\) 30;
• For 90% power, total \(n=\) 36.

Conclusion

The total sample size needed based on each parameter is listed below:

Power	N (Dslow)	N (Dfast)	N (F)
80%	106	22	30
90%	137	24	36

Meal challenge

We will estimate the required sample size to detect a difference in mean post‐meal \((Vb)\) increase (absolute \(\Delta V_b\)) between healthy individuals and portal‐hypertensive patients. Based on the pilot data:

• Healthy mean \(\Delta V_b\) ≈ 0.43 mm/s
  
• Portal‐HTN mean \(\Delta V_b\) ≈ 0.07 mm/s
  
• Thus, δ = 0.36 mm/s (difference in means)
  
• Common standard deviation \(\sigma\) = 0.27 mm/s

We set α = 0.05 (two‐sided) and aim for 80%/90% power.

• For 80% power, 10 in each group;
• For 90% power, 13 in each group.

     Two-sample t test power calculation 

              n = 9.889048
              d = 1.333333
      sig.level = 0.05
          power = 0.8
    alternative = two.sided

NOTE: n is number in *each* group

     Two-sample t test power calculation 

              n = 12.86184
              d = 1.333333
      sig.level = 0.05
          power = 0.9
    alternative = two.sided

NOTE: n is number in *each* group

References

Ren, Hao, Hui Xu, Dawei Yang, Xiaofei Tong, Xinyan Zhao, Qianyi Wang, Yameng Sun, et al. 2024. “Intravoxel Incoherent Motion Assessment of Liver Fibrosis Staging in MASLD.” Abdominal Radiology, March. https://doi.org/10.1007/s00261-024-04207-w.