Testing for homogeneity of relative differences under inverse sampling

Construction of confidence intervals for the risk differences in stratified design with correlated bilateral data

A stratified study is often designed for adjusting a confounding effect or effect of different centers/groups in two treatments or diagnostic tests, and the risk difference is one of the most frequently used indices in comparing efficiency between two treatments or diagnostic tests. This article presented five simultaneous confidence intervals (CIs) for risk differences in stratified bilateral designs accounting for the intraclass correlation and developed seven CIs for the common risk difference under the homogeneity assumption. The performance of the CIs is evaluated with respect to the empirical coverage probabilities, empirical coverage widths and ratios of mesial noncoverage probability and the noncoverage probability under various scenarios. Empirical results show that Wald simultaneous CI, Haldane simultaneous CI, Score simultaneous CI based on Bonferroni method and simultaneous CI based on bootstrap-resampling method perform satisfactorily and hence be recommended for applications, the CI based on the weighted-least-square (WLS) estimator, the CIs based on Mantel-Haenszel estimator, the CI based on Cochran statistic and the CI based on Score statistic for the common risk difference behave well even under small sample sizes. A real data example is used to demonstrate the proposed methodologies.

Testing for homogeneity of gametic disequilibrium across strata

Background

Assessing the non-random associations of alleles at different loci, or gametic disequilibrium, can provide clues about aspects of population histories and mating behavior and can be useful in locating disease genes. For gametic data which are available from several strata with different allele probabilities, it is necessary to verify that the strata are homogeneous in terms of gametic disequilibrium.

Results

Using the likelihood score theory generalized to nuisance parameters we derive a score test for homogeneity of gametic disequilibrium across several independent populations. Simulation results demonstrate that the empirical type I error rates of our score homogeneity test perform satisfactorily in the sense that they are close to the pre-chosen 0.05 nominal level. The associated power and sample size formulae are derived. We illustrate our test with a data set from a study of the cystic fibrosis transmembrane conductance regulator gene.

Conclusion

We propose a large-sample homogeneity test on gametic disequilibrium across several independent populations based on the likelihood score theory generalized to nuisance parameters. Our simulation results show that our test is more reliable than the traditional test based on the Fisher's test of homogeneity among correlation coefficients.

A test of homogeneity of Hardy-Weinberg disequilibrium across strata

For genotype data being sampled from several strata with different allele frequencies, it is necessary to verify the assumption of homogeneity of Hardy-Weinberg disequilibrium across strata before testing Hardy-Weinberg law across strata. In practice, disequilibrium can be measured via fixation coefficients (ie, ratios of genotypic frequencies) or disequilibrium coefficients (ie, differences of genotypic frequencies). Test for homogeneity of Hardy-Weinberg disequilibrium using data from several populations has been derived according to fixation coefficients. In this article, using the likelihood score theory extended to nuisance parameters, we derive a homogeneity score test for comparing disequilibrium coefficients across several independent strata. Simulation results demonstrate that the homogeneity score test performs satisfactorily in the sense that its empirical size seldom exceeds the pre-chosen nominal level by more than 10% even for small sample sizes. Corresponding power and sample size formulae are provided as well. We illustrate our test with a real glyoxalase genotype data set.