Sample size and power statement

Author

Kostas Moschonas

This a technical report examining the optimal sample size and resource allocation of the CMR study in patients with Hypertrophic Cardiomyopathy (HCM) receiving mavacamten.

Summary

The aims of this study are to investigate whether mavacamten changes tissue perfusion and myocardial fibrosis. We will conduct paired analysis of HCM patients at baseline, before initiation of mavacamten, and at a pre-specified follow-up interval after mavacamten treatment, which is yet to be determined (between 6 and 12 months).

Myocardial perfusion will be assessed locally, if there are perfusion abnormalities, and globally. To detect a change in global myocardial blood flow (MBF) of 0.3 mL/g/min, with a 5% type I error and 90% power, we need 32 participants. To account for loss of follow-up, missing and suboptimal data, we can aim to recruit 50 participants. This would confer 98% power.

A sample size of 50 would confer enough power to detect a change in LV mass indexed (LVMi) between 5 and 6 g/m2, in late-gadolinium enhancement (LGE) between 1 and 1.5 g, and in extra-cellular volume (ECV) of < 1%.

To detect a change in MBF

Global stress MBF in HCM patients has been reported in two papers from our group to date.

Global stress MBF in HCM patients
Source μ σ N comments
(Hughes et al. 2021) G+LVH+ 1.91 0.6 5 1.5 T
(Joy et al. 2023) G+LVH+ 1.77 0.52 51 3 T
(Joy et al. 2023) G-LVH+ 1.59 0.48 50 3 T
Weighted μ & pooled σ 1.69 0.5 
sample_size_0.3_dif <- pwrss.t.2means(mu1 = weighted_mu, 
                                      mu2 = (weighted_mu - 0.3), 
                                      sd1 = sd_pooled, paired = TRUE, 
                                      paired.r = 0.50, power=0.9, 
                                      alpha = 0.05, alternative = "not equal")
 Difference between Two means 
 (Paired Samples t Test) 
 H0: mu1 = mu2 
 HA: mu1 != mu2 
 ------------------------------ 
  Statistical power = 0.9 
  n = 32 
 ------------------------------ 
 Alternative = "not equal" 
 Degrees of freedom = 31 
 Non-centrality parameter = 3.362 
 Type I error rate = 0.05 
 Type II error rate = 0.1

For a conservative minimally detectable difference in stress MBF of 0.3 mL/g/min before and after treatment with mavacamten, at 90% power, we need 32 participants. To account for loss to follow-up and missing data, we can aim to recruit 50 participants. This way, baseline and follow-up recruitment would last ~6 months each. The follow-up interval has not been determined yet.

Figure 1: This graph shows how statistical power changes with increasing sample size. We reach 98% power with 49 participants. Even considering losses to follow-up and missing/suboptimal data, recruiting 100 participants seems uncessary to detect a change in global stress MBF.

To detect changes in ventricular remodeling

Ventricular remodeling is a rather vague term which includes a number of measures:

  • Wall thickness or LV mass.

  • Fibrosis, measured with LGE and ECV.

  • Myocardial disarray, measured histologically or with cardiac Diffusion Tensor Imaging (cDTI).

LV mass, wall thickness, LGE and ECV have already been reported in a research letter of the CMR sub-study of EXPLORER-HCM (Saberi et al. 2021). It recruited only 35 of the 251 participants in EXPLORER-HCM with essentially no LGE and reported a significant decrease in LV mass index (LMVi) with mavacamten of 15.8 (95% CI, -22.6 to -9.0) g/m2, compared to placebo1, at 30 weeks follow-up. Compared to baseline, mavacamten was associated with a decrease in LVMi of 17.4 (12.1) g/m2. Baseline LVMi is not reported.

LV mass indexed

Therefore, for sample size estimation, a baseline LVMi of 96 (SD 11.4) g/m2 was used, from G-LVH+ HCM patients reported in Joy et al. (2023), with a minimally detectable change of 17.4 (12.1) before and after mavacamten in EXPLORER-HCM. For 90% power, we need only 7 participants. By recruiting ~ 50, we will have enough power to detect changes between 5 and 6 g/m2 (Figure 2).

pwrss.t.2means(mu1 = 96, mu2 = (96-17.4), sd1 = 11.4,
               paired = TRUE, paired.r = 0.50,
               power=0.9, alpha = 0.05,
               alternative = "not equal")
 Difference between Two means 
 (Paired Samples t Test) 
 H0: mu1 = mu2 
 HA: mu1 != mu2 
 ------------------------------ 
  Statistical power = 0.9 
  n = 7 
 ------------------------------ 
 Alternative = "not equal" 
 Degrees of freedom = 6 
 Non-centrality parameter = 4.038 
 Type I error rate = 0.05 
 Type II error rate = 0.1

Figure 2: To detect a decrease in LVMi of \(17.4 ~ {g/m}^2\) as in EXPLORER-HCM, we only need 7 participants. By recruiting ~ 50, we will have enough power to detect changes as small as \(5 ~ {g/m}^2\).

