# Thread: Meta-analysis - mean (target mean correction)

1. ## Meta-analysis - mean (target mean correction)

I had a statistical question which I'll mention here if you have time to have a look at it then I'd be very grateful for your thoughts.

Im looking at the tibial coronal angle for post-operative knee arthroplasty alignment assessment, referred to as the beta angle, The optimum value is basically 90 degrees.

In the literature the figures are expressed as the actual angle rather than the error from the optimum.

The first table table refers to two implant types, each showing different series that compare beta angle for the differing implants

My question is (basically I want to do a meta-analysis to compare the accuracy of alignment) ie. how close they are to 90 degrees....... can I "correct" the values as shown in table 2 in order to do a sensitivity analysis (meta analysis) comparing the two groups and basically use the values for SD as outlined in table two? I also have values for n for each group.

Am a bit stuck with this basically.

Would be grateful for any thoughts . ideas?

Author Coronal tibia – Implant A Coronal tibia – Implant B
Smith 2007 88.8 (+/- 1.59) 88.6 (+/- 2.58)
Franken 2011 90.0 (+/- 1.3) 90.7 (+/- 1.1)
Judet 2013 90.1 (+/- 0.9) 90.7 (+/- 1.8)
Martinez 2014 89.7 (+/- 1.1) 89.1 (+/- 1.8)

Table 1: showing mean and SD for beta angle in two comparative implant types, authors refer to different studies that report comparisons

Author Coronal tibia – Implant A Coronal tibia – Implant B
Smith 2007 -1.2 (+/- 1.59) -1.4 (+/- 2.58)
Franken 2011 0 (+/- 1.3) 0.7 (+/- 1.1)
Judet 2013 0.1 (+/- 0.9) 0.7 (+/- 1.8)
Martinez 2014 0.3 (+/- 1.1) 0.9 (+/- 1.8)

Table 2: proposed correction to enable meta-analysis comparison

2. ## Re: Meta-analysis - mean (target mean correction)

I once asked a similar question about 4 years ago and got no answer for it. The problem is that angular measurements can jump between complementary values (ie, original values and those calculated by subtracting 90 from the original angle) without any change in the meaning. However, their standard deviations can't jump between such values.

So if you convert 88.8 (+/- 1.59) to -1.2 (+/- 1.59), the new angle will be still valid but the new standard deviation will be completely misleading and computationally useless (and incorrect). Statistical tests look at the SD and how small is it compared to the mean, and if it is small enough they gain more power. Now when you convert a very large angle to its complimentary angle, it becomes smaller than its SD which this makes all statistical tests incorrectly underpowered. In other words, if an SD is properly small compared to its mean, the mean will be treated as a more reliable and more accurate finding but if the SD is not small enough, the mean will be treated as some not-so-accurate or not-so-definite finding. In your case, the old SD was about 80 times smaller than the mean, showing that the mean was very accurately identified and thus very reliable. But after converting the mean from 88 to -1, the SD is now larger than the new Mean, indicating that the newly calculated mean is not a reliable or accurate finding.

I have a suggestion that just passed my mind: In order to feed a proper pair of Mean/SD to the statistical test, you can convert the SD to a new SD that holds the same ratio to the mean. For this purpose you should first calculate the CV (coefficient of variation) which basically addresses the question that "how much an SD is small compared to its mean?" It is possible to calculate the CV (coefficient of variation) for the original angle [from its SD, CV = SD / Mean, which is 0.0179 = 1.59 / 88.8] and then use it to compute a NEW standard deviation that goes along with the new angle. New SD = CV * |new Mean| = 0.0179 * 1.2 = 0.02149.

This new SD allows the meta-analysis test to treat the new means exactly the same way it would treat the original means with their original SDs. So the new "Mean (SD)" should look like:

Smith 2007 -1.2 (+/- 0.02149)

3. ## The Following User Says Thank You to victorxstc For This Useful Post:

jbwettergreen (11-24-2016)

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