Homogeneity test for correlated binary data

Interval estimation of relative risks for combined unilateral and bilateral correlated data

Measurements are generally collected as unilateral or bilateral data in clinical trials, epidemiology, or observational studies. For example, in ophthalmology studies, the primary outcome is often obtained from one eye or both eyes of an individual. In medical studies, the relative risk is usually the parameter of interest and is commonly used. In this article, we develop three confidence intervals for the relative risk for combined unilateral and bilateral correlated data under the equal dependence assumption. The proposed confidence intervals are based on maximum likelihood estimates of parameters derived using the Fisher scoring method. Simulation studies are conducted to evaluate the performance of proposed confidence intervals with respect to the empirical coverage probability, the mean interval width, and the ratio of mesial non-coverage probability to the distal non-coverage probability. We also compare the proposed methods with the confidence interval based on the method of variance estimates recovery and the confidence interval obtained from the modified Poisson regression model with correlated binary data. We recommend the score confidence interval for general applications because it best controls converge probabilities at the 95% level with reasonable mean interval width. We illustrate the methods with a real-world example.

A comprehensive comparison of multilocus association methods with summary statistics in genome-wide association studies

BACKGROUND

Multilocus analysis on a set of single nucleotide polymorphisms (SNPs) pre-assigned within a gene constitutes a valuable complement to single-marker analysis by aggregating data on complex traits in a biologically meaningful way. However, despite the existence of a wide variety of SNP-set methods, few comprehensive comparison studies have been previously performed to evaluate the effectiveness of these methods.

RESULTS

We herein sought to fill this knowledge gap by conducting a comprehensive empirical comparison for 22 commonly-used summary-statistics based SNP-set methods. We showed that only seven methods could effectively control the type I error, and that these well-calibrated approaches had varying power performance under the simulation scenarios. Overall, we confirmed that the burden test was generally underpowered and score-based variance component tests (e.g., sequence kernel association test) were much powerful under the polygenic genetic architecture in both common and rare variant association analyses. We further revealed that two linkage-disequilibrium-free P value combination methods (e.g., harmonic mean P value method and aggregated Cauchy association test) behaved very well under the sparse genetic architecture in simulations and real-data applications to common and rare variant association analyses as well as in expression quantitative trait loci weighted integrative analysis. We also assessed the scalability of these approaches by recording computational time and found that all these methods can be scalable to biobank-scale data although some might be relatively slow.

CONCLUSION

In conclusion, we hope that our findings can offer an important guidance on how to choose appropriate multilocus association analysis methods in post-GWAS era. All the SNP-set methods are implemented in the R package called MCA, which is freely available at https://github.com/biostatpzeng/ .

Risk difference tests for stratified binary data under Dallal's model

In medical studies, the binary data is often encountered when the paired organs or body parts receive treatment. However, the same treatment may lead to different therapeutic effects based on the stratified factors or confounding effects. Under Dallal's model, the paper proposes the homogeneity test of risk difference to determine the necessity of stratified treatment. When the stratification is not necessary, common test is introduced to investigate if the risk difference is equal to a fixed constant between two groups. Several statistical tests are derived to analyze homogeneity and common hypotheses, respectively. Monte Carlo simulations show that the score tests behave well in both of hypotheses. Wald-type and Rosner's statistics are always liberal but have higher empirical powers. Especially, the likelihood ratio statistic is better for the homogeneity test in the case of smaller data with larger strata. Two real examples are provided to illustrate the effectiveness of the proposed methods in ankle instability and otolaryngology studies.

Homogeneity test of relative risk ratios for stratified bilateral data under different algorithms

Medical clinical studies about paired body parts often involve stratified bilateral data. The correlation between responses from paired parts should be taken into account to avoid biased or misleading results. This paper aims to test if the relative risk ratios across strata are equal under the optimal algorithms. Based on different algorithms, we obtain the desired global and constrained maximum likelihood estimations (MLEs). Three asymptotic test statistics (i.e. T L , T S C and T W ) are proposed. Monte Carlo simulations are conducted to evaluate the performance of these algorithms with respect to mean square errors of MLEs and convergence rate. The empirical results show Fisher scoring algorithm is usually better than other methods since it has effective convergence rate for global MLEs, and makes mean-square error lower for constrained MLEs. Three test statistics are compared in terms of type I error rate (TIE) and power. Among these statistics, T S C is recommended according to its robust TIEs and satisfactory power.

Statistical tests under Dallal's model: Asymptotic and exact methods

This paper proposes asymptotic and exact methods for testing the equality of correlations for multiple bilateral data under Dallal’s model. Three asymptotic test statistics are derived for large samples. Since they are not applicable to small data, several conditional and unconditional exact methods are proposed based on these three statistics. Numerical studies are conducted to compare all these methods with regard to type I error rates (TIEs) and powers. The results show that the asymptotic score test is the most robust, and two exact tests have satisfactory TIEs and powers. Some real examples are provided to illustrate the effectiveness of these tests.

Interval estimation of proportion ratios for stratified bilateral correlated binary data

Confidence interval (CI) methods for the ratio of two proportions in the presence of correlated bilateral binary data are constructed for comparative clinical trials with stratified design. Simulations are conducted to evaluate the performance of the presented CIs with respect to mean coverage probability (MCP), mean interval width (MIW), and the ratio of mesial non-coverage probability to the distal non-coverage probability (RMNCP). Based on the empirical results, we suggest the use of the proposed CI method based on the complete score statistics (CS) for general applications. An example from a rheumatology study is used to demonstrate the proposed methodologies.

Asymptotic confidence interval construction for proportion ratio based on correlated paired data

In ophthalmological and otolaryngology studies, measurements obtained from both organs (e.g., eyes or ears) of an individual are often highly correlated. Ignoring the intraclass correlation between paired measurements may yield biased inferences. In this article, four different confidence interval (CI) construction methods (maximum likelihood estimates based Wald-type CI, profile likelihood CI, asymptotic score CI and an existing method adjusted for correlated bilateral data) are applied to this type of correlated bilateral data to construct CI for proportion ratio, taking the intraclass correlation into consideration. The coverage probabilities and widths of the resulting CIs are compared with each other in a Monte Carlo simulation study to evaluate their performances. A real dataset from an ophthalmologic study is used to illustrate our methodology.

Common risk difference test and interval estimation of risk difference for stratified bilateral correlated data

Bilateral correlated data are often encountered in medical researches such as ophthalmologic (or otolaryngologic) studies, in which each unit contributes information from paired organs to the data analysis, and the measurements from such paired organs are generally highly correlated. Various statistical methods have been developed to tackle intra-class correlation on bilateral correlated data analysis. In practice, it is very important to adjust the effect of confounder on statistical inferences, since either ignoring the intra-class correlation or confounding effect may lead to biased results. In this article, we propose three approaches for testing common risk difference for stratified bilateral correlated data under the assumption of equal correlation. Five confidence intervals of common difference of two proportions are derived. The performance of the proposed test methods and confidence interval estimations is evaluated by Monte Carlo simulations. The simulation results show that the score test statistic outperforms other statistics in the sense that the former has robust type I error rates with high powers. The score confidence interval induced from the score test statistic performs satisfactorily in terms of coverage probabilities with reasonable interval widths. A real data set from an otolaryngologic study is used to illustrate the proposed methodologies.