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I'm conducting a meta-analysis and trying to figure out the best way to determine the effectiveness of a particular treatment using results from multiple studies. As the studies vary in several important characteristics (ex. patient population, sample size, co-morbidities, training level of provider, etc.), my initial thought was to use standardized mean differences (SMD), which I have computed for each individual study. I am unsure of how to proceed now, though. In particular, I have a few questions:

  1. Is using the SMD the most appropriate method of analysis, or should I use another approach (ex. random effects model)?
  2. Because the studies I am analyzing do not contain standard deviations, I am expressing sample means as proportions (p) to apply the Central Limit Theorem and estimate standard errors (SE) via the formula s=sqrt(p(1-p)/n). Is this reasonable?
  3. If it is appropriate to use SMD, how can I combine the individual SMDs of each study to generate a cumulative confidence interval/p-value that can tell me whether or not the treatment is non-inferior to the standard of care?
  4. Two of my studies have a sample proportion (and hence SE) of 0. How should I incorporate this data in my meta-analysis?

A sample table of data that reflects what I have done so far is below.

Study Treatment Mean (n) Treatment SE Control Mean (n) Control SE SMD SE of SMD
A 0.3 (100) 0.046 0.2 (150) 0.033 2.60 0.17
B 0.2 (150) 0.033 0.3 (150) 0.037 -2.85 0.16
C 0.4 (200) 0.035 0.35 (200) 0.034 1.46 0.11
D 0 (100) 0 0 (100) 0 Undefined Undefined

Thanks in advance!

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  • $\begingroup$ If the "studies vary in several important characteristics" then there is no simple statistical algorithm to allow you to get an average (e.g., pooled estimate). I would recommend you reconsider whether a meta-analysis should be done in the first place, rather than the approach to conducting it. $\endgroup$
    – abousetta
    Commented Jan 30, 2023 at 18:16
  • $\begingroup$ That makes sense. Let's say I'm able to control for these characteristics, and I subsequently calculate the standardized mean difference for each study (along with the respective standard error). How would I "average" these standardized mean differences and standard errors to create an overall confidence interval to see if the treatment group is significantly different than the control group? $\endgroup$
    – Keshav
    Commented Jan 30, 2023 at 18:33
  • $\begingroup$ You pool SMDs using inverse variance. Any popular meta-analysis software will have this option. You will need the Mean, SD and sample size for each group (or just mean and SE depending on the software). Having said that, unless you have the raw data from each of these studies then you wouldn't be able to control for the characteristics you mentioned above. $\endgroup$
    – abousetta
    Commented Jan 30, 2023 at 22:08

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