Functional Non-Inferiority Hypothesis Testing for Longitudinal Data

Abstract

The study pattern of non-inferiority trials is increasingly used to show the non-inferiority of new health intervention. Although in such studies the data are longitudinally collected (data held over a period of time), the conclusion of these non-inferiority trials is based on data observed at a specific time during the study period (usually at the end of the study period). In this study, we present a method that takes into account all the data observed during the study period to perform non-inferiority test. Thus, we approximate the observed data on a statistical unit by a function of time. This allows to transform the observed data on a time grid into functional data on a continuum domain. Although it could have some relevant applications, the functional data analysis for non-inferiority test has not been addressed. In this study, the functional non-inferiority hypothesis testing has been introduced. The optimal point-wise test and simultaneous confidence bands have been adapted and adopted for the purpose. The assessment of the methods has been done through simulations example. Both methods have good performances for large sample sizes. For small sample sizes, the optimal point-wise test would be too conservative while the simultaneous confidence bands based test would be a bit liberal.