Empirical single sample quantification of bias and variance in Q-ball imaging

Sample size estimation: Current practice and considerations for original investigations in MRI technical development studies

PURPOSE

To investigate and to provide guidance for sample size selection based on the current practice in MR technical development studies in which healthy volunteers are examined.

METHODS

All original articles published in Magnetic Resonance in Medicine between 2017 and 2019 were investigated and categorized according to technique, anatomical region, and magnetic field strength. The number of examined healthy volunteers (ie, the sample size) was collected and evaluated, whereas the number of patients was not considered. Papers solely measuring patients, animals, phantoms, specimens, or studies using existing data, for example, from an open databank, or consisting only of theoretical work or simulations were excluded.

RESULTS

The median sample size of the 882 included studies was 6. There were some peaks in the sample size distribution (eg, 1, 5, and 10). In 49.9%, 82.1%, and 95.6% of the studies, the sample size was smaller or equal to 5, 10, and 20, respectively.

CONCLUSION

We observed a large variance in sample sizes reflecting the variety of studies published in Magnetic Resonance in Medicine. Therefore, it can be concluded that it is current practice to balance the need for statistical power with the demand to minimize experiments involving healthy humans, often by choosing small sample sizes between 1 and 10. Naturally, this observation does not release an investigator from ensuring that sufficient data are acquired to reach statistical conclusions.

A deep learning approach to estimation of subject-level bias and variance in high angular resolution diffusion imaging

The ability to evaluate empirical diffusion MRI acquisitions for quality and to correct the resulting imaging metrics allows for improved inference and increased replicability. Previous work has shown promise for estimation of bias and variance of generalized fractional anisotropy (GFA) but comes at the price of computational complexity. This paper aims to provide methods for estimating GFA, bias of GFA and standard deviation of GFA quickly and accurately. In order to provide a method for bias and variance estimation that can return results faster than the previously studied statistical techniques, three deep, fully-connected neural networks are developed for GFA, bias of GFA, and standard deviation of GFA. The results of these networks are compared to the observed values of the metrics as well as those fit from the statistical techniques (i.e. Simulation Extrapolation (SIMEX) for bias estimation and wild bootstrap for variance estimation). Our GFA network provides predictions that are closer to the true GFA values than a Q-ball fit of the observed data (root-mean-square error (RMSE) 0.0077 vs 0.0082, p < .001). The bias network also shows statistically significant improvement in comparison to the SIMEX-estimated error of GFA (RMSE 0.0071 vs. 0.01, p < .001).

Evaluation of inter-site bias and variance in diffusion-weighted MRI

An understanding of the bias and variance of diffusion weighted magnetic resonance imaging (DW-MRI) acquisitions across scanners, study sites, or over time is essential for the incorporation of multiple data sources into a single clinical study. Studies that combine samples from various sites may be introducing confounding due to site-specific artifacts and patterns. Differences in bias and variance across sites may render the scans incomparable, and, without correction, any inferences obtained from these data are misleading. We present an analysis of the bias and variance of scans of the same subjects across different sites and evaluate their impact on statistical analyses. In previous work, we presented a simulation extrapolation (SIMEX) technique for bias estimation as well as a wild bootstrap technique for variance estimation in metrics obtained from a Q-ball imaging (QBI) reconstruction of empirical high angular resolution diffusion imaging (HARDI) data. We now apply those techniques to data acquired from 5 healthy volunteers on 3 independent scanners under closely matched acquisition protocols. The bias and variance of GFA measurements were estimated on a voxel-wise basis for each scan and compared across study sites to identify site-specific differences. Further, we provide model recommendations that can be used to determine the extent of the impact of bias and variance as well as aspects of the analysis to account for these differences. We include a decision tree to help researchers determine if model adjustments are necessary based on the bias and variance results.