Content
Effect size estimation

Effect size estimation (for single group)

1. Dichotomous data pooling

(for indirect meta-analysis, prevalence [proportional] meta-analysis)

A) Needed values

To estimate the effect size and its logit transformation for dichotomous data, you need the following values:

  1. Events number

  2. Total patients’ number

B) Steps

  1. In the Input table: put each of the previous values into the corresponding cells
  2. Click submit
  3. In the Output table: you will get the log of risk ratio or odds ratio, with their log standard error (SE)

C) Equations

The output was calculated upon the following equations:

1) Prevalence:

Prevalence estimate= Event  Total  \textbf{Prevalence estimate}=\frac{\text { Event } }{\text { Total }}

2) Log Prevalence = log (Prevalence)

3) Standard error **(**SE) [log transformed]:

SE=1Event−1TotalSE = \sqrt{\frac{1}{Event}-\frac{1}{Total}}

D) Citation and equations source

1) Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.4 (updated August 2023). Cochrane, 2023. Available from www.training.cochrane.org/handbook (opens in a new tab). (Chapter: 6.4.1.2 Measures of relative effect: the risk ratio and odds ratio, URL: Chapter 6: Choosing effect measures and computing estimates of effect | Cochrane Training (opens in a new tab))

2) Package ‘meta’ (meta: General Package for Meta-Analysis (r-project.org) (opens in a new tab))

3) Barendregt, Jan & Doi, Suhail & Lee, Yong Yi & Pacella, Rosana & Vos, Theo. (2013). Meta-analysis of prevalence. Journal of epidemiology and community health. 67. 10.1136/jech-2013-203104. (Meta-analysis of prevalence | Journal of Epidemiology & Community Health (bmj.com) (opens in a new tab))

4) Barker, T.H., Migliavaca, C.B., Stein, C. et al. Conducting proportional meta-analysis in different types of systematic reviews: a guide for synthesisers of evidence. BMC Med Res Methodol 21, 189 (2021). https://doi.org/10.1186/s12874-021-01381-z (opens in a new tab). (Conducting proportional meta-analysis in different types of systematic reviews: a guide for synthesisers of evidence | BMC Medical Research Methodology | Full Text (biomedcentral.com) (opens in a new tab))

E) Additional notes

A) For indirect meta-analysis, in dichotomous outcomes, we need to do this conversion if we want to compare intervention A and intervention B indirectly (in case of no direct comparisons), hence we need to calculate the logarithm of treatment effect (log TE) (log RR or log OR) and the standard error of logarithm treatment effect (SE-logTE) for each study (intervention), then enter them as different subgroups and check for “between subgroups difference” option.

B) For prevalence (proportional) meta-analysis, we use this conversion as if we used event and total provided by each study for pooling, probably we will face the following two problems: “Firstly, the confidence limits fall outside of the established zero to one range [4]; this may impact on the readability and presentation of the pooled data as a forest-plot. The second concern, and by far the most prudent, is that the variance from studies contributing proportional data at the extreme ends of the zero to one range tends toward zero. This in turn, artificially inflates the weight that these studies contribute towards the pooled-prevalence estimate. Transformation of that data is therefore required during the meta-analysis process to deal with these problems.” Therefore, we provide you with the logit transformed version of data.

Also, in certain cases, some of the included studies only provide the prevalence (with no event and total), so we need to pool other studies to get the prevalence of all studies then pool them together in the meta-analysis.

C) A correction of 0.5 may be added to each count in the case of zero events as recommended by Cochrane.

2. Continuous data pooling

(for indirect meta-analysis)

A) Needed values

To estimate the effect size for continuous data, you need the following values:

  1. Mean

  2. Standard deviation (SD)

  3. Total patients’ number

B) Steps

  1. In the Input table: put each of the previous values into the corresponding cells
  2. Click submit
  3. In the Output table: you will get the mean difference (MD) and its standard error (SE).

C) Equations

The output was calculated upon the following equations:

1) Mean = Entered mean

2) Log mean= log (mean)

2) Standard error (SE) [raw]:

SE=SDNSE=\frac{SD}{\sqrt{N}}

D) Citation and equations source

  1. Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.5 (updated August 2023). Cochrane, 2023. Available from www.training.cochrane.org/handbook (opens in a new tab). (Chapter: 6.5 Continuous outcome data, URL: https://training.cochrane.org/handbook/current/chapter-06#section-6-5 (opens in a new tab))

  2. Package ‘meta’ (meta: General Package for Meta-Analysis (r-project.org) (opens in a new tab))

E) Additional notes

In the meta-analysis of continuous outcomes, we need to do this conversion if we want to compare intervention A and intervention B indirectly (in case of no direct comparisons), hence we need to calculate the treatment effect (TE) (mean difference between intervention and control groups) and standard error of the treatment effect (SE-TE) for each study (intervention), then enter them as different subgroups and check for “between subgroups difference” option.

Mean & SD conversionsGroup combination