Region-Based Analysis Program through Bayesian Multilevel Modeling #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Version 1.0.10, Feb 28, 2022 Author: Gang Chen (email@example.com) Website - https://afni.nimh.nih.gov/gangchen_homepage SSCC/NIMH, National Institutes of Health, Bethesda MD 20892 #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
RBA performs region-based analysis (RBA) as theoretically elaborated in the manuscript: https://rdcu.be/bhhJp and is conducted with a shell script (as shown in the examples below). The input data should be formulated in a pure-text table that codes the regions and variables. The response variable is some effect at the individual subject level. Thanks to Paul-Christian Bürkner and the Stan/R communities for the strong support.
Chen G, Xiao Y, Taylor PA, Riggins T, Geng F, Redcay E, 2019. Handling Multiplicity in Neuroimaging through Bayesian Lenses with Multilevel Modeling. Neuroinformatics. https://rdcu.be/bhhJp Read the following carefully!!! A data table in pure text format is needed as input for an RBA script. The data table should contain at least 3 columns that specify the information about subjects, regions and the response variable values with the following fixed header. The header lables are case-sensitive, and their order does not matter. Subj ROI Y Age S1 Amyg 0.2643 11 S2 BNST 0.3762 16 0) You are performing Bayesian analysis. So, you will directly obtain the probability of the respective effect being positive or negative with your data and adopted model, instead of looking for the p-value (weirdness of your data under the modeling assumptions when pretending that absolutely no effect exists). 1) Avoid using pure numbers to code the labels for categorical variables. The column order does not matter. You can specify those column names as you prefer, but it saves a little bit scripting if you adopt the default naming for subjects ('Subj'), regions ('ROI') and response variable ('Y'). 2) Add more columns if explanatory variables are considered in the model. Currently only between-subjects variables (e.g., sex, patients vs. controls, age) are allowed. Capability of modeling within-subject or repeated-measures variables may be added in the future. Each label in a between-subjects factor (categorical variable) should be coded with at least 1 character (labeling with pure numbers is fine but not recommended). If preferred, you can quantitatively code the levels of a factor yourself by creating k-1 columns for a factor with k levels. However, be careful with your coding strategy because it would impact how to interpret the results. Here is a good reference about factor coding strategies: https://stats.idre.ucla.edu/r/library/r-library-contrast-coding-systems-for-categorical-variables/ 3) It is strongly suggested that a quantitative explanatory variable be standardized with option -stdz; that is, remove the mean and scale by the standard deviation. This will improve the chance of convergence with each Markov chain. If a between-subjects factor (e.g., sex) is involved, it may be better to standardize a quantitative variable within each group in terms of interpretability if the mean value differs substantially. However, do not standardize a between-subjects factor if you quantitatively code it. And do not standardize the response variable if the intercept is of interest! 4) For within-subject variables, try to formulate the data as a contrast between two factor levels or as a linear combination of multiple levels. 5) The results from RBA are effect estimates for each region. They can be slightly different across different runs or different computers and R package versions due to the nature of randomness involved in Monte Carlo simulations. 6) The evidence for region effects in the output can be assessed through P+, the probability that the effect is positive conditional on the current model and dataset. Unlike the NHST convention, we emphasize that a decision about the strength of statistical evidence should not be purely based on an artificial threshold. Instead, we encourage full results reporting: highlight some results with strong evidence and literature support (if available) without hiding the rest. 7) WARNING: If the results are pretty homogenized across regions, it is an indication that presumably partial pooling becomes full pooling. Most likely the cross-region variability is so negligible that the model renders the overall average as individual effects for all regions. When this occurs, you may need much more data for the model to differentiate the subtle effects.
