So, in the forest plot or in the meta analysis.

Each study summarized by an estimator effect or the result.

For example, the risk ratio.

In the overall measure of effect is a weighted average of the results

of the individual studies.

So the overall measure of effect is the yellow diamond

you saw from the previous slide.

And the weighted average reflect varying component of the trial.

And trials would desire more weight if it has more information and

more information mainly refers to the sample size.

More information leads to increased precision.

If you still remember from the previous figure.

We have the squares representing each individual study.

The larger square means that particular study is taking more weight

in the meta-analysis.

More formally, you can write the inverse variance weighted average.

Using this formula.

So let's say we have estimates from individual studies, and

now we're just combining them as a weighted average.

Here, YI refers to the intervention effect,

measures of association or measures of the effect, estimating the study.

And the WI is the weight given to the ice study.

And as we can see from the formula, the point estimate or where the center of

that diamond lies, is just the weighted average which sums up the estimate times

the weight in the the numerator divided by the sum of the weights.

In addition to getting the point estimate from the meta-analysis,

we also want to know the variance.

And we use the variance to construct 95% confidence interval.

And the variance for the weighted average equals to one over the sum of the weights.

And we will

show how you

can use this

formula to get the

meta-analytical

results in

the next slide.

Here's one

example.

Let's say from the first study,

if you look at the table, on the upper left corner.

So here we showed you the results from the first study.

Of those treated, 12 experienced the events and

53 did not experience the event.

And of those in the comparison group, 16 experienced events and

49 did not have the event.

So and we can use the formula odds ratio, which is the cross-product,

the ratio of the cross product to get the odds ratio from this particular study, and

this should not be something new to you because you have learned this in your and

Biostat that course is.

By plotting the numbers, we have an odds ratio of 0.69.

Now, we're going to get the YI, the YI

of the formula I showed you previously by taking the log of that odds ratio.

So the log of the show equals -.36.

And the variance for that YI, again, by plugging the formula you have seen

in other courses, especially the biostat courses, you can get the variance,

which equals .18.

And now the weight for the particular study if you remember from the formula I

showed you in the previous slides, WI equals 1 over the variance.

And you get the weight for this particular study which equals 5.4, so you follow

the same steps to get the log (OR1) ratio as well as the variance and weights for

each individual study that you're going to include in your meta analysis.

And now here are all the data you have.

Let's say for this particular meta analysis you have 6 studies.

And I just showed you how to get the odds ratio, log odds ratio,

variance in weight for the very first study.

And if you remember the data from the previous two by two table,

their reflected here in this table as well.

So you follow the same steps and you calculate the odds ratio,

log odds ratio variance in weight for each individual study and

the results are showing in the table on the bottom.

If we focus on the variance column of the table on the bottom,

you will see the variance for the first study is .19.

The variance for the second study is .29.

And comparing these two studies, which one is more precise?

Well, we know the smaller the variance, the more precise the study.

Which means that study will take more weight in your meta-analysis.

So let's move on to the next column on the same table.

You will see that the weight for the first study is 5.4, and the weight for

the second study is 3.45.

And if you look across all 6 studies,

you will notice that study four takes the largest weight, which is 17.

16.

So that's the most precise study among the 6 and

that study, while dominate to your meta analysis.

Which means that will take the largest of weight, relative to all the other studies.

If you sum up all the weight, that equals 42.25, and

then if you do the calculation times the weight for

each individual study with the log odds ratio and

sum them up, you get the summation of WI times YI which equals -30.59.

And the reason I'm emphasizing those

two numbers is because you can use those two numbers and plug them

in in the formula I showed you previously to get a better analytical result.