Assessing Nonsuperiority, Noninferiority, or Equivalence When Comparing Two Regression Models Over a Restricted Covariate Region

Abstract

In many scientific problems the purpose of the comparison of two regression models, which describe the relationship between a same response variable and several same covariates for two different groups, is to demonstrate that one model is no higher than the other by a negligible amount, or to demonstrate that the models have only negligible differences and so they can be regarded as describing practically the same relationship between the response variable and the covariates. In this article, methods based on one-sided pointwise confidence bands are proposed for assessing the nonsuperiority of one model to the other and for assessing the equivalence of two regression models. Examples from QT/QTc study and from drug stability study are used to illustrate the methods.

Multiple Comparisons of Repeated Measured Response: Issues of Assessment of Prolongation of QT Interval in Thorough QT Trials

“…showing Max t∈ 0 t K U s Y TR Y PL t < 10 ms implies Max k=1 to K U Y TR Y PL t k < 10 ms. Liu et al (2009) proposed a more general approach than Garnett et al (2008). First, they propose to use a model more general than the linear or log-linear to fit the data.…”

“…Second, it compares the maximum modeled difference between test and placebo treatment within the range of observed time points instead of predicting the QT difference at a single estimated value of the covariate concentration of the test drug. Third, Liu et al (2009) fits the model with design factors instead of pairing the data by ignoring the design factors. However, this approach involves two steps.…”

“…More recently Liu et al (2009) proposed to model QTc against time using the polynomial regression model…”

“…Other researchers tried to improve the power by modeling the QTc response against concentration (Garnett et al, 2008) or against the time of measurement (Liu et al, 2009) under the assumption of equal variance across time. The modeling approaches lead to the testing of H 0 Max t∈ t 1 t K TR t − PL t ≥ 10, which is more general than the null hypotheses of (1), (2), or (3).…”

Optimal simultaneous confidence bands in simple linear regression

“…There are several recent papers that consider applications of confidence bands. For example, Al-Saidy et al (2003) and Piegorsch et al (2005) used confidence bands in risks analysis, whereas Spurrier (1999) and Liu et al (2004Liu et al ( , 2009) used confidence bands for comparisons of linear regression models in some medical problems. Liu et al (2008) provided a review on the construction of exact confidence bands for a simple linear regression model.…”