In addition to R installation, the R package "brms" is required for RBA. Make sure you have the most recent version of R. To install "brms", run the following command at the terminal: rPkgsInstall -pkgs "brms" -site http://cran.us.r-project.org" Alternatively you may install them in R: install.packages("brms") *** To take full advantage of parallelization, install both 'cmdstan' and 'cmdstanr' and use the option -WCP in MBA. However, extra stpes are required: both 'cmdstan' and 'cmdstanr' have to be installed. To install 'cmdstanir', execute the following command in R: install.packages('cmdstanr', repos = c('https://mc-stan.org/r-packages/', getOption('repos'))) Then install 'cmdstan' using the following command in R: cmdstanr::install_cmdstan(cores = 2) # Follow the instruction here for the installation of 'cmdstan': # https://mc-stan.org/cmdstanr/articles/cmdstanr.html # If 'cmdstan' is installed in a directory other than home, use option -StanPath # to specify the path (e.g., -StanPath '~/my/stan/path'). In addition, if you want to show the ridge plots of the posterior distributions through option -ridgePlot, make sure that the following R packages are installed: data.table ggplot2 ggridges dplyr tidyr scales
Once the RBA command script is constructed, it can be run by copying and pasting to the terminal. Alternatively (and probably better) you save the script as a text file, for example, called myRBA.txt, and execute it with the following (assuming on tcsh shell), nohup tcsh -x myRBA.txt > diary.txt & nohup tcsh -x myRBA.txt |& tee diary.txt & The advantage of the commands above is that the progression is saved into the text file diary.txt and, if anything goes awry, can be examined later. The 'nohup' command allows the analysis running in the background even if the terminal is killed.
Example 1 --- Simplest scenario. Values from regions are the input from each subject. No explanatory variables are considered. Research interest is about the population effect at each region. RBA -prefix output -dataTable myData.txt \ The above script is equivalent to RBA -prefix myResult -chains 4 -iterations 1000 -model 1 -EOI 'Intercept' \ -r2z -dataTable myData.txt \ The 2nd version above is recommended because of its explicit specifications. If the data are skewed or have outliers, use Student's t-distribution: RBA -prefix myResult -chains 4 -iterations 1000 -model 1 -EOI 'Intercept' \ -distY 'student' -dataTable myData.txt \ If a computer is equipped with as many CPUs as a factor 4 (e.g., 8, 16, 24, ...), a speedup feature can be adopted through within-chain parallelization with the option -WCP. For example, the script assumes a computer with 24 CPUs (6 CPUs per chain): RBA -prefix myResult -chains 4 -WCP 6 \ -iterations 1000 -model 1 -EOI 'Intercept' -distY 'student' \ -dataTable myData.txt \ The input file 'myData.txt' is a data table in pure text format as below: Subj ROI Y S01 lFFA 0.162 S02 lAmygdala -0.598 S03 DMNLAG 0.249 S04 DMNPCC 0.568 If t-statistic (or standard error) values corresponding to the response variable Y are available, add the t-statistic (or standard error) values as a column in the input data table so that they can be incorporated into the BML model using the option -tstat or -se with the following script (assuming the tstat column is named as 'tvalue), RBA -prefix myResult -chains 4 -WCP 6 \ -iterations 1000 -model 1 -EOI 'Intercept' -distY 'student' -tstat tvalue \ -dataTable myData.txt \ or (assuming the se column is named as 'SE'), RBA -prefix myResult -chains 4 -WCP 6 \ -iterations 1000 -model 1 -EOI 'Intercept' -distY 'student' -se SE \ -dataTable myData.txt \
RBA -prefix output -Subj subject -ROI region -Y zscore -ridgePlot 10 8 \ -chains 4 -iterations 1000 -model '1+sex+group' \ -cVars 'sex,group' -EOI 'Intercept,sex,group' \ -dataTable myData.txt If a computer is equipped with as many CPUs as a factor 4 (e.g., 8, 16, 24, ...), a speedup feature can be adopted through within-chain parallelization with the option -WCP. For example, For example, consider adding '-WCP 6' on a computer with 24 CPUs. The input file 'myData.txt' is formatted as below: subject region zscore sex group S1 DMNLAG 0.274 F patient S1 DMNLHC 0.443 F patient S2 DMNRAG 0.455 M contorl S2 DMNRHC 0.265 M control Notice that the interaction between 'sex' and 'group' is not modeled in this case. The option -ridgePlot generates a stacked list of posterior distributions in a sequential order among the regions for each effect of interest specified through -EOI. The two numbers of 10 and 8 associated with the option -ridgePlot specifies the figure window size with 10" wide and 8" high. Example 3 --- one between-subjects factor (sex), one within-subject factor (two conditions), one between-subjects covariate (age), and one quantitative
RBA -prefix result -ridgePlot 8 6 -Subj Subj -ROI region -Y value \ -chains 4 -iterations 1000 -model '1+sex+age+SA' -qVars 'sex,age,SA' \ -EOI 'Intercept,sex,age,SA' -dataTable myData.txt If a computer is equipped with as many CPUs as a factor 4 (e.g., 8, 16, 24, ...), a speedup feature can be adopted through within-chain parallelization with the option -WCP. For example, For example, consider adding '-WCP 6' on a computer with 24 CPUs. The input file 'myData.txt' is formatted as below: Subj region value sex age SA S1 DMNLAG 0.274 1 1.73 1.73 S1 DMNLHC 0.443 1 1.73 1.73 S2 DMNRAG 0.455 -1 -0.52 0.52 S2 DMNRHC 0.265 -1 -0.52 0.52 Notice 1) the 'Y' column is the contrast between the two conditions. 2) since we want to model the interaction between 'sex' and 'age', 'sex' is coded through deviation coding. 3) 'age' has already been standardized within each sex due to large age difference between the two sexes. 4) the 'SA' column codes for the interaction between 'sex' and 'age', which is the product of the two respective columns.
