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Combining Correlated P-values From Primary Data Analyses

Author

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  • Jai Won Choi
  • Balgobin Nandram
  • Boseung Choi

Abstract

Research results on the same subject, extracted from scientific papers or clinical trials, are combined to determine a consensus. We are primarily concerned with combining p-values from experiments that may be correlated. We have two methods, a non-Bayesian method and a Bayesian method. We use a model to combine these results and assume the combined results follow a certain distribution, for example, chi-square or normal. The distribution requires independent and identically distributed (iid) random variables. When the data are correlated or non-iid, we cannot assume such distribution. In order to do so, the combined results from the model need to be adjusted, and the adjustment is done “indirectly” through two test statistics. Specifically, one test statistic (TS** ) is obtained for the non-iid data and the other is the test statistic (TS) is obtained for iid data. We use the ratio between the two test statistics to adjust the model test statistic (TS**) for its non-iid violation. The adjusted TS** is named as “effective test statistics” (ETS), which is then used for statistical inferences with the assumed distribution. As it is difficult to estimate the correlation, to provide a more coherent method for combining p-values, we also introduce a novel Bayesian method for both iid data and non-iid data. The examples are used to illustrate the non-Bayesian method and additional examples are given to illustrate the Bayesian method.

Suggested Citation

  • Jai Won Choi & Balgobin Nandram & Boseung Choi, 2022. "Combining Correlated P-values From Primary Data Analyses," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(6), pages 1-12, November.
    • Handle: RePEc:ibn:ijspjl:v:11:y:2022:i:6:p:12
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    References listed on IDEAS

    as
    1. Jai Won Choi & Balgobin Nandram, 2021. "Large Sample Problems," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 1-81, March.
    2. Hari K. Iyer & C.M. Jack Wang & Thomas Mathew, 2004. "Models and Confidence Intervals for True Values in Interlaboratory Trials," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1060-1071, December.
    3. Loughin, Thomas M., 2004. "A systematic comparison of methods for combining p-values from independent tests," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 467-485, October.
    4. Balgobin Nandram & Jai Won Choi & Yang Liu, 2021. "Integration of Nonprobability and Probability Samples via Survey Weights," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(6), pages 1-5, December.
    5. N A Heard & P Rubin-Delanchy, 2018. "Choosing between methods of combining $p$-values," Biometrika, Biometrika Trust, vol. 105(1), pages 239-246.
    Full references (including those not matched with items on IDEAS)

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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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