Operability Region Equivalence: Simultaneous Confidence Bands for the Equivalence of Two Regression Models over Restricted Regions

Liu, Wei; Hayter, Anthony J.; Wynn, Henry P.

doi:10.1002/bimj.200610322

Cited by 10 publications

(5 citation statements)

References 22 publications

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“…From a theoretical point of view, we will show that our approach provides a statistically valid procedure and we will empirically verify, via simulations and data analysis, that it is particularly suited for small sample sizes. We also expect that the new procedures will be more powerful than tests based on common statistical principles such as the union-intersection principle [ 67 , 68 ]. Consequently, our methods are particularly well suited for studying rare diseases such as the Dravet syndrome.…”

Section: Identifying Similarity Between Subgroup and The Populationmentioning

confidence: 99%

Istore: a project on innovative statistical methodologies to improve rare diseases clinical trials in limited populations

Schoenen,

Verbeeck,

Koletzko

et al. 2024

Orphanet J Rare Dis

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Background The conduct of rare disease clinical trials is still hampered by methodological problems. The number of patients suffering from a rare condition is variable, but may be very small and unfortunately statistical problems for small and finite populations have received less consideration. This paper describes the outline of the iSTORE project, its ambitions, and its methodological approaches. Methods In very small populations, methodological challenges exacerbate. iSTORE’s ambition is to develop a comprehensive perspective on natural history course modelling through multiple endpoint methodologies, subgroup similarity identification, and improving level of evidence. Results The methodological approaches cover methods for sound scientific modeling of natural history course data, showing similarity between subgroups, defining, and analyzing multiple endpoints and quantifying the level of evidence in multiple endpoint trials that are often hampered by bias. Conclusion Through its expected results, iSTORE will contribute to the rare diseases research field by providing an approach to better inform about and thus being able to plan a clinical trial. The methodological derivations can be synchronized and transferability will be outlined.

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Section: Identifying Similarity Between Subgroup and The Populationmentioning

confidence: 99%

Istore: a project on innovative statistical methodologies to improve rare diseases clinical trials in limited populations

Schoenen,

Verbeeck,

Koletzko

et al. 2024

Orphanet J Rare Dis

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“…and Σ denotes the estimator of the variance in (3.4), which is obtained by replacing the parameters σ , β and ζ ,i by their estimators σ , β , and n ,i /n ( = 1, 2). Gsteiger et al (2011) proposed a test based on the pointwise confidence bands derived by Liu et al (2007a), that is…”

Section: Finite Sample Propertiesmentioning

confidence: 99%

“…For example, Liu et al (2009) proposed tests for the hypothesis of equivalence of two regression functions, which are applicable in linear models. Gsteiger et al (2011) considered non-linear models and suggested a bootstrap method which is based on a confidence band for the difference of the two regression models [see also Liu et al (2007a)]. Both references use the intersection-union principle [see for example Berger (1982)] to construct an overall test for equivalence.…”

Section: Introductionmentioning

confidence: 99%

Equivalence of Regression Curves

Dette

Möllenhoff

Volgushev

et al. 2018

Journal of the American Statistical Association

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This paper investigates the problem whether the difference between two parametric models m 1 , m 2 describing the relation between a response variable and several covariates in two different groups is practically irrelevant, such that inference can be performed on the basis of the pooled sample. Statistical methodology is developed to test the hypotheses H 0 : d(m 1 , m 2 ) ≥ ε versus H 1 : d(m 1 , m 2 ) < ε to demonstrate equivalence between the two regression curves m 1 , m 2 for a pre-specified threshold ε, where d denotes a distance measuring the distance between m 1 and m 2 . Our approach is based on the asymptotic properties of a suitable estimator d(m 1 ,m 2 ) of this distance. In order to improve the approximation of the nominal level for small sample sizes a bootstrap test is developed, which addresses the specific form of the interval hypotheses. In particular, data has to be generated under the null hypothesis, which implicitly defines a manifold for the parameter vector. The results are illustrated by means of a simulation study and a data example. It is demonstrated that the new methods substantially improve currently available approaches with respect to power and approximation of the nominal level. 1 arXiv:1505.05266v3 [stat.ME] 7 Jun 2016 particular difficulties arising in the problem of testing (parametric) interval hypotheses. In particular, resampling has to be performed under the null hypothesis H 0 : d(m 1 , m 2 ) ≥ ε, which defines (implicitly) a manifold in the parameter space. We prove consistency of the bootstrap test and demonstrate by means of a simulation study that it yields an improvement of the approximation of the nominal level for small sample sizes. In Section 4 the maximal deviation between the two curves is considered as a measure of similarity, for which corresponding results are substantially harder to derive. For example, we prove weak convergence of a corresponding test statistic, but the limit distribution depends in a complicated way on the extremal points of the difference between the "true" curves. This problem is again solved by developing a bootstrap test. The finite sample properties of the new methodology are illustrated in Section 5, where we also provide a comparison with the method of Gsteiger et al. (2011). In particular, it is demonstrated that the methodology proposed in this paper is more powerful than the test proposed by these authors. The methods are illustrated with an example in Section 6. Technical details and proofs are deferred to an appendix in Section 7. Equivalence of regression curvesWe consider two, possibly different, regression models m 1 , m 2 to describe the relationship between a response variable Y and several covariates for two different groups = 1, 2:Y ,i,j = m (x ,i , β ) + η ,i,j , j = 1, . . . , n ,i , i = 1, . . . , k .(2.1)Here, the covariate region is denoted by X ⊂ R d , x ,i denotes the ith dose level (in group ), n ,i the number of patients treated at dose level x ,i and k the number of different dose levels in group . Further, n ...

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“…For assessing the equivalence of the two linear regression models given in over a given region of the covariates x , Liu, Hayter, and Wynn (2007, denoted as LHW hereafter) provide an exact 1 −α level upper confidence bound on and this upper confidence bound is based on the statistic F in . This approach differs from the method here in the following two major aspects.…”

Section: A Hypotheses Test For Assessing Equivalencementioning

confidence: 99%

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

et al. 2009

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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.

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Operability Region Equivalence: Simultaneous Confidence Bands for the Equivalence of Two Regression Models over Restricted Regions

Cited by 10 publications

References 22 publications

Istore: a project on innovative statistical methodologies to improve rare diseases clinical trials in limited populations

Istore: a project on innovative statistical methodologies to improve rare diseases clinical trials in limited populations

Equivalence of Regression Curves

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

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