On the optimally weighted z-test for combining probabilities from independent studies

Researchers have shown that the optimally weighted z-test, where the weights are the standardized expected difference in means, is more powerful than other methods when combining p-values from independent studies. However, in practice the effect for each independent study is usually unknown, which makes the optimally weighted z-test not applicable. A new test similar to the optimally weighted z-test, but with the effects being estimated from data, is derived. This new test is another generalized Fisher test which can be very powerful under certain situations. The new test is compared with existing methods through simulated data. Some suggestions for choosing tests to combine p-values from independent studies are given. The use of the new test is also illustrated by a real data application.

[1]  Qingzhong Liu,et al.  A new statistical approach to detecting differentially methylated loci for case control Illumina array methylation data , 2012, Bioinform..

[2]  Zhongxue Chen.  Association tests through combining p-values for case control genome-wide association studies , 2013 .

[3]  R. Fisher,et al.  Statistical Methods for Research Workers , 1930, Nature.

[4]  Saralees Nadarajah,et al.  Detecting differentially methylated loci for Illumina Array methylation data based on human ovarian cancer data , 2013, BMC Medical Genomics.

[5]  D. Zaykin,et al.  Optimally weighted Z‐test is a powerful method for combining probabilities in meta‐analysis , 2011, Journal of evolutionary biology.

[6]  R. Fisher.  Statistical methods for research workers , 1927, Protoplasma.

[7]  I. J. Good,et al.  On the Weighted Combination of Significance Tests , 1955 .

[8]  Robert D. Cousins,et al.  Annotated Bibliography of Some Papers on Combining Significances or p-values , 2007, 0705.2209.

[9]  L. Tippett,et al.  The Methods of Statistics. , 1933 .

[10]  R. Elston,et al.  Choosing an optimal method to combine P‐values , 2009, Statistics in medicine.

[11]  Thomas M. Loughin,et al.  A systematic comparison of methods for combining p , 2004, Comput. Stat. Data Anal..

[12]  S. Stouffer.  Adjustment during army life , 1977 .

[13]  Xudong Huang,et al.  Age-adjusted nonparametric detection of differential DNA methylation with case–control designs , 2013, BMC Bioinformatics.

[14]  Hon Keung Tony Ng,et al.  Testing for association in case-control genome-wide association studies with shared controls , 2016, Statistical methods in medical research.

[15]  Arthur Cohen,et al.  Asymptotically Optimal Methods of Combining Tests , 1979 .

[16]  Gang Zheng,et al.  Genetic model selection in two-phase analysis for case-control association studies. , 2008, Biostatistics.

[17]  H. O. Lancaster.  THE COMBINATION OF PROBABILITIES: AN APPLICATION OF ORTHONORMAL FUNCTIONS , 1961 .

[18]  Z Chen,et al.  Is the weighted z‐test the best method for combining probabilities from independent tests? , 2011, Journal of evolutionary biology.

[19]  E. S. Pearson.  THE PROBABILITY INTEGRAL TRANSFORMATION FOR TESTING GOODNESS OF FIT AND COMBINING INDEPENDENT TESTS OF SIGNIFICANCE , 1938 .

[20]  Hon Keung Tony Ng,et al.  A Robust Method for Testing Association in Genome-Wide Association Studies , 2011, Human Heredity.

[21]  Zhongxue Chen.  A new association test based on Chi‐square partition for case‐control GWA studies , 2011, Genetic epidemiology.

[22]  A. Ardizzoni,et al.  Cisplatin- versus carboplatin-based chemotherapy in first-line treatment of advanced non-small-cell lung cancer: an individual patient data meta-analysis. , 2007, Journal of the National Cancer Institute.

[23]  Joseph L. Gastwirth,et al.  Choice of scores in trend tests for case-control studies of candidate-gene associations , 2003 .

[24]  Allan Birnbaum,et al.  Combining Independent Tests of Significance , 1954 .

[25]  Hon Keung Tony Ng,et al.  Design and analysis of multiple diseases genome-wide association studies without controls. , 2012, Gene.

[26]  M. Whitlock.  Combining probability from independent tests: the weighted Z‐method is superior to Fisher's approach , 2005, Journal of evolutionary biology.