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Meta-analysis of correlation

Interface

This module can conduct Bayesian meta-analysis with power prior. The URL for this module is http://webbugs.psychstat.org/modules/metacorr/.

The module has an interface as shown in the figure below.

Data

To use the program, one needs either to upload a new data file or select an existing file.

To upload a new file, in the DATA box of Method 1, click on the button "Choose file" or "Browse ..." or other text depending on your OS. Once click on the button, you will be directed to select a file on your computer and its name will be shown.

Use an exiting file

You can also use existing data files that have been uploaded. All data files are automatically shown in the drop down menu. One can simply select a file to use.

Data format

The data should be always separated by one or more white spaces. The first line of the data file will be the variable names, which will be used in the model. A simple example is given below

n cor a x
215 0.21 1 1
132 0.252 1 1
309 0.123 1 1
117 0.33 1 1
307 0.4 0.8 0
1212 0.34 1 1
175 0.11 1 1
380 0.147 1 1
86 0.11 1 1
74 0.36 1 1
361 0.138 1 1


How to use

1. Information on the model should first be provided.
1. A user can name the analysis in the field of "Name of model". The name can be used to distinguish different analyses.
2. A user then chooses the model to use. For example, the user can choose to use either the random-effects model (default option) or the fixed-effects model. For meta-regression, the random-effects model option should be selected.
3. Detailed information on the model is provided using the variable names provided in the data file.
1. Correlation is required for all analysis and can be specified using the variable names in the data set. For example, in the data set, "cor" is the variable name for correlation. Therefore, "cor" should be input in the field of Correlation in the interface.
2. Sample size is required for all analysis and can be specified using the variable names in the data set. In the example, “n” is used in the Sample size field because in the data set, “n” is also the variable name for sample size.
3. Power: A user can also specify the variable for power assigned to each study. If left blank, the power 1 is used for all studies.
4. Reliability: A user can also specify reliability variable to adjust for correlation. The adjusted correlation is equal to the original correlation divided by the reliability.
5. For meta-regression analysis, covariates can be provided. More than one covariates should be separated by space.
2. One can control Markov chain Monte Carlo (MCMC) method and output of the meta-analysis.
1. The total number of Monte Carlo iteration and the burn-in period can be specified.
2. In the output, one can require the output of the estimates for random effects $$\zeta_{i}$$, DIC, and diagnostic plots for all model parameters including the random effects.
3. Funnel plot can also be required for publication bias analysis.
4. If one checks the option Email notification, an email will be sent to the user once the analysis is completed.
3. With the required information, one can click the button "Run meta-analysis" to carry out the analysis.

Output

• Typical analysis includes the following section of output:
• The model in mathematical format: This gives the exact model fitted by the program. The parameters are used in the table and figures below.
• Descriptive statistics of data: Sample size, mean, sd, etc.
• DIC if required: Can be used for model comparison.
• Parameter estimates: Mean and SD are similar to parameter estimates and standard error in frequentist analysis. M/SD measures the accuracy, a value smaller than 0.05 is recommended. The last column provides the either Geweke or Gelman-Rubin test of convergence. A value will be highlighted if not convergent.
• Trace, autocorrelaiton, and density plot for each parameter
• Funnel plot if required.
• Test of publication bias.