Equivalence Test And Sample Size Determination For Risk Difference Based On Partially Validated Data With An Imperfect Gold Standard

It is important to estimate the prevalence of a disease in the population in clinical trials and medical research,and the prevalence of a disease can be obtained by classifying the subjects according to whether they have the disease or not.Under the double sampling design,all individuals are classified by the fallible classifier,and some individuals are classified by the gold standard again,so the partially validated data can be obtained.Gold standard classifier can classify individuals without misclassification,however,the gold standard classifier does not exist or be very expensive or time-consuming in practical applications.Therefore,the equivalence test for risk difference based on partially validated data when two classifiers are fallible are considered in this article,four asymptotical test procedures based on Wald test,Score test and likelihood ratio test are proposed under two double-sampling models: the model with conditional independence assumption(i.e.Model I)and the model without conditional independence assumption(i.e.,Model II).Sample size determination based on the proposed tests to achieve the pre-specified power at the given nominal level is also investigated in this article.Simulation results show that:(i)Score test performs satisfactorily in the sense that it's empirical type I error rates are usually close to the nominal level with higher powers even for small sample sizes under both models,and hence be recommended for practical applications;(ii)Except for very small disease prevalence,all test procedures have good performance for small sample sizes under Model II,while for moderate and large sample size designs,all test procedures have empirical type I error rates close to the nominal level with higher powers even for small disease prevalence,and hence be recommended;(iii)In general,sample size formulae based on the Wald statistic with the variance being estimated under the null hypothesis and score statistic are accurate and hence be recommended in practical applications.A real data example is used to illustrate the methods proposed in this article.