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Combining dependent tests of significance has broad applications but the related p-value calculation is challenging. For Fisher's combination test, current p-value calculation methods (eg, Brown's approximation) tend to inflate the type I error rate when the desired significance level is substantially less than 0.05. The problem could lead to significant false discoveries in big data analyses. This paper provides two main contributions. First, it presents a general family of Fisher type statistics, referred to as the GFisher, which covers many classic statistics, such as Fisher's combination, Good's statistic, Lancaster's statistic, weighted Z-score combination, and so forth. The GFisher allows a flexible weighting scheme, as well as an omnibus procedure that automatically adapts proper weights and the statistic-defining parameters to a given data. Second, the paper presents several new p-value calculation methods based on two novel ideas: moment-ratio matching and joint-distribution surrogating. Systematic simulations show that the new calculation methods are more accurate under multivariate Gaussian, and more robust under the generalized linear model and the multivariate t-distribution. The applications of the GFisher and the new p-value calculation methods are demonstrated by a gene-based single nucleotide polymorphism (SNP)-set association study. Relevant computation has been implemented to an R package GFisher available on the Comprehensive R Archive Network.

Although strong evidence exists that certain activities can increase bone density and structure in people, it is unclear what specific mechanical factors govern the response. This is important because understanding the effect of mechanical signals on bone could contribute to more effective osteoporosis prevention methods and efficient clinical trial design. The degree to which strain rate and magnitude govern bone adaptation in humans has never been prospectively tested. Here, we studied the effects of a voluntary upper extremity compressive loading task in healthy adult women during a 12-month prospective period. A total of 102 women age 21 to 40 years participated in one of two experiments: (i) low (n = 21) and high (n = 24) strain magnitude; or (ii) low (n = 21) and high (n = 20) strain rate. Control (n = 16) no intervention. Strains were assigned using subject-specific finite element models. Load cycles were recorded digitally. The primary outcome was change in ultradistal radius integral bone mineral content (iBMC), assessed with QCT. Interim time points and secondary outcomes were assessed with high resolution pQCT (HRpQCT) at the distal radius. Sixty-six participants completed the intervention, and interim data were analyzed for 77 participants. Likely related to improved compliance and higher received loading dose, both the low-strain rate and high-strain rate groups had significant 12-month increases to ultradistal iBMC (change in control: −1.3 ± 2.7%, low strain rate: 2.7 ± 2.1%, high strain rate: 3.4 ± 2.2%), total iBMC, and other measures. “Loading dose” was positively related to 12-month change in ultradistal iBMC, and interim changes to total BMD, cortical thickness, and inner trabecular BMD. Participants who gained the most bone completed, on average, 128 loading bouts of (mean strain) 575 με at 1878 με/s. We conclude that signals related to strain magnitude, rate, and number of loading bouts contribute to bone adaptation in healthy adult women, but only explain a small amount of variance in bone changes. © 2020 The Authors. Journal of Bone and Mineral Research published by American Society for Bone and Mineral Research.