The DerSimonian-Laird confidence interval for the average treatment effect in meta-analysis is widely used in practice when there is heterogeneity between studies. However, it is well known that its coverage probability (the probability that the interval actually includes the true value) can be substantially below the target level of 95 per cent. It can also be very sensitive to publication bias. In this paper, we propose a new confidence interval that has better coverage than the DerSimonian-Laird method, and that is less sensitive to publication bias. The key idea is to note that fixed effects estimates are less sensitive to such biases than random effects estimates, since they put relatively more weight on the larger studies and relatively less weight on the smaller studies. Whereas the DerSimonian-Laird interval is centred on a random effects estimate, we centre our confidence interval on a fixed effects estimate, but allow for heterogeneity by including an assessment of the extra uncertainty induced by the random effects setting. Properties of the resulting confidence interval are studied by simulation and compared with other random effects confidence intervals that have been proposed in the literature. An example is briefly discussed.

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The loci of the three amino acid residues that contribute their prosthetic groups to form the stable, nonreducible, trifunctional intermolecular cross-link histidinohydroxylysinonorleucine in skin collagen fibrils were identified. Two apparently homogeneous three-chained histidinohydroxylysinonorleucine cross-linked peptides were chromatographically isolated. They were obtained from a tryptic digest of denatured unreduced 6 M guanidine hydrochloride insoluble bovine skin collagen. Amino acid and sequence analyses demonstrated that the prosthetic groups of alpha 1(I)-chain Hyl-87, alpha 1(I)-chain Lys-16c, and alpha 2(I)-chain His-92 formed the cross-link. The latter results served to define the locus of the stable, nonreducible trifunctional moiety. Identical types of analyses were performed on the three-chained peptides isolated after bacterial collagenase digestion of the cross-linked tryptic peptides. This confirmed the initial identification and location of the three peptides linked by the cross-link. In addition, data reported here provide for a correction of the micromolecular structure for the alpha 2(I) chain. Stereochemical considerations concerning this trifunctional cross-link's specific locus indicate that the steric relationships between the alpha chains of skin and skeletal tissue collagens are fundamentally different and the intermolecular relationships in skin fibrils are specific for skin. The same molecular relationships also indicate that histidinohydroxylysinonorleucine links three molecules of collagen. The stereochemistry of cross-linking for skin collagen is in accordance with and explains the X-ray findings of a 65-nm periodicity found for this tissue [Stinson, R. H., & Sweeny, P. R. (1980) Biochim. Biophys. Acta 621, 158; Brodsky, B., Eikenberry, E. F., & Cassidy, K. (1980) Biochim. Biophys. Acta 621, 162].

Summary. We study publication bias in meta analysis by supposing there is a population (y, σ) of studies which give treatment effect estimates y ∼ N(θ, σ 2 ). A selection function describes the probability that each study is selected for review. The overall estimate of θ depends on the studies selected, and hence on the (unknown) selection function. Our previous paper, Copas and Jackson (2004, A bound for publication bias based on the fraction of unpublished studies, Biometrics 60, 146-153), studied the maximum bias over all possible selection functions which satisfy the weak condition that large studies (small σ) are as likely, or more likely, to be selected than small studies (large σ). This led to a worstcase sensitivity analysis, controlling for the overall fraction of studies selected. However, no account was taken of the effect of selection on the uncertainty in estimation. This paper extends the previous work by finding corresponding confidence intervals and P-values, and hence a new sensitivity analysis for publication bias. Two examples are discussed.

The concept of the canonical divergence is defined for dually flat statistical manifolds in terms of the Legendre transform between dual affine coordinates. In this article, we introduce a new two point function defined for any triple (g,∇, ∇*) of a Riemannian metric g and two affine connections ∇ and ∇*. We show that this interprets the canonical divergence without refering to the existence of special coordinates (dual affine coordinates) but in terms of only classical mechanics concerning ∇- and ∇*-geodesics. We also discuss the properties of the two point function and show that this shares some important properties with the canonical divergence defined on dually flat statistical manifolds.