# Analysis and interpretation of results using meta analysis

The previous article illustrated the manual data entry procedure to facilitate data analysis for performing meta-analysis in **comprehensive meta analysis (CMA)** application. Taking it further the present article introduces procedures of analyzing the entered data and interpretation of the results. The article will introduce the results and analysis interface to probe the association of Cholecystitis with gallbladder carcinoma.

**Running the analysis**

The spreadsheet is taken from the previous article, as shown below. Click on ‘Run analyses’ tab.

**Results obtained **

The figure below shows the results window upon running the analysis. There are seven different analysis options in it. The tabs for ‘Fixed’, ‘Random’ and ‘Both’ models allow to select the appropriate statistical model for analysis. This window presents the results of the basic statistical analysis. It shows the summary effect size, individual study effect sizes, limit of the confidence interval and values of tests and statistics of the null hypothesis (z & p-value). Also, the forest plot is the visual representation of summary and individual effect sizes.

**Alternating between different effect measures **

As shown above, **CMA** calculates two effect size measures, ‘Event rate’, and ‘Logit event rate’*.* Any one of them could be used to report the summary effect size. Select between the two effects sizes, using the ‘Effect measure’ tab, as shown below. The figure also shows the difference in the basic statistics and forest plot for the two effect measures.

Here, one should note that the difference in the effect size, however, does not mean a change in results of the research study. The different effect measures demand different interpretation.

The above image shows the forest plot for Logit event rate to be indiscernible and the effect sizes cannot be seen properly. This problem is overcome by adjusting the scale of the forest plot, as shown below. As seen, upon selecting the suitable scale range, the plot became comprehensible.

If the observations of the forest plot are still not clear, then use the ‘Customized’ option to enter the desired scale values. It involves entering the appropriate values in the ‘Customize scale’ dialog box, as shown below.

## Selecting an appropriate model

The selection of either fixed or random effects model depends upon the researcher’s assumption with respect to true effect size. True effect size occurs in a study with infinitely large sample size. True effect sizes are just a measure of assumption, whereas the observed effect size is the one actually observed*.*

The fixed effect model assumes that a single true effect size underlies all the studies under consideration. When all the factors impacting the effect size are same then all the studies have same true effect size. The summary effect size in these models is an estimate of true effect size and any dispersion reflects sampling error.

The selection of random effect model ensues when the effect size is not consistent across all the studies. This is because the studies tend to have variation in effect sizes due to differences in population demographics, nature of interventions or any other variable. Upon conducting such studies with an infinitely large sample the true effect sizes will show distribution about some mean. Both models tab allows to observe the results from both the models in a single window, as shown below.

The random effects model is most common, as it is implausible that all the studies in the systematic review will be identical with respect to true effect size.

As the present analysis does not follow the assumption of identical true effect size hence, the analysis involves selection of random effects model.

## Alternating between different analysis options

Seen below are the summary results, shown after selecting different types of analysis options that is, ‘One study removed’ and ‘Cumulative analysis’*. *The ‘One study removed’ tab allows to observe the impact of each study on the summary effect. The ‘Cumulative analysis’ is useful to observe how the evidence for the particular effect has shifted over the time. Also note how the forest plot changes upon selecting the different analysis options. The ‘Calculations’ tab, on the other hand, allows to view all the calculation performed in reaching the basic.

The software allows to customize the analysis by offering the afore-discussed functionalities.

## Selecting different studies for results

The figure below depicts the ‘Select by’ option offered by **CMA**, wherein one or more studies can be removed, to assess their degree of impact on the summary effect size. This option also helps to conduct an analysis of specific studies, to obtain differential results. Upon selecting the ‘Select by’ option, which allows the selection of studies. The figure shows the change in the value of summary effect size upon removing the study by Grleyik et al.

**Quick display options**

Shown below are the different quick display options for displaying different statistical measures (shown by the respective color scheme). These options help the user in customizing the display of results.

**Individual studies:**Toggle between displays for the area enclosed in the green. It refers to statistics and forest plots for individual studies.**Basic stats:**Toggle between displays for the area enclosed in blue. It pertains to the display of statistics for individual studies.**Residuals:**Toggle between displays for the area enclosed in purple. It pertains to the display of residuals for individual studies.**Overall summary:**Toggle between displays for the area enclosed in pink. It pertains to statistics and forest plots for individual studies.**Counts:**Toggle between displays for the area enclosed in magenta. It pertains to the display of counts for individual studies.**Weights:**Toggle between displays for the area enclosed in yellow. It pertains to the display of weights given to individual studies in the analysis.

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