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The meta-analysis of P-values is a widely used method in integrating information from multiple studies, and much research has focused on combining P-values. Among the established approaches, Fisher's test may be the most popular one. Many studies have been devoted to extending or modifying Fisher's statistic. For example, Lancaster’s variation of Fisher’s method may outperform the weighted Z-test and recently has drawn noteworthy attention. In this study, we first extend Lancaster's statistic by incorporating a weighting scheme. An approximation and an algorithm that are suitable for use under both independence and dependence assumptions are proposed for calculating the distribution of the weighted Lancaster statistic. The relationships between this method and existing ones are discussed. An application of the main results to a linkage test method in human gene mapping is then provided to show its use.

Distribution of weighted Lancaster’s statistic for combining independent or dependent P-values, with applications to human genetic studies