Hello Gang, I've two datasets to compare: one is with TR 640 ms, and the other 2.5 sec. It seems that the connectivity (z-score) of the latter is (systemically) lower compared with that of the former.

I happen to notice a paper that addresses the sampling rate problem in rsfMRI analysis:

Impact of sampling rate on statistical significance for single subject fMRI connectivity analysis. Hum Brain Mapp. 2019;40:3321 – 3337.

It seems that fMRI from different TRs cannot be properly compared unless the sampling rate difference is adjusted.

Could you please comment whether "variance correction" is recommended?

If yes, which function should I use? It seems that 3dNetCorr does not have this feature for now.

An associated question: is variance correction procedure applicable for censor-oriented approach (e.g., 3dLombScargle)?

3dLombScargle is related to a specific issue with time sampling: when analyzing resting state data, many resting state functional connectivity (RSFC) parameters use bandpassing as part of their estimation---for example, low frequence fluctuation (LFF) estimation and looking at signals within a restricted frequency band of 0.01-0.1 Hz, say (the exact bands can be flexible). However, performing a Fourier Transform/Series calculation requires having uniformly sampled data, and many FMRI datasets are censored due to motion/data quality. Such censored datasets are no longer uniformly sampled, so the Fourier can't be used there.

The Lomb-Scargle transform is a generalization of Fourier, allowing one to estimate frequencies in the same Nyquist-limited band when there are (non-systematic) differences in sampling rate across time. The theory behind the mathematics and algorithms of this is due to separate groups, mainly in the realm of astrophysical applications: Vaníček (1969, 1971), Lomb (1976), Scargle (1982), and Press & Rybicki (1989).

The case at hand here relates to sampling rate variability in a different way: not to having variability of sampling rate within a subject dataset, but to having different datasets with different sampling rates. I don't think that the Lomb-Scargle approach will be so useful for variance correction per se. I would note that even the Lomb-Scargle estimates have some bias in RSFC parameters as the amount of censoring gets large (say more than 10-20% of the original number of points).

I'll have to look more at the approach you cited from the HBM paper, but I can see different ways that sampling rate would affect things, sure. If the two groups have same overall time of data acquisition but one group has much faster TR, there is an imbalance in the amount of data per subject. The aliasing of physiological effects, such as breathing and heartrate, will be different. Given the different in number of time points (or in degrees of freedom) between the groups, the analytic uncertainty of Pearson correlation measure (i.e., "functional connectivity" in most cases) would be different, since that depends directly on the number of time points.

Hi Paul, many thanks for the comments. Those points all make great sense. Still hope to know how to address the issue of different sampling rate (SR) and data length and so on to facilitate the comparability of different fMRI datasets. Some adjustment that may not be perfect but still much better than none is highly appreciated. In EEG field, people may apply different impulse functions of different brands of EEG amplifers to enhance the comparability (comparing the datasets recorded from different EEG systems). In EEG research, people also used to downsample the data to the same SR. I personally think this issue in MRI field has been inadequately addressed.
No hurry, and thanks again.

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