Fibrosis by LGE and ECV

Participants in CMR sub-study of EXPLORER-HCM had only a small amount of LGE and there was no decrease in LGE or ECV with mavacamten. I anticipate more fibrosis in our cohort.

For LGE, using baseline LGE of 6.5 (2.81) g from G-LVH+ patients in Joy et al. (2023), to detect a conservative detectable change of 1.5 g, we need 39 participants.

pwrss.t.2means(mu1 = 6.5, mu2 = (6.5 - 1.5), sd1 = 2.8,
               paired = TRUE, paired.r = 0.50,
               power=0.9, alpha = 0.05,
               alternative = "not equal")
 Difference between Two means 
 (Paired Samples t Test) 
 H0: mu1 = mu2 
 HA: mu1 != mu2 
 ------------------------------ 
  Statistical power = 0.9 
  n = 39 
 ------------------------------ 
 Alternative = "not equal" 
 Degrees of freedom = 38 
 Non-centrality parameter = 3.346 
 Type I error rate = 0.05 
 Type II error rate = 0.1

Similarly, for ECV, using a baseline ECV of 27.1 (1.3) % from G-LVH+ patients in Joy et al. (2023), to detect a 1% change, we need 20 participants.

pwrss.t.2means(mu1 = 27.1, mu2 = (27.1 - 1), sd1 = 1.3,
               paired = TRUE, paired.r = 0.50,
               power=0.9, alpha = 0.05,
               alternative = "not equal")
 Difference between Two means 
 (Paired Samples t Test) 
 H0: mu1 = mu2 
 HA: mu1 != mu2 
 ------------------------------ 
  Statistical power = 0.9 
  n = 20 
 ------------------------------ 
 Alternative = "not equal" 
 Degrees of freedom = 19 
 Non-centrality parameter = 3.44 
 Type I error rate = 0.05 
 Type II error rate = 0.1

Myocardial disarray

Myocardial disarray starts in utero (Garcia-Canadilla et al. 2019), before LVH, and constitutes, to date, the earliest detectable abnormality of HCM at the cellular level. Mavacamten has been shown to improve cardiomyocute alignment in mice only without LVH, but not after LVH is established (Green et al. 2016). Therefore, there is no reason to suspect that mavacamten would improve disarray in our cohort of patients with advanced, symptomatic, HCM who are awaiting septal reduction surgery.

References

Garcia-Canadilla, Patricia, Andrew C. Cook, Timothy J. Mohun, Onyedikachi Oji, Saskia Schlossarek, Lucie Carrier, William J. McKenna, James C. Moon, and Gabriella Captur. 2019. “Myoarchitectural Disarray of Hypertrophic Cardiomyopathy Begins Pre-Birth.” Journal of Anatomy 235 (5): 962–76. https://doi.org/10.1111/joa.13058.
Green, Eric M., Hiroko Wakimoto, Robert L. Anderson, Marc J. Evanchik, Joshua M. Gorham, Brooke C. Harrison, Marcus Henze, et al. 2016. “A Small-Molecule Inhibitor of Sarcomere Contractility Suppresses Hypertrophic Cardiomyopathy in Mice.” Science 351 (6273): 617–21. https://doi.org/10.1126/science.aad3456.
Hughes, Rebecca K., Claudia Camaioni, João B. Augusto, Kristopher Knott, Ellie Quinn, Gabriella Captur, Andreas Seraphim, et al. 2021. “Myocardial Perfusion Defects in Hypertrophic Cardiomyopathy Mutation Carriers.” Journal of the American Heart Association 10 (15): e020227. https://doi.org/10.1161/JAHA.120.020227.
Joy, George, Christopher I. Kelly, Matthew Webber, Iain Pierce, Irvin Teh, Louise McGrath, Paula Velazquez, et al. 2023. “Microstructural and Microvascular Phenotype of Sarcomere Mutation Carriers and Overt Hypertrophic Cardiomyopathy.” Circulation 148 (10): 808–18. https://doi.org/10.1161/CIRCULATIONAHA.123.063835.
Saberi, Sara, Nuno Cardim, Mohamad Yamani, Jeanette Schulz-Menger, Wanying Li, Victoria Florea, Amy J. Sehnert, et al. 2021. “Mavacamten Favorably Impacts Cardiac Structure in Obstructive Hypertrophic Cardiomyopathy.” Circulation 143 (6): 606–8. https://doi.org/10.1161/CIRCULATIONAHA.120.052359.

Footnotes

  1. The spread of change in LVMi and wall thickness in the placebo group, at 30 weeks, is rather large, which may be attributed to measurement variability. At 30 weeks, LVMi decreased by -1.6 g/m2 but with a SD of 7.4 g/m2 and thickness by ~0.5-1 mm, with a 95% CI of ~ -3 to +3.5 to 4 mm (only present in a figure). Our automated AI measurement may address this issue.↩︎