By Dankmar Bohning, Sasivimol Rattanasiri, Ronny Kuhnert
Supplying trustworthy info on an intervention impact, meta-analysis is a strong statistical device for interpreting and mixing effects from person experiences. Meta-Analysis of Binary facts utilizing Profile probability specializes in the research and modeling of a meta-analysis with separately pooled facts (MAIPD). It provides a unifying method of modeling a therapy influence in a meta-analysis of scientific trials with binary results.
After illustrating the meta-analytic state of affairs of an MAIPD with numerous examples, the authors introduce the profile chance version and expand it to deal with unobserved heterogeneity. They describe components of log-linear modeling, methods for locating the profile greatest probability estimator, and substitute ways to the profile chance process. The authors additionally speak about how you can version covariate details and unobserved heterogeneity concurrently and use the profile probability option to estimate odds ratios. the ultimate chapters examine quantifying heterogeneity in an MAIPD and exhibit how meta-analysis might be utilized to the surveillance of scrapie.
Containing new advancements no longer to be had within the present literature, in addition to easy-to-follow inferences and algorithms, this e-book allows clinicians to successfully examine MAIPDs.
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Extra resources for Meta-analysis of Binary Data Using Profile Likelihood
For the general construction of the PNMLE, numerical algorithms are required. 3 The PNMLE via the EM algorithm A major tool for constructing the maximum likelihood estimates is the EM algorithm (Dempster et al. (1977), McLachlan and Krishnan (1997)). 9) where yij = 1, if center i belongs to subpopulation j, and 0 otherwise. 10) . 11) which can be maximized in θj and qj , separately. This established the M-step of the EM algorithm. In fact, we find easily that qˆj = 1 k k eij . 14). 4 The EMGFU for the profile likelihood mixture When the gradient function indicates heterogeneity, usually the number of components adequate to model this heterogeneity will be unknown and several values for m need to be considered.
Again, convergent † This follows from a second order Taylor expansion of Γ(θ) around θ: ˆ Γ(θ (n) ) ≈ Γ(θ) ˆ + (n) (n) 2 (n) 2 ˆ ˆ ˆ ˆ ˆ ˆ ˆ Γ (θ)(θ − θ) + Γ (θ)(θ − θ) /2 = Γ(θ) + Γ (θ)(θ − θ) /2. We assume that ˆ 2 × C which serves as boundedness of the second derivative. 5 behavior appears to be quadratic (a general proof is still outstanding), and it can be expected that the iteration will only need a few steps. Indeed, for this case iteration based upon Γ stops only after 5 steps, whereas the iteration based upon Φ stops after 60 steps.
34) is given on the log-relative risk scale. One ˆ could use the δ-method, so that var(θˆM H ) ≈ (eθM H )2 var(log(θˆM H )), though we prefer to give a more direct comparison. 33) i=1 where αi = ˆ T θn i ˆ T niC +θn i . The Mantel-Haenszel estimate of the common relative T C x n /n T risk is given as θˆM H = i xCi niT /nii with ni = nC i + ni (Greenland and Robins i i i (1985), see also Woodward (1999)). 34) T where xi = xC i + xi as before. 34) has been developed for the situation of identical person-times in the centers reflecting a binomial sampling plan.
Meta-analysis of Binary Data Using Profile Likelihood by Dankmar Bohning, Sasivimol Rattanasiri, Ronny Kuhnert