TESTING EQUALITY OF CORRELATION COEFFICIENTS FOR PAIRED BINARY DATA FROM MULTIPLE GROUPS

Outline Background Testing Methods Simulation Study Real Work Example Conclusion

Background

Introduction In clinical trials studying diseases at paired body parts, each person contributes two measurements to the study. Outcomes from the same patient can be highly correlated. Taking eyes as an example, for a single patient, the probability that one eye has disease often increases given the knowledge that the other one does. One of the models to deal with these binary correlated data is the equal correlation coefficients model. Before using this model, here we need to test if the correlation coefficients in each groups are actually equal.

Two Possible Method Rosner’s model Assume that for a single patient, the conditional probability of one eye having disease given disease response at the other eye is R times the unconditional probability. where Z ijk =1 if the kth eye of jth individual in the ith group has a response at the end of the study, and 0 otherwise. Where constant R is the same in each of the g groups. Donner’s model Assumes that the g groups share a common intra-class correlation coefficient. Basically focus on this model in this paper.

Binary correlated data structure

Testing Method

Method(Equal correlation coefficients model)

Log Likelihood Function

Likelihood Ratio Test

Wald-type test

Score test

Simulation Study

g g 2 4 8

Real Work Examples

Example1:218 outpatients, aged from 20 to 29 with retinitis pigmentosa (RP),were assigned into 4 genetic type groups. Table of the data(number of effected eyes for persons in each genetic type group) Table of result(Statistic values and p-values of different test statistics)

Example2:the extend and causes of blindness and visual impairment (VI). Table of the data prevalence of VI by age groups in the sample population. Table of result(Statistic values and p-values of different test statistics)

Example3:the MRSS case-control clinical trial which enrolled 168 patients with diffuse scleroderma. Patients are randomly given oral native collagen or placebo, and compare the MRSS(modified Rodnan Skin Scores) in treatment group and control group.

Conclusion

Introduce three test statistics for testing the equality of correlation coefficients in paired binary data with different groups. Score test is recommended in practical use. Since simulation study showed that the Score test has not only robust empirical type I error for various number of groups and sample sizes, but also satisfactory power. With these asymptotic methods studied in this work, we consider developing exact tests for small samples as interesting future work.

Thank you!