Homogeneity Test And Sample Size Determination For Disease Prevalence Rates Under Stratified Double-sampling Design

The prevalence rates of a certain disease in different populations often need to be compared in biomedical studies.Based on the partially validated series under the stratified design,the homogeneity testing and sample size determination for disease prevalence rates are considered in this article.First,seven test statistics,i.e.,the Weighted-Least-Squares?WLS?statistic,Logarithmic transformation of WLS statistic,log-transformation-based WLS statistic,logit-transformation-based WLS statistic,double log-transformation-based WLS statistic,Score statistic and Likelihood test statistic for testing the homogeneity of disease prevalence rates are proposed in this article.Simulation results show that asymptotic test procedures based on Score statistic and Likelihood ratio statistic can usually well control the empirical type I error rates with higher powers and hence be recommended to practical applications.When sample sizes are moderate and large,test procedures based on log-transformation-based WLS statistic,logit-transformation-based WLS statistic,double logarithmic-transformation-based WLS statistic also perform satisfactory in the sense that their empirical type I error rates are close to the nominal level,and hence also be recommended.Second,the approximate sample size formulas which achieve the pre-specified power at a given significant level for the homogeneity test are also investigated.Approximate sample size formulae based on WLS statistic,likelihood rate statistic,Score statistic and double log-transformation-based WLS statistic are developed in this article.Simulation results show that sample size decreases with the increase of the sensitivity ? of the fallible classifier and the validated ratio k₁.In general,Sample size based on Score test statistic and Likelihood ratio test statistic are usually smaller than those based on WLS test statistic and double-log-transformation-based WLS statistic,and they are more accurate in the sense that their empirical powers are closer to the pre-specified power based on the estimated sample sizes and hence be recommended for practical applications.Finally,two real data are used to illustrate the proposed method.