Confidence intervals and P-valves for meta analysis with publication bias

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, σ2). 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 Our previous paper, Copas and Jackson (2004, A bound for publication bias based on the fraction of unpublished studies, Biometrics 60, 146-153), studied the maximum bias over all possible selection functions which satisfy the weak condition that large studies (small σ)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

確率密度空間のパス連結性

Open House, ISM in Tachikawa, 2015.6.19統計数理研究所オープンハウス（立川）、H27.6.19ポスター発

A Reconsideration of Mathematical Statistics

Open House, ISM in Tachikawa, 2016.6.17統計数理研究所オープンハウス（立川）、H28.6.17ポスター発

Likelihood for all equivalent models

Open House, ISM in Tachikawa, 2012.6.15統計数理研究所オープンハウス（立川）、H24.6.15ポスター発

Identification of biomarkers from mass spectrometry data using a "common" peak approach

BACKGROUND: Proteomic data obtained from mass spectrometry have attracted great interest for the detection of early-stage cancer. However, as mass spectrometry data are high-dimensional, identification of biomarkers is a key problem. RESULTS: This paper proposes the use of "common" peaks in data as biomarkers. Analysis is conducted as follows: data preprocessing, identification of biomarkers, and application of AdaBoost to construct a classification function. Informative "common" peaks are selected by AdaBoost. AsymBoost is also examined to balance false negatives and false positives. The effectiveness of the approach is demonstrated using an ovarian cancer dataset. CONCLUSION: Continuous covariates and discrete covariates can be used in the present approach. The difference between the result for the continuous covariates and that for the discrete covariates was investigated in detail. In the example considered here, both covariates provide a good prediction, but it seems that they provide different kinds of information. We can obtain more information on the structure of the data by integrating both results

正定値行列の一般化平均 -色度認知問題への応用-

Open House, ISM in National Center of Sciences Building, 2019.6.05統計数理研究所オープンハウス（学術総合センター）、R1.6.5ポスター発

A class of tests for a general covariance structure

AbstractLet S be a p × p random matrix having a Wishart distribution Wp(n,n−1Σ). For testing a general covariance structure Σ = Σ(ξ), we consider a class of test statistics Th = n inf ϱh(S, Σ(ξ)), where ϱh(Σ1, Σ2) = Σj = 1ph(λj) is a distance measure from Σ1 to Σ2, λi's are the eigenvalues of Σ1Σ2−1, and h is a given function with certain properties. This paper gives an asymptotic expansion of the null distribution of Th up to the order n−1. Using the general asymptotic formula, we give a condition for Th to have a Bartlett adjustment factor. Two special cases are considered in detail when Σ is a linear combination or Σ−1 is a linear combination of given matrices