Options in alphabetical order: -chains N: Specify the number of Markov chains. Make sure there are enough processors available on the computer. Most of the time 4 cores are good enough. However, a larger number of chains (e.g., 8, 12) may help achieve higher accuracy for posterior distribution. Choose 1 for a single-processor computer, which is only practical only for simple models. -cVars variable_list: Identify categorical (qualitive) variables (or factors) with this option. The list with more than one variable has to be separated with comma (,) without any other characters such as spaces and should be surrounded within (single or double) quotes. For example, -cVars "sex,site" -dataTable TABLE: List the data structure in a table of long format (cf. wide format) in R with a header as the first line. NOTE: 1) There should have at least three columns in the table. These minimum three columns can be in any order but with fixed and reserved with labels: 'Subj', 'ROI', and 'Y'. The column 'ROI' is meant to code the regions that are associated with each value under the column Y. More columns can be added in the table for explanatory variables (e.g., groups, age, site) if applicable. Only subject-level (or between-subjects) explanatory variables are allowed at the moment. The labels for the columns of 'Subj' and 'ROI' can be any identifiable characters including numbers. 2) Each row is associated with one and only one 'Y' value, which is the response variable in the table of long format (cf. wide format) as defined in R. With n subjects and m regions, there should have totally mn rows, assuming no missing data. 3) It is fine to have variables (or columns) in the table that are not used in the current analysis. 4) The context of the table can be saved as a separate file, e.g., called table.txt. In the script specify the data with '-dataTable table.txt'. This option is useful when: (a) there are many rows in the table so that the program complains with an 'Arg list too long' error; (b) you want to try different models with the same dataset. -dbgArgs: This option will enable R to save the parameters in a file called .RBA.dbg.AFNI.args in the current directory so that debugging can be performed. -distROI distr_name: Use this option to specify the distribution for the ROIs. The default is Gaussian when this option is not invoked. When the number of regions is small (e.g., less than 20), consider adopting the Student's t-distribution by using this option with 'student'. -distSubj distr_name: Use this option to specify the distribution for the subjects. The default is Gaussian when this option is not invoked. When the number of regions is small (e.g., less than 20), consider adopting the Student's t-distribution by using this option with 'student'. -distY distr_name: Use this option to specify the distribution for the response variable. The default is Gaussian when this option is not invoked. When skewness or outliers occur in the data, consider adopting the Student's t-distribution or exGaussian by using this option with 'student' or 'exgaussian'. -EOI variable_list: Identify effects of interest in the output by specifying the variable names separated with comma (,). For example, -EOI "sex,age". By default the Intercept is considered to be an effect of interest. Currently only variables, not their interactions, can be directly requested for output. However, most interaction effects can be obtained by either properly coding the variables (see example 3) or post processing. -help: this help message -iterations N: Specify the number of iterations per Markov chain. Choose 1000 (default) for simple models (e.g., one or no explanatory variables). If convergence problem occurs as indicated by Rhat being great than 1.1, increase the number of iterations (e.g., 2000) for complex models, which will lengthen the runtime. Unfortunately there is no way to predict the optimum iterations ahead of time. -MD: This option indicates that there are missing data in the input. With n regions, at least n(n-1)/2 values are assumed from each subject in the input with no missing data (default). When missing data are present, invoke this option so that the program will handle it properly. -model FORMULA: This option specifies the effects associated with explanatory variables. By default (without user input) the model is specified as 1 (Intercept). Currently only between-subjects factors (e.g., sex, patients vs. controls) and quantitative variables (e.g., age) are allowed. When no between-subject factors are present, simply put 1 (default) for FORMULA. The expression FORMULA with more than one variable has to be surrounded within (single or double) quotes (e.g., '1+sex', '1+sex+age'. Variable names in the formula should be consistent with the ones used in the header of data table. A+B represents the additive effects of A and B, A:B is the