A Novel Method to Use Coordinate Based Meta-Analysis to Determine a Prior Distribution for Voxelwise Bayesian Second-Level fMRI Analysis

Round 1

Reviewer 1 Report

The comments for authors are exist in the attached file

Comments for author File: Comments.pdf

Author Response

1. Why only Cauchy distribution has been used in Bayesian analysis.

Response: Thank you very much for your comment about the rationale regarding why the Cauchy distribution was employed in the present study. In the revised manuscript, I elaborated several benefits that justify use of the Cauchy distribution instead of other non-informative priors:

The Cauchy distribution was employed as a default prior distribution in the fields of psychology and neuroscience [9]. In fact, it has been utilized in statistical analysis tools for generic purposes in psychological research, such as JASP and BayesFactor R package[8]. The Cauchy distribution has several benefits, such as robustness in BF-based inference and less likelihood to produce false positives compared with other non-informative priors [9, 56], so the distribution has been employed in the present study. (p. 8, lines 308-314)

2. The author should write more details about the Bayesian analysis derivations and

estimation.

Response: Thanks a lot for your suggestion regarding the addition of explanations about Bayesian analysis performed in the present study. I created a new subsection describing the nature of analysis performed via Bayesian approach:

2.2. Basis of Voxelwise Second-level fMRI Analysis

In the present study, the brain images reporting results from first-level (individual-level) fMRI analysis were analyzed at the second (group) level. As explained above, five datasets containing first-level analysis results across three task categories (i.e., working memory, speech, face) were acquired from open repositories for this purpose. For inputs, contrast images reporting differences in activity across two conditions (e.g., n-back vs. control) at the individual level were used. These input images were converted with a standard MNI space for further analyses.

Basically, the voxelwise second-level analysis was performed following the general rules of t-test. Let us assume that we are interested in comparing brain activity in a specific voxel between two conditions, Conditions A and B. The current second-level fMRI analysis is done by performing a one-sample t-test examining whether brain activity value in a specific voxel is significantly higher (or lower) than zero. For each voxel, results from first-level (or individual-level) fMRI analyses are used as inputs. Each input value, a contrast value reported by a specific first-level fMRI analysis, represents the calculated difference in brain activity in Condition A versus Condition B in a specific subject. Then, with the input values, a one-sample t-test is performed following t=  x ̅/(s/√n), where x ̅ is the mean brain activity value, s is the standard deviation of brain activity values, and n is the number of subjects analyzed at the first level. With the result from the conducted t-test, it is possible to examine whether there is significant brain activity in a specific voxel of interest.

2.3. Voxelwise Bayesian Second-level fMRI Analysis

In the present study, whether brain activity in a specific voxel of interest, which was examined following the theme of a t-test, was significant was examined through Bayesian approach. (p. 6, lines 217-240)

2. What are the used values of hyperparameter Sigma of the Cauchy distribution?

Response: I appreciate your comment regarding the Cauchy distribution hyperparameter. In the revised manuscript, I explained further details about the hyperparameter in determination of the Cauchy distribution:

This default Cauchy prior is centered around x0 = 0, while having a scale, σ = .707 [8]. x0 determines where the peak of the distribution shall be located. A scale parameter, σ, determines the width of the distribution and fattiness of tails. As σ increases, the dis-tribution becomes more dispersed and has fatter tails. (p. 8, lines 315-318)

Reviewer 2 Report

The author extend his method presented in other article on the use of prior. In the past article the author use image bases meta analysis in this article the authoe extendthe method using meta-analitic data and differewnt method of calculation of the map.

I have some concer about the exposition:

1) I suggest to insert a section in which describe in deep with formula and image the procedure to calculate the bayesian second level because it is not clear what kind of data are used (t-image z image or other) and what model a linear model with gaussian noise or other=

2) the author must be better justify the calculation of the prior distribution and the P percentuale to calculate the Cauchy scale

3) check the bibliography; some citation in the bibliography are not complete like [16] de Jong

Author Response

1. I suggest to insert a section in which describe in deep with formula and image the procedure to calculate the bayesian second level because it is not clear what kind of data are used (t-image z image or other) and what model a linear model with gaussian noise or other=

Response: Thanks a lot for your suggestion regarding creating a new subsection describing further details about the analysis performed in the present study. In the revised manuscript, I created such a new subsection describing the nature of the t-test performed in the present study with which data was used as an input:

2.2. Basis of Voxelwise Second-level fMRI Analysis

In the present study, the brain images reporting results from first-level (individual-level) fMRI analysis were analyzed at the second (group) level. As explained above, five datasets containing first-level analysis results across three task categories (i.e., working memory, speech, face) were acquired from open repositories for this purpose. For inputs, contrast images reporting differences in activity across two conditions (e.g., n-back vs. control) at the individual level were used. These input images were converted with a standard MNI space for further analyses.

Basically, the voxelwise second-level analysis was performed following the general rules of t-test. Let us assume that we are interested in comparing brain activity in a specific voxel between two conditions, Conditions A and B. The current second-level fMRI analysis is done by performing a one-sample t-test examining whether brain activity value in a specific voxel is significantly higher (or lower) than zero. For each voxel, results from first-level (or individual-level) fMRI analyses are used as inputs. Each input value, a contrast value reported by a specific first-level fMRI analysis, represents the calculated difference in brain activity in Condition A versus Condition B in a specific subject. Then, with the input values, a one-sample t-test is performed following t=  x ̅/(s/√n), where x ̅ is the mean brain activity value, s is the standard deviation of brain activity values, and n is the number of subjects analyzed at the first level. With the result from the conducted t-test, it is possible to examine whether there is significant brain activity in a specific voxel of interest. (p. 6, lines 217-236)

2. the author must be better justify the calculation of the prior distribution and the P percentuale to calculate the Cauchy scale

Response: I appreciate your suggestion regarding justifying use of the current prior distribution and that of the P value. First, in the revised manuscript, I elaborated why the Cauchy distribution was employed:

The Cauchy distribution was employed as a default prior distribution in the fields of psychology and neuroscience [9]. In fact, it has been utilized in statistical analysis tools for generic purposes in psychological research, such as JASP and BayesFactor R package[8]. The Cauchy distribution has several benefits, such as robustness in BF-based inference and less likelihood to produce false positives compared with other non-informative priors [9, 56], so the distribution has been employed in the present study. (p. 8, lines 308-314)

Second, I added explanations about how the P value can contribute to the current analysis:

The P is a hyperparameter that was employed to let users change the overall shape of the adjusted Cauchy prior distribution. When X is constant, a higher P ends up with a smaller Cauchy distribution scale, σ, so the adjusted distribution becomes less dispersed and has a steeper peak at x0. The P value is supposed to be determined by users, so it allows them to customize the shape of the resulting adjusted prior distribution to be used with ra-tionale. As explained in the original study that developed and tested the prior adjustment method [20], use of the P value would be a possible way to customize the shape of the adjusted prior distribution in a less arbitrary manner based on expectation about the overall strength of brain activity in voxels to be analyzed. (p. 9, lines 363-371)

3. check the bibliography; some citation in the bibliography are not complete like [16] de Jong

Response: Thank you very much for your suggestion regarding the reference list. Because [16] was a preprint, several specific information was missing. I revised the item with additional information.