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

ABSTRACT

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.

KEYWORDS:

• Bootstrap-resampling method
• correlated bilateral data
• risk difference
• simultaneous confidence interval
• stratified design

Additional information

Funding

The work of SF Qiu was supported by the National Natural Science Foundation of China: Grant Numbers [11471060 and 11871124], the Key Project of Statistical Science of China: Grant Number [2017LZ27] and the Basic Research and Frontier Exploration Project of Chongqing: Grant Number [cstc2018jcyjAX0241]. The work of ML Tang was supported by the Research Fund of the Project: Grant Number [UGC/FDS14/P01/16].