Case Study: The effectiveness of face masks in preventing the spread of COVID-19
This is a prototype and case study of an ‘interactive meta-analysis’. The main aim is to showcase how an interactive meta-study could look like and thereby explore its potential to be used as a tool to improve evidence-based decision making. More on the concept of an interactive meta-study here.
Like a normal Meta Study, this page aims to combine results from multiple studies on the same topic (in this case mask wearing to prevent the spread of COVID-19) to create one "overall" estimate. However, contrary to a traditional meta study you can choose what studies are included and what criteria they have to meet. Hover over the visualisation to get addtional explanations.
Based on the studies included our current best estimate is that those who don't wear a mask are times more likely to get COVID than those who wear masks. If we assume that people without a mask have a % chance of getting COVID (which is the median from all included studies), this means that (in expectation) more people would need to wear mask to prevent one COVID case.The odds ratio in this case represents the odds that someone without a mask will get COVID divided by the odds that someone with a mask will get COVID: It is calculated as follows: $$ OR =\frac{\frac{\text{people who wore a mask & got COVID}}{\text{people who wore a mask & didn't get COVID}}}{\frac{\text{people who did not wear a mask & got COIVD}}{\text{people who did not wear a mask & didn't get COVID}}}$$
More information: Szumilas, M. (2010): Explaining Odds Ratios.
A so-called 'fixed effects model' is probably the simplest version of calculating meta-estimates. It uses the 'inverse-variance method' to calculate the weighted average of the included studies as:
$$ \text{meta-estimate} = \frac{\sum{Y_iW_i}}{\sum{W_i}} $$
where \( Y_i \) is the estimated effect size from the \( i^{th} \) study, \( W_i \) is the weight assigend to study \( i\) and the summation is across all studies.
In the fixed effects model,
$$W_i =\frac{1}{SE_i^2}$$
with \( SE_i \) being the standard error of study \( i \).
This type of analysis assumes that all effect estimates are estimating the same underlying effect.
More information: Borenstein, M.; Hedges, L.; Higgins, J.; Rothstein, H (2009): A basic introduction to fixed-effect and
random-effects models for meta-analysis
Random effects models are a variation of the 'inverse-variance method' that is also used in fixed effects models. However, they operate on the assumption that the different studies included in the meta-analysis estimate different but related effects.
The general formula for calculating the aggregated effect estimate is the same as in the fixed effects model:
$$ \text{meta-estimate} = \frac{\sum{Y_iW_i}}{\sum{W_i}} $$
where \( Y_i \) is the estimated effect size from the \( i^{th} \) study, \( W_i \) is the weight assigend to study \( i\) and the summation is across all studies.
However, the weights of the studies take into account the between-study variance \( T^2 \):
$$W_i =\frac{1}{(T^2 + SE_i^2)}$$
You can find information on how to calculate \(T^2 \) in: Borenstein, M.; Hedges, L.; Higgins, J.; Rothstein, H (2009): A basic introduction to fixed-effect and
random-effects models for meta-analysis
We have included studies that we sourced from the following existing meta-studies: