Calculating SMD in meta analysis with pre-post scores ?

Yes, it is possible to calculate the Standardized Mean Difference (SMD) for each follow-up time for both CCT (Central Corneal Thickness) and ECC (Endothelial Cell Count) in your meta-analysis, even if you do not have the raw data or the correlation coefficient (r) for each study. One common approach is to estimate the SMD using the means and standard deviations of the pre-and post-operative measurements for each outcome separately, without accounting for the correlation between the pre-and postoperative measurements.

Here's a step-by-step guide on how to calculate the SMD for each follow-up time for CCT and ECC:

Extract the relevant data: Collect the mean and standard deviation (SD) values for both pre-and post-operative measurements for CCT and ECC from each study included in your meta-analysis.

Calculate the mean difference (MD): For each study, calculate the mean difference (MD) between the pre-and post-operative measurements for CCT and ECC separately, by subtracting the pre-operative mean from the post-operative mean.

Calculate the pooled standard deviation (SDp): Pool the standard deviations of the pre-and post-operative measurements for CCT and ECC separately using the following formula:

SDp = sqrt(((n1-1)*SD1^2 + (n2-1)*SD2^2) / (n1 + n2 - 2))

where SDp is the pooled standard deviation, SD1 and SD2 are the standard deviations of the pre-and@ post-operative measurements, respectively, and n1 and n2 are the sample sizes of the pre-and post-operative measurements, respectively, for each study.

Calculate the SMD: Using the MD and the pooled standard deviation (SDp), calculate the SMD for each study using the following formula:

SMD = MD / SDp

where SMD is the Standardized Mean Difference, MD is the mean difference calculated in Step 2, and SDp is the pooled standard deviation calculated in Step 3.

Perform meta-analysis: Once you have calculated the SMD for each study at each follow-up time separately for both CCT and ECC, you can use standard meta-analysis techniques, such as random-effects or fixed-effects models, to combine the SMD estimates and generate a summary estimate of the effect size for each outcome at each follow-up time.

It's important to note that estimating the SMD without accounting for the correlation between the pre-and post-operative measurements may introduce some limitations and potential bias into your meta-analysis. However, this approach can be used as a rough estimate when raw data or correlation coefficients (r) are not available. It's always recommended to consult with a statistician or an expert in meta-analysis to ensure that your approach is appropriate for your specific analysis and to interpret the results correctly.

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