Host Institution: |
LaTrobe University |
Title of Seminar: |
Variance stabilisation approach to meta-analysis: combining the evidence |
Speaker's Name: |
Elena Kulinskaya |
Speaker's Institution: |
Imperial College |
Time and Date: |
11am Wednesday 26 November 2008 |
Seminar Abstract: |
In the traditional fixed effects model (FEM) of meta analysis, given the estimated effects from K studies θ_{1},…, θ_{K} , with θ_{i} ~N(θ, σ_{i}^{2}) , the combined effect θ is estimated as the weighted mean θ_{est }=(w_{i }θ_{1}+…+ w_{K} θ_{K})/W ~N(θ ,1/ W ) , where w_{i}=σ_{i}^{-2} and W= (w_{1}+…+ w_{K} ). If the homogeneity of the effects is rejected, the random effects model can be used: θ_{i} ~N(θ, σ_{i}^{-2} +τ^{2}). (Sutton et al, 2000). When the variance stabilizing transformation (vst) is applied to the estimated effects, we deal instead with the transformed standardised effects K(δ_{i}). They are estimated by κ_{i}_{ }=n_{i}^{-1/2}h(S_{i}) ~N(K(δ),1/n_{i}) and can be added with known weights n_{i} in meta-analysis (Kulinskaya, Morgenthaler and Staudte, 2008) Given variance stabilized statistics from K studies T_{1},…,T_{K} , with T_{1} ~N(n_{i}^{1/2 }κ ,1) the combined effect κ_{est}=(n_{1} κ_{1}+…+n_{K} κ_{K}))/ N ~N(K(δ),1/ N ) where N= n_{1} +…+n_{K}. The back-transformation is used to obtain the inference on the standardised effects δ. If the homogeneity of the transformed effects is rejected, the random transformed effects model can be used: κ _{i }~N(κ , n_{i}^{-1} +τ^{2}). When there are no nuisance parameters (as in the 1-sample Binomial or Poisson case) these two approaches to meta analysis are equivalent. In the general case, the variance stabilization approach can be used even when the inference on the original, non-standardised effects is of primary interest. In this case the optimal weights depend on the nuisance parameters. An example is the variance stabilizing arcsine transformation for the difference in absolute risks, with the average risk as the nuisance parameter. |
Seminar Convenor: |
This email address is being protected from spambots. You need JavaScript enabled to view it. |
AGR IT support: |
This email address is being protected from spambots. You need JavaScript enabled to view it. |