Test Procedures Of The Disease Prevalence Based On Stratified Partially Validated Series With Gold Standard

Estimating the prevalence of a disease is an important topic in biostatistical studies.Screening tests are inexpensive and can produce results in a timely manner,but suffer from high levels of misclassification.Gold standard tests are not subject to misclassification,but such devices are usually costly and time consuming.In order to overcome the drawbacks of these two approaches,double-sampling method is often used to obtain data.The data obtained by the double-sampling method is also called as partially validated data.Since the estimation of the prevalence may be affected by some confounding factors,such as age,living habit and so on,then these confounding factors are often treated as stratified variables.Under the heterogeneity of sensitivities(and specificities)of the screening test,the homogeneity test procedures for disease prevalence rates based on stratified partially validated series are considered,and the test procedures for the hypothesis testing of the common prevalence under the assumption of the homogeneity are also investigated in this article.For the homogeneity test procedures of the disease prevalence,we considered the weighted-least-squares test statistic and its logarithmic transformation statistic,the weighted-least-squares test statistics with logarithmic transformation,logit transformation and double-logarithmic transformation,Score test statistic and likelihood ratio test statistic for the homogeneity testing.Based on the proposed test statistics,the asymptotical test procedures and Bootstrap-resampling test procedures are developed.Monte Carlo simulation studies are conducted to evaluate the performance of these test procedures.Simulation results show that all tests can well control their empirical type I error rates around the nominal level when sample sizes are large;when sample sizes are small,Score test performs well in the sense that its empirical type I error is generally close to the nominal level with higher powers.It is worth noting that Bootstrap-resampling test procedures based on all test statistics have good performance even for small sample sizes.Under the assumption of the homogeneity,two wald-type test statistics,three wald test statistics based on the logarithmic transformation,logit transformation and doublelogarithmic transformation,and Score test statistic are developed for the hypothesis testing of the common disease prevalence.The asymptotical and Bootstrap test procedures are considered.Simulation results show that the asymptotical wald test with variance calculated by the parameter estimations under the null hypothesis,the asymptotical Score test,and all Bootstrap test procedures perform well in the sense that their empirical type I error rates are close to the significant level,and hence be recommended to practical applications.Finally,three real data are used to illustrate the proposed methods.