Statistical Inference Of Binomial Proportions Based On Stratified Partially Validated Data Without Gold Standard

In this article,we consider the homogeneity testing of binomial proportions based on stratified partially validated data obtained by double-sampling method with two fallible classifiers.Test procedures based on the weighted-least-squares test statistic,the weighted least-squares test statistics with the log-transformation,the logit-transformation and the double log-transformation,likelihood ratio test statistic and Score test statistic are developed to test the homogeneity under two double-sampling models,distinguished by conditional independence assumption of two classifiers.When sample sizes are small,Bootstrap test procedures based on these test statistics are developed for the homogeneity testing.Comparison of asymptotic methods and the Bootstrap methods is evaluated by simulation study for various sample size designs.Simulation results show that Score test performs better than other tests in the sense that it's empirical size can be generally controlled around the nominal level,and hence be recommended to practical applications.Other tests also perform well when both binomial proportions and sample sizes are not small.And Bootstrap procedures perform better than the corresponding asymptotic procedures in the sense that the former empirical type I error is closer to the nominal level than the latter for small sample sizes,and hence be recommended to practical applications.Moreover,approximate sample sizes based on Score test,likelihood ratio test and the weighted-least-squares test with double log-transformation are generally accurate in terms of the empirical power and type I error rate with the proposed sample sizes,and hence be recommended.A real example about malaria study is used to illustrate the proposed methodologies.