interaction between A and B, and A*B = A+B+A:B. Subject as a variable should not occur in the model specification here. -PDP nr nc: Specify the layout of posterior distribution plot (PDP) with nr rows and nc columns among the number of plots. For example, with 16 regions, you can set nr = 4 and nc = 4. The region names will be shown in each plot. So label the regions concisely. -prefix PREFIX: Prefix is used to specify output file names. The main output is a text with prefix appended with .txt and stores inference information for effects of interest in a tabulated format depending on selected options. The prefix will also be used for other output files such as visualization plots, and saved R data in binary format. The .RData can be used for post hoc processing such as customized processing and plotting. Remove the .RData file to save disk space once you deem such a file is no longer useful. -qContr contrast_list: Identify comparisons of interest between quantitative variables in the output separated with comma (,). It only allows for pair-wise comparisons between two quantitative variables. For example, -qContr "age vs IQ, age vs weight, IQ vs weight", where V1, V2, and V3 are three quantitative variables and three comparisons, V1 - V2, V1 - V3 and V2 - V3 will be provided in the output. Make sure that such comparisons are meaningful (e.g., with the same scale and unit. This can be used to formulate comparisons among factor levels if the user quantitatively codes the factor levels. -qVars variable_list: Identify quantitative variables (or covariates) with this option. The list with more than one variable has to be separated with comma (,) without any other characters such as spaces and should be surrounded within (single or double) quotes. For example, -qVars "Age,IQ" -r2z: This option performs Fisher transformation on the response variable (column Y) if it is correlation coefficient. -ridgePlot width height: This option will plot the posterior distributions stacked together in a sequential order, likely preferable to the one generated with option -PDP. The size of the figure windown is specified through the two parameters of width and height in inches. You can fine-tune the plot yourself by loading up the *.RData file if you know the tricks. -ROI var_name: var_name is used to specify the column name that is designated as as the region variable. The default (when this option is not invoked) is 'ROI'. -scale d: Specify a multiplier for the Y values. When the values for response are too small or large, it may create a convergence problem for MCMC. To avoid the problem, set a scaling factor so that the range of value is around 1-10. The results will be adjusted back to the orignal scale. -se: This option indicates that standard error for the response variable is available as input, and a column is designated for the standard error in the data table. If effect estimates and their t-statistics are the output from preceding analysis, standard errors can be obtained by dividing the effect estimatrs ('betas') by their t-statistics. The default assumes that standard error is not part of the input. -show_allowed_options: list of allowed options -stdz variable_list: Identify quantitative variables (or covariates) to be standardized. To obtain meaningful and interpretable results and to achieve better convergence of Markov chains with reasonable iterations, it is recommended that all quantitative variables be standardized except for the response variable and indicator variables that code for factors. For example, -stdz "Age,IQ". If the mean of a quantitative variables varies substantially between groups, it may make sense to standardize the variable within each group before plugging the values into the data table. Currently RBA does not offer the option to perform within-group standardization. -Subj var_name: var_name is used to specify the column name that is designated as as the measuring unit variable (usually subject). The default (when this option is not invoked) is 'Subj'. -tstat var_name: var_name is used to specify the column name that lists the t-statistic values, if available, for the response variable 'Y'. In the case where standard errors are available for the effect estiamtes of 'Y', use the option -se. -verb VERB: Speicify verbose level. -WCP k: This option will invoke within-chain parallelization to speed up runtime. To take advantage of this feature, you need the following: 1) at least 8 or more CPUs; 2) install 'cmdstan'; 3) install 'cmdstanr'. The value 'k' is the number of thread per chain that is requested. For example, with 4 chains on a computer with 24 CPUs, you can set 'k' to 6 so that each chain will be assigned with 6 threads. -Y var_name: var_name is used to specify the column name that is designated as as the response/outcome variable. The default (when this option is not invoked) is 'Y'.